diff --git a/.codacy.yml b/.codacy.yml deleted file mode 100644 index 0672c33..0000000 --- a/.codacy.yml +++ /dev/null @@ -1,7 +0,0 @@ -languages: - JavaScript: true -exclude_paths: -- "js/dist/*.js" -- "js/dist/**/*.js" -- "test/*.js" -- "test/**/*.js" diff --git a/.codeclimate.yml b/.codeclimate.yml deleted file mode 100644 index 0672c33..0000000 --- a/.codeclimate.yml +++ /dev/null @@ -1,7 +0,0 @@ -languages: - JavaScript: true -exclude_paths: -- "js/dist/*.js" -- "js/dist/**/*.js" -- "test/*.js" -- "test/**/*.js" diff --git a/.groc.json b/.groc.json deleted file mode 100644 index 56e8333..0000000 --- a/.groc.json +++ /dev/null @@ -1,7 +0,0 @@ -{ - "glob": [ - "js/src/**/*.js", - "README.md" - ], - "github": true -} \ No newline at end of file diff --git a/.jshintrc b/.jshintrc deleted file mode 100644 index ffd48eb..0000000 --- a/.jshintrc +++ /dev/null @@ -1,3 +0,0 @@ -{ - "esnext": true -} diff --git a/.travis.yml b/.travis.yml deleted file mode 100644 index 9a0746b..0000000 --- a/.travis.yml +++ /dev/null @@ -1,13 +0,0 @@ -language: node_js -node_js: - - "iojs" - - "0.12" - - "0.11" - - "0.10" -install: - - npm -d install -script: - - npm test -after_success: - - ./node_modules/.bin/coveralls < coverage/lcov.info || true - - ./node_modules/.bin/codeclimate < coverage/lcov.info || true diff --git a/3sum/_3sum_n2.html b/3sum/_3sum_n2.html new file mode 100644 index 0000000..92d1bd5 --- /dev/null +++ b/3sum/_3sum_n2.html @@ -0,0 +1,32 @@ +3sum/_3sum_n2

Hypothesis :

A is sorted in increasing order
B is sorted in increasing order
|A| > 0
|B| > 0

\ No newline at end of file diff --git a/4sum/sortxy_n3.html b/4sum/sortxy_n3.html new file mode 100644 index 0000000..b83ee9b --- /dev/null +++ b/4sum/sortxy_n3.html @@ -0,0 +1,48 @@ +4sum/sortxy_n3

js/src/4sum/sortxy_n3.js

X is sorted in increasing order +Y is sorted in increasing order +compare takes 4 arguments and returns <=> 0 +output takes 4 arguments

var sortxy_n3 = function ( compare , X , Y , Xi1 , Xj1 , Yi1 , Yj1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) { + + var a , b , c , d , s ; + + if ( Xi1 > Xj1 || Yi1 > Yj1 || Xi2 > Xj2 || Yi2 > Yj2 ) { + return ; + }

| X |

Xi Xj

| Y |

Yi Yj

a = X[Xi1] ; + b = Y[Yj1] ; + c = X[Xj2] ; + d = Y[Yi2] ; + + s = compare( a , b , c , d ) ; + + if ( s === 0 ) { + + output( Xi1 , Yj1 , Xj2 , Yi2 ) ; + + sortxy_n3( compare , X , Y , Xi1 + 1 , Xj1 , Yi1 , Yj1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) ; + sortxy_n3( compare , X , Y , Xi1 , Xi1 , Yi1 , Yj1 - 1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) ; + sortxy_n3( compare , X , Y , Xi1 , Xi1 , Yj1 , Yj1 , Xi2 , Xj2 - 1 , Yi2 , Yj2 , output ) ; + + } + + else if ( s < 0 ) { + + sortxy_n3( compare , X , Y , Xi1 + 1 , Xj1 , Yi1 , Yj1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) ; + sortxy_n3( compare , X , Y , Xi1 , Xi1 , Yi1 , Yj1 , Xi2 , Xj2 - 1 , Yi2 , Yj2 , output ) ; + + } + + else { + + sortxy_n3( compare , X , Y , Xi1 , Xj1 , Yi1 , Yj1 - 1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) ; + sortxy_n3( compare , X , Y , Xi1 , Xj1 , Yj1 , Yj1 , Xi2 , Xj2 , Yi2 + 1 , Yj2 , output ) ; + + } + + +} ; + +exports.sortxy_n3 = sortxy_n3 ;

\ No newline at end of file diff --git a/4sum/sortxy_n4.html b/4sum/sortxy_n4.html new file mode 100644 index 0000000..27b8ad8 --- /dev/null +++ b/4sum/sortxy_n4.html @@ -0,0 +1,34 @@ +4sum/sortxy_n4

js/src/4sum/sortxy_n4.js

X is sorted in increasing order +Y is sorted in increasing order +compare takes 4 arguments and returns <=> 0 +output takes 4 arguments

var sortxy_n4 = function ( compare , X , Y , Xi1 , Xj1 , Yi1 , Yj1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) { + + var a , b , c , d , s ; + + if ( Xi1 > Xj1 || Yi1 > Yj1 || Xi2 > Xj2 || Yi2 > Yj2 ) { + return ; + }

| X |

Xi Xj

| Y |

Yi Yj

a = X[Xi1] ; + b = Y[Yi1] ; + c = X[Xi2] ; + d = Y[Yi2] ; + + s = compare( a , b , c , d ) ; + + if ( s === 0 ) { + + output( Xi1 , Yi1 , Xi2 , Yi2 ) ; + + } + + sortxy_n4( compare , X , Y , Xi1 + 1 , Xj1 , Yi1 , Yj1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) ; + sortxy_n4( compare , X , Y , Xi1 , Xi1 , Yi1 + 1 , Yj1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) ; + sortxy_n4( compare , X , Y , Xi1 , Xi1 , Yi1 , Yi1 , Xi2 + 1 , Xj2 , Yi2 , Yj2 , output ) ; + sortxy_n4( compare , X , Y , Xi1 , Xi1 , Yi1 , Yi1 , Xi2 , Xi2 , Yi2 + 1 , Yj2 , output ) ; + +} ; + +exports.sortxy_n4 = sortxy_n4 ;

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If not, see . - -Also add information on how to contact you by electronic and paper mail. - - If your software can interact with users remotely through a computer -network, you should also make sure that it provides a way for users to -get its source. For example, if your program is a web application, its -interface could display a "Source" link that leads users to an archive -of the code. There are many ways you could offer source, and different -solutions will be better for different programs; see section 13 for the -specific requirements. - - You should also get your employer (if you work as a programmer) or school, -if any, to sign a "copyright disclaimer" for the program, if necessary. -For more information on this, and how to apply and follow the GNU AGPL, see -. diff --git a/README.md b/README.md deleted file mode 100644 index 978ff39..0000000 --- a/README.md +++ /dev/null @@ -1,155 +0,0 @@ -:rocket: [Algorithms](https://github.com/make-github-pseudonymous-again/js-algorithms#readme) -[![License](https://img.shields.io/github/license/make-github-pseudonymous-again/js-algorithms.svg?style=flat)](https://raw.githubusercontent.com/make-github-pseudonymous-again/js-algorithms/main/LICENSE) -[![GitHub issues](https://img.shields.io/github/issues/make-github-pseudonymous-again/js-algorithms.svg?style=flat)](https://github.com/make-github-pseudonymous-again/js-algorithms/issues) -== - -

- - -
-© xkcd.com -

- -Playground for algorithms in JavaScript. -This is a child project of [js-library](https://github.com/make-github-pseudonymous-again/js-library) -and -the twin project of [js-data-structures](https://github.com/make-github-pseudonymous-again/js-data-structures). - - -## :newspaper: Description - -This project is just a playground for any algorithm that doesn't fit in any -of those projects, - -### :flashlight: Searching - - [@aureooms/js-search](https://github.com/make-github-pseudonymous-again/js-search): - Searching algorithms for JavaScript - -### :waning_gibbous_moon: Merging - - - [aureooms/js-merging](https://github.com/make-github-pseudonymous-again/js-merging): merging for JavaScript - -### :cake: Partitioning - - [@aureooms/js-partition](https://github.com/make-github-pseudonymous-again/js-partition): - Partitioning algorithms for JavaScript - - [@aureooms/js-splitting](https://github.com/make-github-pseudonymous-again/js-splitting): - Array splitting algorithms for JavaScript - -### :point_down: Selection - - [aureooms/js-selection](https://github.com/make-github-pseudonymous-again/js-selection): selection for JavaScript - -### :signal_strength: Sorting - - [@aureooms/js-sort](https://github.com/make-github-pseudonymous-again/js-sort): - Sorting algorithms for JavaScript - -#### :balance_scale: Comparison sorting - - - :notebook_with_decorative_cover: [@comparison-sorting/specification](https://github.com/comparison-sorting/specification): Comparison sorting specification for JavaScript - - :leaves: [@comparison-sorting/heap-sort](https://github.com/comparison-sorting/heap-sort): Heapsort for JavaScript - - :rabbit2: [@comparison-sorting/quick-sort](https://github.com/comparison-sorting/quick-sort): Quicksort for JavaScript - - :rewind: [@comparison-sorting/insertion-sort](https://github.com/comparison-sorting/insertion-sort): Insertion sorting algorithms for JavaScript - - :person_fencing: [@comparison-sorting/merge-insertion-sort](https://github.com/comparison-sorting/merge-insertion-sort): Ford-Johnson algorithm for JavaScript - - :dragon: [@comparison-sorting/merge-sort](https://github.com/comparison-sorting/merge-sort): Mergesort for JavaScript - - :musical_score: [@comparison-sorting/odd-even-merge-sort](https://github.com/comparison-sorting/odd-even-merge-sort): Batcher's odd-even mergesort for JavaScript - -#### :zzz: Integer sorting - - - :oden: [@integer-sorting/radix-sort](https://github.com/integer-sorting/radix-sort): Radix sorting algorithms for JavaScript - - [aureooms/js-countingsort](https://github.com/make-github-pseudonymous-again/js-countingsort): countingsort for JavaScript - - [aureooms/js-bucketsort](https://github.com/make-github-pseudonymous-again/js-bucketsort): bucketsort for JavaScript - -### :symbols: Strings - Nothing yet. - -### :hocho: Hashing - Nothing yet. - -### :triangular_ruler: Geometry - - [@aureooms/js-cg](https://github.com/make-github-pseudonymous-again/js-cg) : computational geometry code bricks for JavaScript - -### :globe_with_meridians: Graphs - - [@aureooms/js-gn](https://github.com/make-github-pseudonymous-again/js-gn) : graphs and networks code bricks for JavaScript - - :oden: [@graph-algorithm/topological-sorting](https://github.com/graph-algorithm/topological-sorting): - Topological sorting algorithms for Javascript - - :haircut_woman: [@graph-algorithm/minimum-cut](https://github.com/graph-algorithm/minimum-cut): - Minimum cut algorithms for JavaScript - - :blossom: [@graph-algorithm/maximum-matching](https://github.com/graph-algorithm/maximum-matching): - Maximum matching algorithms for JavaScript - -### :1234: Numbers - - - :zzz: [@aureooms/js-integer](https://github.com/make-github-pseudonymous-again/js-integer) : - Integers for JavaScript (ℤ) - - :woman_farmer: [@aureooms/js-rational-field](https://github.com/make-github-pseudonymous-again/js-rational-field) : Rational field for JavaScript (ℚ) - -#### :symbols: Arithmetic - - :elephant: [@aureooms/js-integer-big-endian](https://github.com/make-github-pseudonymous-again/js-integer-big-endian): Arbitrary precision arithmetic for integers in big-endian order for JavaScript - - :pizza: [@aureooms/js-rational](https://github.com/make-github-pseudonymous-again/js-rational) : rational numbers code bricks for JavaScript - - :mermaid: [@aureooms/js-modular-arithmetic](https://github.com/make-github-pseudonymous-again/js-modular-arithmetic): Modular arithmetic for JavaScript. - - :globe_with_meridians: [@aureooms/js-complex](https://github.com/make-github-pseudonymous-again/js-complex) : complex numbers code bricks for JavaScript - - :wavy_dash: [@aureooms/js-polynomial](https://github.com/make-github-pseudonymous-again/js-polynomial) : sparse and dense polynomials code bricks for JavaScript - -#### :two: :three: :five: :seven: Number theory - - :butterfly: [@aureooms/js-fft](https://github.com/make-github-pseudonymous-again/js-fft) : Fast Fourier transform algorithms for JavaScript - - [@aureooms/js-prime](https://github.com/make-github-pseudonymous-again/js-prime) : Prime numbers for JavaScript - -#### :shell: Integer sequences - - [@aureooms/js-integer-sequences](https://github.com/make-github-pseudonymous-again/js-integer-sequences) : Integer sequences for JavaScript - - [@aureooms/js-fibonacci](https://github.com/make-github-pseudonymous-again/js-fibonacci) : Fibonacci numbers for JavaScript - -### :game_die: Randomness - - [@randomized/random](https://github.com/randomized-algorithm/random): Randomness algorithms for JavaScript - - [@entropy-source/pseudo-random](https://github.com/entropy-source/pseudo-random) : Pseudorandom number generators for JavaScript - -### :brain: Hard problems - - :satisfied: [@aureooms/js-sat](https://github.com/make-github-pseudonymous-again/js-sat) : Boolean formula satisfiability algorithms for Javascript - - :school_satchel: [@aureooms/js-knapsack](https://github.com/make-github-pseudonymous-again/js-knapsack) : - Knapsack problem algorithms for JavaScript - - :test_tube: [@aureooms/js-metaheuristics](https://github.com/make-github-pseudonymous-again/js-metaheuristics) : - Metaheuristic algorithms for JavaScript - -### :left_right_arrow: Sytems of equalities and inequalities - - [@aureooms/js-equation](https://github.com/make-github-pseudonymous-again/js-equation) : equations system code bricks for JavaScript - -### :broom: Combinatorics - - :exclamation: [@combinatorics/factorial](https://github.com/computational-combinatorics/factorial): Factorial function for JavaScript - - :seat: [@combinatorics/permutation](https://github.com/computational-combinatorics/permutation): Permutations library for JavaScript - - :zebra: [@combinatorics/n-permutations](https://github.com/computational-combinatorics/n-permutations): Set n-permutations for JavaScript - - :hippopotamus: [@combinatorics/n-combinations](https://github.com/computational-combinatorics/n-combinations): Set n-combinations for JavaScript - - :rhinoceros: [@combinatorics/n-multicombinations](https://github.com/computational-combinatorics/n-multicombinations): Set n-multicombinations for JavaScript - - :bento: [@combinatorics/set-partition](https://github.com/computational-combinatorics/set-partition): Set partition algorithms for Javascript - - -Those packages aim to provide *code bricks* that are as generic as possible. -Some examples are a Gauss-Jordan method that can work with any number model, a -Karatsuba algorithm that can handle any input size, a Graham Scan algorithm -that works with clockwise or counter clockwise ordering, and a Monotone Chain -algorithm that can be used as a triangulation algorithm without any change. - -## :scroll: Reference - -A list of links and projects focusing on algorithm implementation. - -### :coffee: Projects implementing algorithms in JavaScript - - - https://github.com/felipernb/algorithms.js - - https://github.com/mgechev/javascript-algorithms - - https://github.com/nzakas/computer-science-in-javascript - - https://github.com/benoitvallon/computer-science-in-javascript - - http://www.nayuki.io - -### :peacock: Projects implementing algorithms in other languages - - - https://github.com/xtaci/algorithms (C++) - - https://github.com/fragglet/c-algorithms (C) - - https://github.com/nryoung/algorithms (Python) - - https://github.com/kanwei/algorithms (Ruby) - - https://github.com/phishman3579/java-algorithms-implementation (Java) - - https://github.com/patmorin/ods (C++, Java, Python) - - http://www.nayuki.io (C, C++, Java, C#, Python, Haskell, MATLAB and others) - - http://rosettacode.org (All kinds of languages) - -### :link: Others - - - http://stackoverflow.com/questions/26301/your-favourite-algorithm-and-the-lesson-it-taught-you - - http://cglab.ca/publications.html diff --git a/array/iter.html b/array/iter.html new file mode 100644 index 0000000..8269a0f --- /dev/null +++ b/array/iter.html @@ -0,0 +1,16 @@ +array/iter

js/src/array/iter.js

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js/src/bdp/bdpdc.js

Bichromatic dominating pairs using the divide and conquer chainsaw.

see F. P. Preparata and M. I. Shamos, Computational Geometry, NY, 1985, p. 366.

Here the algorithm handles non-strict ( >= ) dominance.

select( f, a, i, j, k ) where + f is a comparator + a the array of points + [i, j[ the range to search in the array + k the index to select

select(...) partitions the array in tree regions

| <= h | h | >= h |

i .... k k+1 .... j-1

eq( d, v ) template for a function eq( a ) + returns true iff coordinate d of a equals v

ne( d, v ) template for a function ne( y ) + returns true iff coordinate d of a is not equal to v

color( point ) + = 0 if point is blue + = 1 if point is red

p = split( predicate, a, i, j ) + rearranges an array so that all elements for which predicate is false + are in interval [i, p[ and all other elements are in interval [p, j[

swap( a, ai, aj, b, bi ) + swap elements from a in interval [ai, aj[ with elements from b in interval + [bi, bi + aj - ai[

let __bdpdc__ = function ( select, __eq__, __ne__, color, split, swap ) {

a is an array of points

note that we only consider points starting
+at index i and ending at index j-1 in a

points are arrays of coordinates

d = dj - di is the number of coordinates of each point

f is a template for a function {coordinates^2} -> {<0, =0, >0} named f

i.e. for coordinates a and b
+
+  f( a, b ) < 0 means a < b;
+  f( a, b ) = 0 means a = b;
+  f( a, b ) > 0 means a > b.

out is the output array

let bdpdc = function* ( __f__, a, i, j, di, dj ) { + + let k, h, x, y, p, q, m, n, _m, _n;

empty or one element array case

if ( i >= j - 1 ) return ;

base case : dj - di = d = 0 +enumerate all red / blue pairs +[i, p[ contains only blue points +[p, j[ contains only red points +p = index of first red point

if ( di === dj ) {

move all blue points left and all red points right +(arbitrary choice)

p = split( color, a, i, j );

for each red point

for ( x = p ; x < j ; ++x ) {

for each blue point

for ( y = i ; y < p ; ++y ) { + + yield [ a[x], a[y] ] ; + + } + } + + }

recursion fairy

we compute m such that h is the median of +the ith coordinate of all points

else {

| b&r scrambled |

i j

k = ( i + j ) / 2 | 0;

| b&r scrambled |

i k j

select median element +O(n)

select( __f__( di ), a, i, j, k ); + + h = a[k][di];

| b&r <= h | h | b&r >= h |

i k j

we do 3 recursive calls

first: for red and blue points with di < h in R^d +we do not consider points with di = h because either

red = h, blue < h --> handled by last call
red < h, blue = h --> red cannot dominate blue
red = h, blue = h --> handled by last call +(would be "red cannot dominate blue" for strict dominance +in this 3rd case)

second: for red and blue points with di > h in R^d +we do not consider points with di = h for similar reasons as above

last: for red points with di >= h and blue points with di <= h in R^{d-1} +(would be > and < for strict dominance)

note that we do not need to handle the case where red < h and blue >= h +or red <= h and blue > h since red cannot dominate blue in those cases

first recursive call +we only consider points that have di < h +since all points that have di = h will be handled later

move median elements from [ i, k [ in the [ x, k [ interval, x >= i +O(n)

x = split( __eq__( di, h ), a, i, k );

| b&r < h | b&r = h | h | b&r > h |

i x k j

yield* bdpdc( __f__, a, i, x, di, dj );

move median elements from [ k + 1, j [ in the [ y, j [ interval, y <= j +O(n)

y = split( __ne__( di, h ), a, k + 1, j );

| b&r < h | b&r = h | h | b&r = h | b&r > h |

i x k y j

yield* bdpdc( __f__, a, y, j, di, dj );

since we do not touch median elements in the first two +recursive calls they are still at the correct place

Now we want to

move red points such that di < h to the right
move red points such that di >= h to the left

/!\ Note that we also might think that we should

move blue points such that di > h to the right
move blue points such that di <= h to the left +but after the selection algorithm this is already the case

| b&r < h | b&r = h | h | b&r = h | b&r > h |

i x k y j

p = split( color, a, i, x );

| b < h | r < h | b&r = h | h | b&r = h | b&r > h |

i p x k y j

q = split( color, a, y, j );

| b < h | r < h | b&r = h | h | b&r = h | b > h | r > h |

i p x k y q j

we now want to swap r < h elements with r > h elements +we have 3 cases

x - p = j - q
x - p < j - q
x - p > j - q

m = x - p; + n = j - q;

x - p = j - q

if ( m === n ) { + swap( a, q, j, a, p );

| b < h | r > h | b&r = h | h | b&r = h | b > h | r < h |

i p x k y q j

j = y;

| b < h | r > h | b&r = h | h | b&r = h | b > h | r < h |

i p x k j ...

}

x - p < j - q

else if ( m < n ) { + + swap( a, p, x, a, q );

| b < h | r > h | b&r = h | h | b&r = h | b > h | r < h | r > h |

i p x k y q q+m j

we now want to swap b > h and r < h elements with r > h elements + [y,q[ [q,q+m[ [q+m,j[ +we have 2 cases

(q + m) - y >= j - (q + m) [OR >]
(q + m) - y < j - (q + m) [OR <=]

_m = (q + m) - y; + _n = j - (q + m);

(q + m) - y >= j - (q + m)

if ( _m >= _n ) { + swap( a, q + m, j, a, y ); + }

(q + m) - y < j - (q + m)

else { + swap( a, j - _m, j, a, y ); + }

| b < h | r > h | b&r = h | h | b&r = h | r > h | b>h & r<h |

i p x k y y+_n j

j = y + _n;

| b < h | r > h | b&r = h | h | b&r = h | r > h | b>h & r<h |

i p x k y j ...

}

x - p > j - q

else { + + swap( a, q, j, a, p );

| b < h | r > h | r < h | b&r = h | h | b&r = h | b > h | r < h |

i p p+n x k y q j

we now want to swap r < h with b&r = h elements +we have 2 cases

x - (p + n) >= y - x
x - (p + n) < y - x

_m = x - (p + n); + _n = y - x;

x - (p + n) >= y - x

if ( _m >= _n ) { + swap( a, x, y, a, p + n ); + }

x - (p + n) < y - x

else { + swap( a, y - _m, y, a, p + n ); + }

| b < h | r > h | b&r = h | h | b&r = h | b>h & r<h |

i p p+n k y-_m j

j = y - _m;

| b < h | r > h | b&r = h | h | b&r = h | b>h & r<h |

i p p+n k j ...

}

[i, j[ now contains only b <= h and r >= h points +in this new interval, all r points dominate b points +for the ith coordinate +we can thus ask the recursion fairy to take care of the other +dj - di - 1 dimensions left

yield* bdpdc( __f__, a, i, j, di + 1, dj ); + + } + + }; + + return bdpdc; + +}; + +exports.__bdpdc__ = __bdpdc__;

\ No newline at end of file diff --git a/bdp/bdpdn2.html b/bdp/bdpdn2.html new file mode 100644 index 0000000..73a4143 --- /dev/null +++ b/bdp/bdpdn2.html @@ -0,0 +1,46 @@ +bdp/bdpdn2

js/src/bdp/bdpdn2.js

Bichromatic dominating pairs using a naïve O(d * n^2) algorithm.

Here the algorithm handles non-strict ( >= ) dominance.

color( point ) + = 0 if point is blue + = 1 if point is red

p = split( predicate, a, i, j ) + rearranges an array so that all elements for which predicate is false + are in interval [i, p[ and all other elements are in interval [p, j[

let __bdpdn2__ = function ( color, split ) {

a is an array of points

note that we only consider points starting
+at index i and ending at index j-1 in a

points are arrays of coordinates

d = dj - di is the number of coordinates of each point

f is a template for a function {coordinates^2} -> {<0, =0, >0} named f

i.e. for coordinates a and b
+
+  f( a, b ) < 0 means a < b;
+  f( a, b ) = 0 means a = b;
+  f( a, b ) > 0 means a > b.

let bdpdn2 = function* ( __f__, a, i, j, di, dj ) { + + let x, y, p, d, f;

empty or one element array case

if ( i >= j - 1 ) return ;

move all blue points left and all red points right +(arbitrary choice)

[i, p[ contains only blue points +[p, j[ contains only red points +p = index of first red point

p = split( color, a, i, j );

for each red point

red : for ( x = p ; x < j ; ++x ) {

for each blue point

blue : for ( y = i ; y < p ; ++y ) { + + for ( d = di ; d < dj ; ++d ) { + + f = __f__( d ); + + if ( f( a[x], a[y] ) < 0 ) { + continue blue; + } + + } + + yield [ a[x], a[y] ] ; + + } + } + + }; + + return bdpdn2; + +}; + +exports.__bdpdn2__ = __bdpdn2__;

\ No newline at end of file diff --git a/birthdays/samebirthday.html b/birthdays/samebirthday.html new file mode 100644 index 0000000..ae88d5a --- /dev/null +++ b/birthdays/samebirthday.html @@ -0,0 +1,26 @@ +birthdays/samebirthday

js/src/birthdays/samebirthday.js

Computes the probability ( [0, 1] ) for at least 1 of k people +out of n to have his birthday the same day as someone else.

hypothesis : k <= n and k <= days

\ No newline at end of file diff --git a/bower.json b/bower.json deleted file mode 100644 index efc624a..0000000 --- a/bower.json +++ /dev/null @@ -1,21 +0,0 @@ -{ - "homepage": "https://make-github-pseudonymous-again.github.io/js-algorithms", - "name": "aureooms-js-algorithms", - "license": "AGPL-3.0", - "description": "playground for algorithmic code bricks in JavaScript", - "version": "3.0.7", - "main": "js/dist/algorithms.js", - "ignore": [ - "js/index.js", - "js/src", - "test", - "pkg.json", - "package.json", - ".groc.json", - ".travis.yml", - ".gitignore", - "README.md", - "inch.json", - ".codeclimate.yml" - ] -} \ No newline at end of file diff --git a/component.json b/component.json deleted file mode 100644 index b1cdf5a..0000000 --- a/component.json +++ /dev/null @@ -1,11 +0,0 @@ -{ - "main": "js/dist/algorithms.js", - "name": "aureooms-js-algorithms", - "scripts": [ - "js/dist/algorithms.js" - ], - "description": "playground for algorithmic code bricks in JavaScript", - "license": "AGPL-3.0", - "version": "3.0.7", - "repo": "aureooms/js-algorithms" -} \ No newline at end of file diff --git a/epsilon/absepsilon.html b/epsilon/absepsilon.html new file mode 100644 index 0000000..c6f55d2 --- /dev/null +++ b/epsilon/absepsilon.html @@ -0,0 +1,16 @@ +epsilon/absepsilon

js/src/epsilon/absepsilon.js

var __absepsilon__ = function ( epsilon ) { + + + return function ( a, b ) { + + var r; + + r = a - b; + + return r < -epsilon ? -1 : r > epsilon ? 1 : 0; + + }; + +}; + +exports.__absepsilon__ = __absepsilon__;

\ No newline at end of file diff --git a/epsilon/relepsilon.html b/epsilon/relepsilon.html new file mode 100644 index 0000000..1acaa35 --- /dev/null +++ b/epsilon/relepsilon.html @@ -0,0 +1,28 @@ +epsilon/relepsilon

js/src/epsilon/relepsilon.js

\ No newline at end of file diff --git a/inch.json b/inch.json deleted file mode 100644 index bb05fa6..0000000 --- a/inch.json +++ /dev/null @@ -1,5 +0,0 @@ -{ - "files" : { - "included": [ "js/src/**/*.js" ] - } -} diff --git a/index.html b/index.html new file mode 100644 index 0000000..2f44857 --- /dev/null +++ b/index.html @@ -0,0 +1,84 @@ +index

README.md

js-algorithms

Algorithms code bricks in JavaScript. This is a child project of +js-library and the twin project +of js-data-structures.

+ + + + + + + + + +

Description

This project is just a playground for any algorithm that doesn't fit in any +of those project,

aureooms/js-cg : computational geometry code bricks for JavaScript
aureooms/js-complex : complex numbers code bricks for JavaScript
aureooms/js-equation : equations system code bricks for JavaScript
aureooms/js-fft : fast Fourier transform code bricks for JavaScript
aureooms/js-fibonacci : Fibonacci numbers code bricks for JavaScript
aureooms/js-gn : graphs and networks code bricks for JavaScript
aureooms/js-hash : hashing algorithms code bricks for JavaScript
aureooms/js-ho : heuristic optimization code bricks for JavaScript
aureooms/js-hypermatrix : hypermatrices code bricks for JavaScript
aureooms/js-integer : multi-precision arithmetic code bricks for JavaScript
aureooms/js-matrix : matrices code bricks for JavaScript
aureooms/js-nlp : natural language processing code bricks for JavaScript
aureooms/js-oro : operations research and optimization algorithm templates for JavaScript
aureooms/js-permutation : permutations code bricks for JavaScript
aureooms/js-pfsp-wt : permutation flow-shop problem (PFSP) with weighted tardiness objective (PFSP-WT) code bricks for JavaScript
aureooms/js-polynomial : sparse and dense polynomials code bricks for JavaScript
aureooms/js-prime : prime numbers code bricks for JavaScript
aureooms/js-random : randomness code bricks for JavaScript
aureooms/js-rational : rational numbers code bricks for JavaScript
aureooms/js-search : item retrieval code bricks for JavaScript
aureooms/js-splitting: splitting code bricks for JavaScript
aureooms/js-sort : sorting code bricks for JavaScript
- aureooms/js-in-situ-sort-spec: in place sorting code bricks for JavaScript
  - aureooms/js-heapsort: heapsort code bricks for JavaScript
  - aureooms/js-quicksort: quicksort code bricks for JavaScript
  +
- aureooms/js-mergesort: mergesort code bricks for JavaScript
- aureooms/js-merging: merging code bricks for JavaScript
- aureooms/js-partition: partition code bricks for JavaScript
- aureooms/js-selection: selection code bricks for JavaScript
+
aureooms/js-string : character sequence code bricks for JavaScript

Those packages aim to provide code bricks that are as generic as possible. +Some examples are a Gauss-Jordan method that can work with any number model, a +Karatsuba algorithm that can handle any block size, a Graham Scan algorithm +that works with clockwise or counter clockwise ordering, and a Monotone Chain +algorithm that can be used as a triangulation algorithm without any change.

Reference

A list of links and projects focusing on algorithm implementation.

Projects implementing algorithms in JavaScript

Projects implementing algorithms in other languages

https://github.com/xtaci/algorithms (C++)
https://github.com/fragglet/c-algorithms (C)
https://github.com/nryoung/algorithms (Python)
https://github.com/kanwei/algorithms (Ruby)
https://github.com/phishman3579/java-algorithms-implementation (Java)
https://github.com/patmorin/ods (C++, Java, Python)
http://www.nayuki.io (C, C++, Java, C#, Python, Haskell, MATLAB and others)
http://rosettacode.org (All kinds of languages)

Others

\ No newline at end of file diff --git a/js/dist/algorithms.js b/js/dist/algorithms.js deleted file mode 100644 index 5588699..0000000 --- a/js/dist/algorithms.js +++ /dev/null @@ -1,1193 +0,0 @@ -"use strict"; - -var _slicedToArray = (function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; })(); - -function _toArray(arr) { return Array.isArray(arr) ? arr : Array.from(arr); } - -(function () { - - 'use strict'; - - var definition = function definition(exports, undefined) { - - /* js/src/3sum */ - /* js/src/3sum/_3sum_n2.js */ - - /** - * Hypothesis : - * - A is sorted in increasing order - * - B is sorted in increasing order - * - |A| > 0 - * - |B| > 0 - */ - - var _3sum_n2 = function _3sum_n2(A, ai, aj, B, bi, bj, C, ci, cj, fn) { - - var hi, lo, a, b, c, v; - - for (; ci < cj; ++ci) { - lo = ai; - hi = bj - 1; - - do { - - a = A[lo]; - b = B[hi]; - c = C[ci]; - v = a + b; - - if (-c === v) fn(a, b, c); - - if (-c < v) --hi;else ++lo; - } while (lo < aj && hi >= bi); - } - }; - - exports._3sum_n2 = _3sum_n2; - /* js/src/4sum */ - /* js/src/4sum/sortxy_n3.js */ - - /** - * X is sorted in increasing order - * Y is sorted in increasing order - * compare takes 4 arguments and returns <=> 0 - * output takes 4 arguments - * - */ - var sortxy_n3 = function sortxy_n3(compare, X, Y, Xi1, Xj1, Yi1, Yj1, Xi2, Xj2, Yi2, Yj2, output) { - - var a, b, c, d, s; - - if (Xi1 > Xj1 || Yi1 > Yj1 || Xi2 > Xj2 || Yi2 > Yj2) { - return; - } - - // ----------------------------- - // | X | - // ----------------------------- - // Xi Xj - - // ----------------------------- - // | Y | - // ----------------------------- - // Yi Yj - - a = X[Xi1]; - b = Y[Yj1]; - c = X[Xj2]; - d = Y[Yi2]; - - s = compare(a, b, c, d); - - if (s === 0) { - - output(Xi1, Yj1, Xj2, Yi2); - - sortxy_n3(compare, X, Y, Xi1 + 1, Xj1, Yi1, Yj1, Xi2, Xj2, Yi2, Yj2, output); - sortxy_n3(compare, X, Y, Xi1, Xi1, Yi1, Yj1 - 1, Xi2, Xj2, Yi2, Yj2, output); - sortxy_n3(compare, X, Y, Xi1, Xi1, Yj1, Yj1, Xi2, Xj2 - 1, Yi2, Yj2, output); - } else if (s < 0) { - - sortxy_n3(compare, X, Y, Xi1 + 1, Xj1, Yi1, Yj1, Xi2, Xj2, Yi2, Yj2, output); - sortxy_n3(compare, X, Y, Xi1, Xi1, Yi1, Yj1, Xi2, Xj2 - 1, Yi2, Yj2, output); - } else { - - sortxy_n3(compare, X, Y, Xi1, Xj1, Yi1, Yj1 - 1, Xi2, Xj2, Yi2, Yj2, output); - sortxy_n3(compare, X, Y, Xi1, Xj1, Yj1, Yj1, Xi2, Xj2, Yi2 + 1, Yj2, output); - } - }; - - exports.sortxy_n3 = sortxy_n3; - - /* js/src/4sum/sortxy_n4.js */ - - /** - * X is sorted in increasing order - * Y is sorted in increasing order - * compare takes 4 arguments and returns <=> 0 - * output takes 4 arguments - * - */ - var sortxy_n4 = function sortxy_n4(compare, X, Y, Xi1, Xj1, Yi1, Yj1, Xi2, Xj2, Yi2, Yj2, output) { - - var a, b, c, d, s; - - if (Xi1 > Xj1 || Yi1 > Yj1 || Xi2 > Xj2 || Yi2 > Yj2) { - return; - } - - // ----------------------------- - // | X | - // ----------------------------- - // Xi Xj - - // ----------------------------- - // | Y | - // ----------------------------- - // Yi Yj - - a = X[Xi1]; - b = Y[Yi1]; - c = X[Xi2]; - d = Y[Yi2]; - - s = compare(a, b, c, d); - - if (s === 0) { - - output(Xi1, Yi1, Xi2, Yi2); - } - - sortxy_n4(compare, X, Y, Xi1 + 1, Xj1, Yi1, Yj1, Xi2, Xj2, Yi2, Yj2, output); - sortxy_n4(compare, X, Y, Xi1, Xi1, Yi1 + 1, Yj1, Xi2, Xj2, Yi2, Yj2, output); - sortxy_n4(compare, X, Y, Xi1, Xi1, Yi1, Yi1, Xi2 + 1, Xj2, Yi2, Yj2, output); - sortxy_n4(compare, X, Y, Xi1, Xi1, Yi1, Yi1, Xi2, Xi2, Yi2 + 1, Yj2, output); - }; - - exports.sortxy_n4 = sortxy_n4; - - /* js/src/array */ - /* js/src/array/iter.js */ - - var fiter = function fiter(i, j, fn) { - for (; i < j; ++i) { - fn(i); - } - }; - - var biter = function biter(i, j, fn) { - while (--j >= i) { - fn(j); - } - }; - - exports.fiter = fiter; - exports.biter = biter; - - /* js/src/bdp */ - /* js/src/bdp/bdpdc.js */ - - /** - * Bichromatic dominating pairs using the divide and conquer chainsaw. - * - * see F. P. Preparata and M. I. Shamos, Computational Geometry, NY, 1985, p. 366. - * - * Here the algorithm handles non-strict ( >= ) dominance. - * - * select( f, a, i, j, k ) where - * f is a comparator - * a the array of points - * [i, j[ the range to search in the array - * k the index to select - * - * select(...) partitions the array in tree regions - * ----------------------------- - * | <= h | h | >= h | - * ----------------------------- - * i .... k k+1 .... j-1 - * - * __eq__( d, v ) template for a function eq( a ) - * returns true iff coordinate d of a equals v - * - * __ne__( d, v ) template for a function ne( y ) - * returns true iff coordinate d of a is not equal to v - * - * color( point ) - * = 0 if point is blue - * = 1 if point is red - * - * p = split( predicate, a, i, j ) - * rearranges an array so that all elements for which predicate is false - * are in interval [i, p[ and all other elements are in interval [p, j[ - * - * swap( a, ai, aj, b, bi ) - * swap elements from a in interval [ai, aj[ with elements from b in interval - * [bi, bi + aj - ai[ - * - */ - - var __bdpdc__ = function __bdpdc__(select, __eq__, __ne__, color, split, swap) { - - /** - * a is an array of points - * - * note that we only consider points starting - * at index i and ending at index j-1 in a - * - * points are arrays of coordinates - * - * d = dj - di is the number of coordinates of each point - * - * - * __f__ is a template for a function {coordinates^2} -> {<0, =0, >0} named f - * - * i.e. for coordinates a and b - * - * f( a, b ) < 0 means a < b; - * f( a, b ) = 0 means a = b; - * f( a, b ) > 0 means a > b. - * - * out is the output array - * - */ - - var bdpdc = regeneratorRuntime.mark(function bdpdc(__f__, a, i, j, di, dj) { - var k, h, x, y, p, q, m, n, _m, _n; - - return regeneratorRuntime.wrap(function bdpdc$(context$4$0) { - while (1) switch (context$4$0.prev = context$4$0.next) { - case 0: - k = undefined, h = undefined, x = undefined, y = undefined, p = undefined, q = undefined, m = undefined, n = undefined, _m = undefined, _n = undefined; - - if (!(i >= j - 1)) { - context$4$0.next = 3; - break; - } - - return context$4$0.abrupt("return"); - - case 3: - if (!(di === dj)) { - context$4$0.next = 19; - break; - } - - // move all blue points left and all red points right - // (arbitrary choice) - - p = split(color, a, i, j); - - // for each red point - - x = p; - - case 6: - if (!(x < j)) { - context$4$0.next = 17; - break; - } - - y = i; - - case 8: - if (!(y < p)) { - context$4$0.next = 14; - break; - } - - context$4$0.next = 11; - return [a[x], a[y]]; - - case 11: - ++y; - context$4$0.next = 8; - break; - - case 14: - ++x; - context$4$0.next = 6; - break; - - case 17: - context$4$0.next = 32; - break; - - case 19: - - // ------------------------------------------------------- - // | b&r scrambled | - // ------------------------------------------------------- - // i j - - k = (i + j) / 2 | 0; - - // ------------------------------------------------------- - // | b&r scrambled | - // ------------------------------------------------------- - // i k j - - // select median element - // O(n) - - select(__f__(di), a, i, j, k); - - h = a[k][di]; - - // ------------------------------------------------------- - // | b&r <= h | h | b&r >= h | - // ------------------------------------------------------- - // i k j - - // we do 3 recursive calls - // - // first: for red and blue points with di < h in R^d - // we do not consider points with di = h because either - // - // 1. red = h, blue < h --> handled by last call - // 2. red < h, blue = h --> red cannot dominate blue - // 3. red = h, blue = h --> handled by last call - // (would be "red cannot dominate blue" for strict dominance - // in this 3rd case) - // - // second: for red and blue points with di > h in R^d - // we do not consider points with di = h for similar reasons as above - // - // last: for red points with di >= h and blue points with di <= h in R^{d-1} - // (would be > and < for strict dominance) - // - // note that we do not need to handle the case where red < h and blue >= h - // or red <= h and blue > h since red cannot dominate blue in those cases - - // first recursive call - // we only consider points that have di < h - // since all points that have di = h will be handled later - - // move median elements from [ i, k [ in the [ x, k [ interval, x >= i - // O(n) - - x = split(__eq__(di, h), a, i, k); - - // ------------------------------------------------------- - // | b&r < h | b&r = h | h | b&r > h | - // ------------------------------------------------------- - // i x k j - - return context$4$0.delegateYield(bdpdc(__f__, a, i, x, di, dj), "t0", 24); - - case 24: - - // move median elements from [ k + 1, j [ in the [ y, j [ interval, y <= j - // O(n) - - y = split(__ne__(di, h), a, k + 1, j); - - // ------------------------------------------------------- - // | b&r < h | b&r = h | h | b&r = h | b&r > h | - // ------------------------------------------------------- - // i x k y j - - return context$4$0.delegateYield(bdpdc(__f__, a, y, j, di, dj), "t1", 26); - - case 26: - - // since we do not touch median elements in the first two - // recursive calls they are still at the correct place - - // Now we want to - // - move red points such that di < h to the right - // - move red points such that di >= h to the left - // - // /!\ Note that we also might think that we should - // - move blue points such that di > h to the right - // - move blue points such that di <= h to the left - // but after the selection algorithm this is already the case - - // ------------------------------------------------------- - // | b&r < h | b&r = h | h | b&r = h | b&r > h | - // ------------------------------------------------------- - // i x k y j - - p = split(color, a, i, x); - - // ------------------------------------------------------- - // | b < h | r < h | b&r = h | h | b&r = h | b&r > h | - // ------------------------------------------------------- - // i p x k y j - - q = split(color, a, y, j); - - // ------------------------------------------------------- - // | b < h | r < h | b&r = h | h | b&r = h | b > h | r > h | - // ------------------------------------------------------- - // i p x k y q j - - // we now want to swap r < h elements with r > h elements - // we have 3 cases - // 1. x - p = j - q - // 2. x - p < j - q - // 3. x - p > j - q - - m = x - p; - n = j - q; - - // 1. x - p = j - q - - if (m === n) { - swap(a, q, j, a, p); - - // ------------------------------------------------------- - // | b < h | r > h | b&r = h | h | b&r = h | b > h | r < h | - // ------------------------------------------------------- - // i p x k y q j - - j = y; - - // ------------------------------------------------------- - // | b < h | r > h | b&r = h | h | b&r = h | b > h | r < h | - // ------------------------------------------------------- - // i p x k j ... - } - - // 2. x - p < j - q - - else if (m < n) { - - swap(a, p, x, a, q); - - // --------------------------------------------------------------- - // | b < h | r > h | b&r = h | h | b&r = h | b > h | r < h | r > h | - // --------------------------------------------------------------- - // i p x k y q q+m j - - // we now want to swap b > h and r < h elements with r > h elements - // [y,q[ [q,q+m[ [q+m,j[ - // we have 2 cases - // 1. (q + m) - y >= j - (q + m) [OR >] - // 2. (q + m) - y < j - (q + m) [OR <=] - - _m = q + m - y; - _n = j - (q + m); - - // 1. (q + m) - y >= j - (q + m) - if (_m >= _n) { - swap(a, q + m, j, a, y); - } - // 2. (q + m) - y < j - (q + m) - else { - swap(a, j - _m, j, a, y); - } - - // --------------------------------------------------------------- - // | b < h | r > h | b&r = h | h | b&r = h | r > h | b>h & r h | b&r = h | h | b&r = h | r > h | b>h & r j - q - - else { - - swap(a, q, j, a, p); - - // --------------------------------------------------------------- - // | b < h | r > h | r < h | b&r = h | h | b&r = h | b > h | r < h | - // --------------------------------------------------------------- - // i p p+n x k y q j - - // we now want to swap r < h with b&r = h elements - // we have 2 cases - // 1. x - (p + n) >= y - x - // 2. x - (p + n) < y - x - - _m = x - (p + n); - _n = y - x; - - // 1. x - (p + n) >= y - x - if (_m >= _n) { - swap(a, x, y, a, p + n); - } - // 2. x - (p + n) < y - x - else { - swap(a, y - _m, y, a, p + n); - } - - // ----------------------------------------------------------- - // | b < h | r > h | b&r = h | h | b&r = h | b>h & r h | b&r = h | h | b&r = h | b>h & r= h points - // in this new interval, all r points dominate b points - // for the ith coordinate - // we can thus ask the recursion fairy to take care of the other - // dj - di - 1 dimensions left - - return context$4$0.delegateYield(bdpdc(__f__, a, i, j, di + 1, dj), "t2", 32); - - case 32: - case "end": - return context$4$0.stop(); - } - }, bdpdc, this); - }); - - return bdpdc; - }; - - exports.__bdpdc__ = __bdpdc__; - - /* js/src/bdp/bdpdn2.js */ - - /** - * Bichromatic dominating pairs using a naïve O(d * n^2) algorithm. - * - * Here the algorithm handles non-strict ( >= ) dominance. - * - * color( point ) - * = 0 if point is blue - * = 1 if point is red - * - * p = split( predicate, a, i, j ) - * rearranges an array so that all elements for which predicate is false - * are in interval [i, p[ and all other elements are in interval [p, j[ - * - */ - - var __bdpdn2__ = function __bdpdn2__(color, split) { - - /** - * a is an array of points - * - * note that we only consider points starting - * at index i and ending at index j-1 in a - * - * points are arrays of coordinates - * - * d = dj - di is the number of coordinates of each point - * - * - * __f__ is a template for a function {coordinates^2} -> {<0, =0, >0} named f - * - * i.e. for coordinates a and b - * - * f( a, b ) < 0 means a < b; - * f( a, b ) = 0 means a = b; - * f( a, b ) > 0 means a > b. - * - */ - - var bdpdn2 = regeneratorRuntime.mark(function bdpdn2(__f__, a, i, j, di, dj) { - var x, y, p, d, f; - return regeneratorRuntime.wrap(function bdpdn2$(context$4$0) { - while (1) switch (context$4$0.prev = context$4$0.next) { - case 0: - x = undefined, y = undefined, p = undefined, d = undefined, f = undefined; - - if (!(i >= j - 1)) { - context$4$0.next = 3; - break; - } - - return context$4$0.abrupt("return"); - - case 3: - - // move all blue points left and all red points right - // (arbitrary choice) - - // [i, p[ contains only blue points - // [p, j[ contains only red points - // p = index of first red point - - p = split(color, a, i, j); - - // for each red point - - x = p; - - case 5: - if (!(x < j)) { - context$4$0.next = 24; - break; - } - - y = i; - - case 7: - if (!(y < p)) { - context$4$0.next = 21; - break; - } - - d = di; - - case 9: - if (!(d < dj)) { - context$4$0.next = 16; - break; - } - - f = __f__(d); - - if (!(f(a[x], a[y]) < 0)) { - context$4$0.next = 13; - break; - } - - return context$4$0.abrupt("continue", 18); - - case 13: - ++d; - context$4$0.next = 9; - break; - - case 16: - context$4$0.next = 18; - return [a[x], a[y]]; - - case 18: - ++y; - context$4$0.next = 7; - break; - - case 21: - ++x; - context$4$0.next = 5; - break; - - case 24: - case "end": - return context$4$0.stop(); - } - }, bdpdn2, this); - }); - - return bdpdn2; - }; - - exports.__bdpdn2__ = __bdpdn2__; - - /* js/src/birthdays */ - /* js/src/birthdays/samebirthday.js */ - - /** - * - * Computes the probability ( [0, 1] ) for at least 1 of k people - * out of n to have his birthday the same day as someone else. - * - * hypothesis : k <= n and k <= days - */ - - var samebirthday = function samebirthday(k, n, days) { - - var i, p; - - p = 1; - - for (i = 1; i < k; ++i) { - - p = p * (days - i) / days; - } - - for (; i < n; ++i) { - - p = p * (days - k) / days; - } - - return 1 - p; - }; - - exports.samebirthday = samebirthday; - - /* js/src/epsilon */ - /* js/src/epsilon/absepsilon.js */ - - var __absepsilon__ = function __absepsilon__(epsilon) { - - return function (a, b) { - - var r; - - r = a - b; - - return r < -epsilon ? -1 : r > epsilon ? 1 : 0; - }; - }; - - exports.__absepsilon__ = __absepsilon__; - - /* js/src/epsilon/relepsilon.js */ - - var __relepsilon__ = function __relepsilon__(epsilon) { - - return function (a, b) { - - var r; - - if (b === 0) { - return a; - } else if (a === 0) { - return -b; - } else { - - r = a / b - 1; - - return r < -epsilon ? -1 : r > epsilon ? 1 : 0; - } - }; - }; - - exports.__relepsilon__ = __relepsilon__; - - /* js/src/matroids */ - /* js/src/matroids/max_independent_set.js */ - - /** - * Greedy algorithm for computing the maximum independent set. - * For max-weight independent set give the input in decreasing order wrt weights. - */ - - var max_independent_set = function max_independent_set(independent, S) { - - var set = []; - - var _iteratorNormalCompletion = true; - var _didIteratorError = false; - var _iteratorError = undefined; - - try { - loop: for (var _iterator = S[Symbol.iterator](), _step; !(_iteratorNormalCompletion = (_step = _iterator.next()).done); _iteratorNormalCompletion = true) { - var u = _step.value; - var _iteratorNormalCompletion2 = true; - var _didIteratorError2 = false; - var _iteratorError2 = undefined; - - try { - - for (var _iterator2 = set[Symbol.iterator](), _step2; !(_iteratorNormalCompletion2 = (_step2 = _iterator2.next()).done); _iteratorNormalCompletion2 = true) { - var v = _step2.value; - - if (!independent(u, v)) continue loop; - } - } catch (err) { - _didIteratorError2 = true; - _iteratorError2 = err; - } finally { - try { - if (!_iteratorNormalCompletion2 && _iterator2["return"]) { - _iterator2["return"](); - } - } finally { - if (_didIteratorError2) { - throw _iteratorError2; - } - } - } - - set.push(u); - } - } catch (err) { - _didIteratorError = true; - _iteratorError = err; - } finally { - try { - if (!_iteratorNormalCompletion && _iterator["return"]) { - _iterator["return"](); - } - } finally { - if (_didIteratorError) { - throw _iteratorError; - } - } - } - - return set; - }; - - exports.max_independent_set = max_independent_set; - - /* js/src/minima */ - /* js/src/minima/clarkson.js */ - - /** - * Output sensitive inplace algorithm to find the minima set of a set S of - * elements according to some partial order. - * - * Uses at most 3nA comparisons where A is the cardinality of the minima set. - * - * For (1), at most nA comparisons are used since we compare each element of S - * with each elements of the minima set which is of cardinality at most A - * during the execution of the algorithm. - * - * For (2), for each executed loop we - * obtain a new minimum and increase the size of the constructed minima set by - * 1, hence there are at most A loops execution, each of which loops over at - * most n elements. (2) uses thus at most nA comparisons. - * - * The running time is dominated by the comparison time and thus the complexity - * of this algorihtm is O(nA). - * - * Description and context in - * ------------------------------------------ - * More Output-Sensitive Geometric Algorithms. - * -------------------- Kenneth L. Clarkson - - */ - - var clarkson = function clarkson(prec, a, i, j) { - - // - // This algorithms reorganizes the input array `a` as follows - // - elements that are minima are put at the front of `a` - // - other elements are put at the back of `a` - // - // During the algorithm, `a` looks like this - // - // ------------------------------------------------------ - // | minima set | candidate elements | discarded elements | - // ------------------------------------------------------ - // i min dis j - - var min, dis, k, inc, tmp; - - min = i; - dis = j - 1; - - // While there are candidate elements left. - - while (min <= dis) { - - // (1) Determine if the right-most candidate should be discarded because it - // is dominated by one of the minima elements of the minima set in - // construction. - - for (k = i; k < min && !prec(a[k], a[dis]); ++k); - - // If so, discard it. - - if (k < min) --dis; - - // (2) Otherwise, scan the candidates for a minimum. If at this point the - // candidate set is not empty, at least one of its elements must be a - // minimum. We scan the candidate list to find such a minimum. - - else { - - // Store the current minimum as the left-most candidate. - - tmp = a[dis]; - a[dis] = a[min]; - a[min] = tmp; - - // For each other candidate, right-to-left. - - for (inc = min + 1; inc <= dis;) { - - // If the current minimum precedes the right-most candidate, - // discard the right-most candidate. - - if (prec(a[min], a[dis])) --dis; - - // Else, if the right-most candidate precedes the current - // minimum, we can discard the current minimum and the - // right-most candidate becomes the current minimum. - - else if (prec(a[dis], a[min])) { - tmp = a[dis]; - a[dis] = a[min]; - a[min] = tmp; - --dis; - } - - // Otherwise, we save the candidate for the next round. - - else { - tmp = a[dis]; - a[dis] = a[inc]; - a[inc] = tmp; - ++inc; - } - } - - // The above loop selects a new minimum from the set of candidates - // and places it at position `min`. We now increase the `min` - // counter to move this minimum from the candidate list to the - // minima set. - - ++min; - } - } - - // The algorithm returns the outer right bound of the minima set a[i:min]. - - return min; - }; - - exports.clarkson = clarkson; - - /* js/src/reductions */ - /* js/src/reductions/chan.js */ - - /** - * Timoty Chan (1999) - * Geometric Applications of a Randomized Optimization Technique - * - * Translates any decision algorithm for a question of the type "is the optimal - * value for this problem less/greater than `c`?" to a randomized optimisation - * algortihm that finds the optimal value of `c*` whose expected time complexity - * is within a constant factor of the complexity of the decision algorithm. - * For this to work we must be capable of splitting a problem into a constant - * number of smaller (by a constant factor) subproblems so that the optimal - * value of the original problem is the min/max of the optimal values for the - * subproblems. For example, given a decision algorithm `decide( G , c )` - * that decides whether graph G has diameter greater than c, we can split the - * problem into k^2 subproblems of size (2n/k), that is, the diameter of G is - * the maximum over the diameters of all subgraphs that are the union of 2 - * disjoint subgraphs taken from a partition of G into k disjoint subgraphs of - * size n/k. Finding the optimal k for a given problem requires to solve a - * reccurence expressing the time-complexity of the following meta-algorithm. - * Read Timoty Chan's paper for more information. - */ - - var chan = function chan(split, shuffle, decide, bruteforce, issmall) { - - var solve = function solve(instance) { - - if (issmall(instance)) return bruteforce(instance); - - var _shuffle = shuffle(split(instance)); - - var _shuffle2 = _toArray(_shuffle); - - var first = _shuffle2[0]; - - var rest = _shuffle2.slice(1); - - var _solve = solve(first); - - var _solve2 = _slicedToArray(_solve, 2); - - var current = _solve2[0]; - var optimum = _solve2[1]; - var _iteratorNormalCompletion3 = true; - var _didIteratorError3 = false; - var _iteratorError3 = undefined; - - try { - - for (var _iterator3 = rest[Symbol.iterator](), _step3; !(_iteratorNormalCompletion3 = (_step3 = _iterator3.next()).done); _iteratorNormalCompletion3 = true) { - var candidate = _step3.value; - - if (decide(candidate, optimum)) { - var _solve3 = solve(candidate); - - var _solve32 = _slicedToArray(_solve3, 2); - - current = _solve32[0]; - optimum = _solve32[1]; - } - } - } catch (err) { - _didIteratorError3 = true; - _iteratorError3 = err; - } finally { - try { - if (!_iteratorNormalCompletion3 && _iterator3["return"]) { - _iterator3["return"](); - } - } finally { - if (_didIteratorError3) { - throw _iteratorError3; - } - } - } - - return [current, optimum]; - }; - - return solve; - }; - - exports.chan = chan; - - /* js/src/reductions/kldt */ - /* js/src/reductions/kldt/evenkldtto2sum.js */ - - /** - * Transforms an instance of the one-set version of kLDT with k >= 4 even into - * a two-set version of 2SUM. - * - * @param {set} S is the input set for the kLDT problem - * @param {coefficients} a is the array of coefficients - * @param {set} A is one of the input set for 2SUM - * @param {set} B is one of the input set for 2SUM - * - * notes: - * - n = Sj - Si - * - k = aj - ai - 1 - * - a_0 = a[ai] - * - A and B must be of size n^(k/2) each - * - B must be initialized to 0 ... 0 - * - */ - - var evenkldtto2sum = function evenkldtto2sum(S, Si, Sj, a, ai, aj, A, Ai, Aj, B, Bi, Bj) { - - var i, j, p, q, n, halfk; - - n = Sj - Si; - - k = aj - ai - 1; - - halfk = 1 + k / 2; - - // We fill A and B for example with S = [ 1 , 2 , 3 ] and a = [ t , v , w , x , y ] - - // ----------------------------------------------------------------------- - // A <- | t | t | t | t | t | t | t | t | t | - // ----------------------------------------------------------------------- - - for (p = Ai; p < Aj; ++p) { - - A[p] = a[ai]; - } - - // ----------------------------------------------------------------------- - // A += | v * 1 | v * 2 | v * 3 | v * 1 | v * 2 | v * 3 | v * 1 | v * 2 | v * 3 | - // ----------------------------------------------------------------------- - // ----------------------------------------------------------------------- - // A += | w * 1 | w * 1 | w * 1 | w * 2 | w * 2 | w * 2 | w * 3 | w * 3 | w * 3 | - // ----------------------------------------------------------------------- - - for (j = 1, i = 1; j < halfk; ++j, i *= n) { - - for (p = Ai, q = 0; p < Aj; ++p, q = ((q + 1) / i | 0) % n) { - - A[p] += a[ai + j] * S[Si + q]; - } - } - - // ----------------------------------------------------------------------- - // B += | x * 1 | x * 2 | x * 3 | x * 1 | x * 2 | x * 3 | x * 1 | x * 2 | x * 3 | - // ----------------------------------------------------------------------- - // ----------------------------------------------------------------------- - // B += | y * 1 | y * 1 | y * 1 | y * 2 | y * 2 | y * 2 | y * 3 | y * 3 | y * 3 | - // ----------------------------------------------------------------------- - - for (i = 1; j <= k; ++j, i *= n) { - - for (p = Bi, q = 0; p < Bj; ++p, q = ((q + 1) / i | 0) % n) { - - B[p] += a[ai + j] * S[Si + q]; - } - } - }; - - exports.evenkldtto2sum = evenkldtto2sum; - - /* js/src/reductions/kldt/oddkldtto3sum.js */ - - /** - * Transforms an instance of the one-set version of kLDT with k >= 3 odd into - * a three-set version of 3SUM. - * - * @param {set} S is the input set for the kLDT problem - * @param {coefficients} a is the array of coefficients - * @param {set} A is one of the input set for 3SUM - * @param {set} B is one of the input set for 3SUM - * @param {set} C is one of the input set for 3SUM - * - * notes: - * - n = Sj - Si - * - k = aj - ai - 1 - * - a_0 = a[ai] - * - A and B must be of size n^((k-1)/2) each - * - A and B must be initialized to 0 ... 0 - * - C must be of size n - * - */ - - var oddkldtto3sum = function oddkldtto3sum(S, Si, Sj, a, ai, aj, A, Ai, Aj, B, Bi, Bj, C, Ci, Cj) { - - var i, j, p, q, n, halfk; - - n = Sj - Si; - - k = aj - ai - 1; - - halfk = 2 + (k - 1) / 2; - - // We fill A and B for example with S = [ 1 , 2 , 3 ] and a = [ t , u , v , w , x , y ] - - // ----------------------------------------------------------------------- - // A += | v * 1 | v * 2 | v * 3 | v * 1 | v * 2 | v * 3 | v * 1 | v * 2 | v * 3 | - // ----------------------------------------------------------------------- - // ----------------------------------------------------------------------- - // A += | w * 1 | w * 1 | w * 1 | w * 2 | w * 2 | w * 2 | w * 3 | w * 3 | w * 3 | - // ----------------------------------------------------------------------- - - for (j = 2, i = 1; j < halfk; ++j, i *= n) { - - for (p = Ai, q = 0; p < Aj; ++p, q = ((q + 1) / i | 0) % n) { - - A[p] += a[ai + j] * S[Si + q]; - } - } - - // ----------------------------------------------------------------------- - // B += | x * 1 | x * 2 | x * 3 | x * 1 | x * 2 | x * 3 | x * 1 | x * 2 | x * 3 | - // ----------------------------------------------------------------------- - // ----------------------------------------------------------------------- - // B += | y * 1 | y * 1 | y * 1 | y * 2 | y * 2 | y * 2 | y * 3 | y * 3 | y * 3 | - // ----------------------------------------------------------------------- - - for (i = 1; j <= k; ++j, i *= n) { - - for (p = Bi, q = 0; p < Bj; ++p, q = ((q + 1) / i | 0) % n) { - - B[p] += a[ai + j] * S[Si + q]; - } - } - - // We fill C - - // ----------------------------------- - // C <- | u * 1 + t | u * 2 + t | u * 3 + t | - // ----------------------------------- - - for (q = 0; q < n; ++q) { - - C[Ci + q] = a[ai + 1] * S[Si + q] + a[ai]; - } - }; - - exports.oddkldtto3sum = oddkldtto3sum; - - return exports; - }; - if (typeof exports === "object") { - definition(exports); - } else if (typeof define === "function" && define.amd) { - define("@aureooms/js-algorithms", [], function () { - return definition({}); - }); - } else if (typeof window === "object" && typeof window.document === "object") { - definition(window["algorithms"] = {}); - } else console.error("unable to detect type of module to define for @aureooms/js-algorithms"); -})(); - -// empty or one element array case - -// base case : dj - di = d = 0 -// enumerate all red / blue pairs -// [i, p[ contains only blue points -// [p, j[ contains only red points -// p = index of first red point - -// for each blue point - -/** - * recursion fairy - * - * we compute m such that h is the median of - * the ith coordinate of all points - * - */ - -// empty or one element array case - -// for each blue point \ No newline at end of file diff --git a/js/dist/algorithms.js.map b/js/dist/algorithms.js.map deleted file mode 100644 index 4bc92dc..0000000 --- a/js/dist/algorithms.js.map +++ /dev/null @@ -1 +0,0 @@ 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v,d,y,b,x,_;for(x=t-e,k=o-a-1,_=1+k/2,y=u;f>y;++y)i[y]=n[a];for(d=1,v=1;_>d;++d,v*=x)for(y=u,b=0;f>y;++y,b=((b+1)/v|0)%x)i[y]+=n[a+d]*r[e+b];for(v=1;d<=k;++d,v*=x)for(y=s,b=0;l>y;++y,b=((b+1)/v|0)%x)c[y]+=n[a+d]*r[e+b]};r.evenkldtto2sum=b;var x=function(r,e,t,n,a,o,i,u,f,c,s,l,v,d,y){var b,x,_,m,p,h;for(p=t-e,k=o-a-1,h=2+(k-1)/2,x=2,b=1;h>x;++x,b*=p)for(_=u,m=0;f>_;++_,m=((m+1)/b|0)%p)i[_]+=n[a+x]*r[e+m];for(b=1;x<=k;++x,b*=p)for(_=s,m=0;l>_;++_,m=((m+1)/b|0)%p)c[_]+=n[a+x]*r[e+m];for(m=0;p>m;++m)v[d+m]=n[a+1]*r[e+m]+n[a]};return r.oddkldtto3sum=x,r};"object"==typeof exports?r(exports):"function"==typeof define&&define.amd?define("@aureooms/js-algorithms",[],function(){return r({})}):"object"==typeof window&&"object"==typeof window.document?r(window.algorithms={}):console.error("unable to detect type of module to define for @aureooms/js-algorithms")}(); -//# sourceMappingURL=js/dist/algorithms.js.map \ No newline at end of file diff --git a/js/index.js b/js/index.js deleted file mode 100644 index e6e928c..0000000 --- a/js/index.js +++ /dev/null @@ -1,15 +0,0 @@ -var pkg = require('aureooms-node-package'); - -var fs = require('fs'); -var data = fs.readFileSync(pkg.config, 'utf8'); -var opt = JSON.parse(data); - -opt = { - name : opt.name, - src : __dirname + '/src/', - exports : module.exports, - base : 0, - debug : opt.debug -}; - -pkg.include(opt); diff --git a/js/src/3sum/_3sum_n2.js b/js/src/3sum/_3sum_n2.js deleted file mode 100644 index 6de6ea7..0000000 --- a/js/src/3sum/_3sum_n2.js +++ /dev/null @@ -1,36 +0,0 @@ - - -/** - * Hypothesis : - * - A is sorted in increasing order - * - B is sorted in increasing order - * - |A| > 0 - * - |B| > 0 - */ - -var _3sum_n2 = function (A, ai, aj, B, bi, bj, C, ci, cj, fn) { - - var hi, lo, a, b, c, v; - - for (; ci < cj; ++ci) { - lo = ai; - hi = bj - 1; - - do { - - a = A[lo]; - b = B[hi]; - c = C[ci]; - v = a + b; - - if (-c === v) fn(a, b, c); - - if (-c < v) --hi; - else ++lo; - - } while (lo < aj && hi >= bi); - } - -}; - -exports._3sum_n2 = _3sum_n2; \ No newline at end of file diff --git a/js/src/4sum/sortxy_n3.js b/js/src/4sum/sortxy_n3.js deleted file mode 100644 index a4373ea..0000000 --- a/js/src/4sum/sortxy_n3.js +++ /dev/null @@ -1,61 +0,0 @@ - -/** - * X is sorted in increasing order - * Y is sorted in increasing order - * compare takes 4 arguments and returns <=> 0 - * output takes 4 arguments - * - */ -var sortxy_n3 = function ( compare , X , Y , Xi1 , Xj1 , Yi1 , Yj1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) { - - var a , b , c , d , s ; - - if ( Xi1 > Xj1 || Yi1 > Yj1 || Xi2 > Xj2 || Yi2 > Yj2 ) { - return ; - } - - // ----------------------------- - // | X | - // ----------------------------- - // Xi Xj - - // ----------------------------- - // | Y | - // ----------------------------- - // Yi Yj - - a = X[Xi1] ; - b = Y[Yj1] ; - c = X[Xj2] ; - d = Y[Yi2] ; - - s = compare( a , b , c , d ) ; - - if ( s === 0 ) { - - output( Xi1 , Yj1 , Xj2 , Yi2 ) ; - - sortxy_n3( compare , X , Y , Xi1 + 1 , Xj1 , Yi1 , Yj1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) ; - sortxy_n3( compare , X , Y , Xi1 , Xi1 , Yi1 , Yj1 - 1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) ; - sortxy_n3( compare , X , Y , Xi1 , Xi1 , Yj1 , Yj1 , Xi2 , Xj2 - 1 , Yi2 , Yj2 , output ) ; - - } - - else if ( s < 0 ) { - - sortxy_n3( compare , X , Y , Xi1 + 1 , Xj1 , Yi1 , Yj1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) ; - sortxy_n3( compare , X , Y , Xi1 , Xi1 , Yi1 , Yj1 , Xi2 , Xj2 - 1 , Yi2 , Yj2 , output ) ; - - } - - else { - - sortxy_n3( compare , X , Y , Xi1 , Xj1 , Yi1 , Yj1 - 1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) ; - sortxy_n3( compare , X , Y , Xi1 , Xj1 , Yj1 , Yj1 , Xi2 , Xj2 , Yi2 + 1 , Yj2 , output ) ; - - } - - -} ; - -exports.sortxy_n3 = sortxy_n3 ; diff --git a/js/src/4sum/sortxy_n4.js b/js/src/4sum/sortxy_n4.js deleted file mode 100644 index 6bd2972..0000000 --- a/js/src/4sum/sortxy_n4.js +++ /dev/null @@ -1,47 +0,0 @@ - -/** - * X is sorted in increasing order - * Y is sorted in increasing order - * compare takes 4 arguments and returns <=> 0 - * output takes 4 arguments - * - */ -var sortxy_n4 = function ( compare , X , Y , Xi1 , Xj1 , Yi1 , Yj1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) { - - var a , b , c , d , s ; - - if ( Xi1 > Xj1 || Yi1 > Yj1 || Xi2 > Xj2 || Yi2 > Yj2 ) { - return ; - } - - // ----------------------------- - // | X | - // ----------------------------- - // Xi Xj - - // ----------------------------- - // | Y | - // ----------------------------- - // Yi Yj - - a = X[Xi1] ; - b = Y[Yi1] ; - c = X[Xi2] ; - d = Y[Yi2] ; - - s = compare( a , b , c , d ) ; - - if ( s === 0 ) { - - output( Xi1 , Yi1 , Xi2 , Yi2 ) ; - - } - - sortxy_n4( compare , X , Y , Xi1 + 1 , Xj1 , Yi1 , Yj1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) ; - sortxy_n4( compare , X , Y , Xi1 , Xi1 , Yi1 + 1 , Yj1 , Xi2 , Xj2 , Yi2 , Yj2 , output ) ; - sortxy_n4( compare , X , Y , Xi1 , Xi1 , Yi1 , Yi1 , Xi2 + 1 , Xj2 , Yi2 , Yj2 , output ) ; - sortxy_n4( compare , X , Y , Xi1 , Xi1 , Yi1 , Yi1 , Xi2 , Xi2 , Yi2 + 1 , Yj2 , output ) ; - -} ; - -exports.sortxy_n4 = sortxy_n4 ; diff --git a/js/src/array/iter.js b/js/src/array/iter.js deleted file mode 100644 index c24c851..0000000 --- a/js/src/array/iter.js +++ /dev/null @@ -1,19 +0,0 @@ - - - -var fiter = function ( i, j, fn ) { - for ( ; i < j ; ++i ) { - fn( i ); - } -}; - -var biter = function ( i, j, fn ) { - while ( --j >= i ) { - fn( j ); - } -}; - - - -exports.fiter = fiter; -exports.biter = biter; diff --git a/js/src/bdp/bdpdc.js b/js/src/bdp/bdpdc.js deleted file mode 100644 index 91cc787..0000000 --- a/js/src/bdp/bdpdc.js +++ /dev/null @@ -1,351 +0,0 @@ - -/** - * Bichromatic dominating pairs using the divide and conquer chainsaw. - * - * see F. P. Preparata and M. I. Shamos, Computational Geometry, NY, 1985, p. 366. - * - * Here the algorithm handles non-strict ( >= ) dominance. - * - * select( f, a, i, j, k ) where - * f is a comparator - * a the array of points - * [i, j[ the range to search in the array - * k the index to select - * - * select(...) partitions the array in tree regions - * ----------------------------- - * | <= h | h | >= h | - * ----------------------------- - * i .... k k+1 .... j-1 - * - * __eq__( d, v ) template for a function eq( a ) - * returns true iff coordinate d of a equals v - * - * __ne__( d, v ) template for a function ne( y ) - * returns true iff coordinate d of a is not equal to v - * - * color( point ) - * = 0 if point is blue - * = 1 if point is red - * - * p = split( predicate, a, i, j ) - * rearranges an array so that all elements for which predicate is false - * are in interval [i, p[ and all other elements are in interval [p, j[ - * - * swap( a, ai, aj, b, bi ) - * swap elements from a in interval [ai, aj[ with elements from b in interval - * [bi, bi + aj - ai[ - * - */ - - -let __bdpdc__ = function ( select, __eq__, __ne__, color, split, swap ) { - - /** - * a is an array of points - * - * note that we only consider points starting - * at index i and ending at index j-1 in a - * - * points are arrays of coordinates - * - * d = dj - di is the number of coordinates of each point - * - * - * __f__ is a template for a function {coordinates^2} -> {<0, =0, >0} named f - * - * i.e. for coordinates a and b - * - * f( a, b ) < 0 means a < b; - * f( a, b ) = 0 means a = b; - * f( a, b ) > 0 means a > b. - * - * out is the output array - * - */ - - let bdpdc = function* ( __f__, a, i, j, di, dj ) { - - let k, h, x, y, p, q, m, n, _m, _n; - - // empty or one element array case - - if ( i >= j - 1 ) return ; - - // base case : dj - di = d = 0 - // enumerate all red / blue pairs - // [i, p[ contains only blue points - // [p, j[ contains only red points - // p = index of first red point - - if ( di === dj ) { - - // move all blue points left and all red points right - // (arbitrary choice) - - p = split( color, a, i, j ); - - // for each red point - - for ( x = p ; x < j ; ++x ) { - - // for each blue point - - for ( y = i ; y < p ; ++y ) { - - yield [ a[x], a[y] ] ; - - } - } - - } - - /** - * recursion fairy - * - * we compute m such that h is the median of - * the ith coordinate of all points - * - */ - - else { - - - // ------------------------------------------------------- - // | b&r scrambled | - // ------------------------------------------------------- - // i j - - k = ( i + j ) / 2 | 0; - - // ------------------------------------------------------- - // | b&r scrambled | - // ------------------------------------------------------- - // i k j - - // select median element - // O(n) - - select( __f__( di ), a, i, j, k ); - - h = a[k][di]; - - // ------------------------------------------------------- - // | b&r <= h | h | b&r >= h | - // ------------------------------------------------------- - // i k j - - - // we do 3 recursive calls - // - // first: for red and blue points with di < h in R^d - // we do not consider points with di = h because either - // - // 1. red = h, blue < h --> handled by last call - // 2. red < h, blue = h --> red cannot dominate blue - // 3. red = h, blue = h --> handled by last call - // (would be "red cannot dominate blue" for strict dominance - // in this 3rd case) - // - // second: for red and blue points with di > h in R^d - // we do not consider points with di = h for similar reasons as above - // - // last: for red points with di >= h and blue points with di <= h in R^{d-1} - // (would be > and < for strict dominance) - // - // note that we do not need to handle the case where red < h and blue >= h - // or red <= h and blue > h since red cannot dominate blue in those cases - - // first recursive call - // we only consider points that have di < h - // since all points that have di = h will be handled later - - // move median elements from [ i, k [ in the [ x, k [ interval, x >= i - // O(n) - - x = split( __eq__( di, h ), a, i, k ); - - // ------------------------------------------------------- - // | b&r < h | b&r = h | h | b&r > h | - // ------------------------------------------------------- - // i x k j - - yield* bdpdc( __f__, a, i, x, di, dj ); - - // move median elements from [ k + 1, j [ in the [ y, j [ interval, y <= j - // O(n) - - y = split( __ne__( di, h ), a, k + 1, j ); - - // ------------------------------------------------------- - // | b&r < h | b&r = h | h | b&r = h | b&r > h | - // ------------------------------------------------------- - // i x k y j - - yield* bdpdc( __f__, a, y, j, di, dj ); - - // since we do not touch median elements in the first two - // recursive calls they are still at the correct place - - // Now we want to - // - move red points such that di < h to the right - // - move red points such that di >= h to the left - // - // /!\ Note that we also might think that we should - // - move blue points such that di > h to the right - // - move blue points such that di <= h to the left - // but after the selection algorithm this is already the case - - - // ------------------------------------------------------- - // | b&r < h | b&r = h | h | b&r = h | b&r > h | - // ------------------------------------------------------- - // i x k y j - - p = split( color, a, i, x ); - - // ------------------------------------------------------- - // | b < h | r < h | b&r = h | h | b&r = h | b&r > h | - // ------------------------------------------------------- - // i p x k y j - - q = split( color, a, y, j ); - - // ------------------------------------------------------- - // | b < h | r < h | b&r = h | h | b&r = h | b > h | r > h | - // ------------------------------------------------------- - // i p x k y q j - - // we now want to swap r < h elements with r > h elements - // we have 3 cases - // 1. x - p = j - q - // 2. x - p < j - q - // 3. x - p > j - q - - m = x - p; - n = j - q; - - - // 1. x - p = j - q - - if ( m === n ) { - swap( a, q, j, a, p ); - - // ------------------------------------------------------- - // | b < h | r > h | b&r = h | h | b&r = h | b > h | r < h | - // ------------------------------------------------------- - // i p x k y q j - - j = y; - - // ------------------------------------------------------- - // | b < h | r > h | b&r = h | h | b&r = h | b > h | r < h | - // ------------------------------------------------------- - // i p x k j ... - - } - - - // 2. x - p < j - q - - else if ( m < n ) { - - swap( a, p, x, a, q ); - - // --------------------------------------------------------------- - // | b < h | r > h | b&r = h | h | b&r = h | b > h | r < h | r > h | - // --------------------------------------------------------------- - // i p x k y q q+m j - - // we now want to swap b > h and r < h elements with r > h elements - // [y,q[ [q,q+m[ [q+m,j[ - // we have 2 cases - // 1. (q + m) - y >= j - (q + m) [OR >] - // 2. (q + m) - y < j - (q + m) [OR <=] - - _m = (q + m) - y; - _n = j - (q + m); - - // 1. (q + m) - y >= j - (q + m) - if ( _m >= _n ) { - swap( a, q + m, j, a, y ); - } - // 2. (q + m) - y < j - (q + m) - else { - swap( a, j - _m, j, a, y ); - } - - // --------------------------------------------------------------- - // | b < h | r > h | b&r = h | h | b&r = h | r > h | b>h & r h | b&r = h | h | b&r = h | r > h | b>h & r j - q - - else { - - swap( a, q, j, a, p ); - - // --------------------------------------------------------------- - // | b < h | r > h | r < h | b&r = h | h | b&r = h | b > h | r < h | - // --------------------------------------------------------------- - // i p p+n x k y q j - - // we now want to swap r < h with b&r = h elements - // we have 2 cases - // 1. x - (p + n) >= y - x - // 2. x - (p + n) < y - x - - _m = x - (p + n); - _n = y - x; - - // 1. x - (p + n) >= y - x - if ( _m >= _n ) { - swap( a, x, y, a, p + n ); - } - // 2. x - (p + n) < y - x - else { - swap( a, y - _m, y, a, p + n ); - } - - // ----------------------------------------------------------- - // | b < h | r > h | b&r = h | h | b&r = h | b>h & r h | b&r = h | h | b&r = h | b>h & r= h points - // in this new interval, all r points dominate b points - // for the ith coordinate - // we can thus ask the recursion fairy to take care of the other - // dj - di - 1 dimensions left - - yield* bdpdc( __f__, a, i, j, di + 1, dj ); - - } - - }; - - return bdpdc; - -}; - -exports.__bdpdc__ = __bdpdc__; diff --git a/js/src/bdp/bdpdn2.js b/js/src/bdp/bdpdn2.js deleted file mode 100644 index d825529..0000000 --- a/js/src/bdp/bdpdn2.js +++ /dev/null @@ -1,87 +0,0 @@ - -/** - * Bichromatic dominating pairs using a naïve O(d * n^2) algorithm. - * - * Here the algorithm handles non-strict ( >= ) dominance. - * - * color( point ) - * = 0 if point is blue - * = 1 if point is red - * - * p = split( predicate, a, i, j ) - * rearranges an array so that all elements for which predicate is false - * are in interval [i, p[ and all other elements are in interval [p, j[ - * - */ - - -let __bdpdn2__ = function ( color, split ) { - - /** - * a is an array of points - * - * note that we only consider points starting - * at index i and ending at index j-1 in a - * - * points are arrays of coordinates - * - * d = dj - di is the number of coordinates of each point - * - * - * __f__ is a template for a function {coordinates^2} -> {<0, =0, >0} named f - * - * i.e. for coordinates a and b - * - * f( a, b ) < 0 means a < b; - * f( a, b ) = 0 means a = b; - * f( a, b ) > 0 means a > b. - * - */ - - let bdpdn2 = function* ( __f__, a, i, j, di, dj ) { - - let x, y, p, d, f; - - // empty or one element array case - - if ( i >= j - 1 ) return ; - - // move all blue points left and all red points right - // (arbitrary choice) - - // [i, p[ contains only blue points - // [p, j[ contains only red points - // p = index of first red point - - p = split( color, a, i, j ); - - // for each red point - - red : for ( x = p ; x < j ; ++x ) { - - // for each blue point - - blue : for ( y = i ; y < p ; ++y ) { - - for ( d = di ; d < dj ; ++d ) { - - f = __f__( d ); - - if ( f( a[x], a[y] ) < 0 ) { - continue blue; - } - - } - - yield [ a[x], a[y] ] ; - - } - } - - }; - - return bdpdn2; - -}; - -exports.__bdpdn2__ = __bdpdn2__; diff --git a/js/src/birthdays/samebirthday.js b/js/src/birthdays/samebirthday.js deleted file mode 100644 index 4fade14..0000000 --- a/js/src/birthdays/samebirthday.js +++ /dev/null @@ -1,34 +0,0 @@ - - -/** - * - * Computes the probability ( [0, 1] ) for at least 1 of k people - * out of n to have his birthday the same day as someone else. - * - * hypothesis : k <= n and k <= days - */ - -var samebirthday = function ( k, n, days ) { - - var i, p; - - p = 1; - - for ( i = 1 ; i < k ; ++i ) { - - p = p * ( days - i ) / days; - - } - - for ( ; i < n ; ++i ) { - - p = p * ( days - k ) / days; - - } - - - return 1 - p; - -}; - -exports.samebirthday = samebirthday; diff --git a/js/src/matroids/max_independent_set.js b/js/src/matroids/max_independent_set.js deleted file mode 100644 index 699572b..0000000 --- a/js/src/matroids/max_independent_set.js +++ /dev/null @@ -1,25 +0,0 @@ - -/** - * Greedy algorithm for computing the maximum independent set. - * For max-weight independent set give the input in decreasing order wrt weights. - */ - -const max_independent_set = function ( independent , S ) { - - const set = [ ] ; - - loop : for ( const u of S ) { - - for ( const v of set ) { - if ( !independent( u , v ) ) continue loop ; - } - - set.push( u ) ; - - } - - return set ; - -} ; - -exports.max_independent_set = max_independent_set ; diff --git a/js/src/reductions/chan.js b/js/src/reductions/chan.js deleted file mode 100644 index 7bf26d5..0000000 --- a/js/src/reductions/chan.js +++ /dev/null @@ -1,49 +0,0 @@ - -/** - * Timoty Chan (1999) - * Geometric Applications of a Randomized Optimization Technique - * - * Translates any decision algorithm for a question of the type "is the optimal - * value for this problem less/greater than `c`?" to a randomized optimisation - * algortihm that finds the optimal value of `c*` whose expected time complexity - * is within a constant factor of the complexity of the decision algorithm. - * For this to work we must be capable of splitting a problem into a constant - * number of smaller (by a constant factor) subproblems so that the optimal - * value of the original problem is the min/max of the optimal values for the - * subproblems. For example, given a decision algorithm `decide( G , c )` - * that decides whether graph G has diameter greater than c, we can split the - * problem into k^2 subproblems of size (2n/k), that is, the diameter of G is - * the maximum over the diameters of all subgraphs that are the union of 2 - * disjoint subgraphs taken from a partition of G into k disjoint subgraphs of - * size n/k. Finding the optimal k for a given problem requires to solve a - * reccurence expressing the time-complexity of the following meta-algorithm. - * Read Timoty Chan's paper for more information. - */ - -const chan = function ( split , shuffle , decide , bruteforce , issmall ) { - - const solve = function ( instance ) { - - if ( issmall( instance ) ) return bruteforce( instance ) ; - - const [ first , ...rest ] = shuffle( split( instance ) ) ; - - let [ current , optimum ] = solve( first ) ; - - for ( const candidate of rest ) { - - if ( decide( candidate , optimum ) ) { - [ current , optimum ] = solve( candidate ) ; - } - - } - - return [ current , optimum ] ; - - } ; - - return solve ; - -} ; - -exports.chan = chan ; diff --git a/js/src/reductions/kldt/evenkldtto2sum.js b/js/src/reductions/kldt/evenkldtto2sum.js deleted file mode 100644 index 24a00d7..0000000 --- a/js/src/reductions/kldt/evenkldtto2sum.js +++ /dev/null @@ -1,79 +0,0 @@ - - -/** - * Transforms an instance of the one-set version of kLDT with k >= 4 even into - * a two-set version of 2SUM. - * - * @param {set} S is the input set for the kLDT problem - * @param {coefficients} a is the array of coefficients - * @param {set} A is one of the input set for 2SUM - * @param {set} B is one of the input set for 2SUM - * - * notes: - * - n = Sj - Si - * - k = aj - ai - 1 - * - a_0 = a[ai] - * - A and B must be of size n^(k/2) each - * - B must be initialized to 0 ... 0 - * - */ - -var evenkldtto2sum = function ( S , Si , Sj , a , ai , aj , A , Ai , Aj , B , Bi , Bj ) { - - var i , j , p , q , n , halfk ; - - n = Sj - Si ; - - k = aj - ai - 1 ; - - halfk = 1 + k / 2 ; - - // We fill A and B for example with S = [ 1 , 2 , 3 ] and a = [ t , v , w , x , y ] - - // ----------------------------------------------------------------------- - // A <- | t | t | t | t | t | t | t | t | t | - // ----------------------------------------------------------------------- - - for ( p = Ai ; p < Aj ; ++p ) { - - A[p] = a[ai] ; - - } - - // ----------------------------------------------------------------------- - // A += | v * 1 | v * 2 | v * 3 | v * 1 | v * 2 | v * 3 | v * 1 | v * 2 | v * 3 | - // ----------------------------------------------------------------------- - // ----------------------------------------------------------------------- - // A += | w * 1 | w * 1 | w * 1 | w * 2 | w * 2 | w * 2 | w * 3 | w * 3 | w * 3 | - // ----------------------------------------------------------------------- - - for ( j = 1 , i = 1 ; j < halfk ; ++j , i *= n ) { - - for ( p = Ai , q = 0 ; p < Aj ; ++p , q = ( ( q + 1 ) / i | 0 ) % n ) { - - A[p] += a[ai + j] * S[Si + q] ; - - } - - } - - // ----------------------------------------------------------------------- - // B += | x * 1 | x * 2 | x * 3 | x * 1 | x * 2 | x * 3 | x * 1 | x * 2 | x * 3 | - // ----------------------------------------------------------------------- - // ----------------------------------------------------------------------- - // B += | y * 1 | y * 1 | y * 1 | y * 2 | y * 2 | y * 2 | y * 3 | y * 3 | y * 3 | - // ----------------------------------------------------------------------- - - for ( i = 1 ; j <= k ; ++j , i *= n ) { - - for ( p = Bi , q = 0 ; p < Bj ; ++p , q = ( ( q + 1 ) / i | 0 ) % n ) { - - B[p] += a[ai + j] * S[Si + q] ; - - } - - } - -} ; - -exports.evenkldtto2sum = evenkldtto2sum; diff --git a/js/src/reductions/kldt/oddkldtto3sum.js b/js/src/reductions/kldt/oddkldtto3sum.js deleted file mode 100644 index 3b1b2cb..0000000 --- a/js/src/reductions/kldt/oddkldtto3sum.js +++ /dev/null @@ -1,83 +0,0 @@ - - -/** - * Transforms an instance of the one-set version of kLDT with k >= 3 odd into - * a three-set version of 3SUM. - * - * @param {set} S is the input set for the kLDT problem - * @param {coefficients} a is the array of coefficients - * @param {set} A is one of the input set for 3SUM - * @param {set} B is one of the input set for 3SUM - * @param {set} C is one of the input set for 3SUM - * - * notes: - * - n = Sj - Si - * - k = aj - ai - 1 - * - a_0 = a[ai] - * - A and B must be of size n^((k-1)/2) each - * - A and B must be initialized to 0 ... 0 - * - C must be of size n - * - */ - -var oddkldtto3sum = function ( S , Si , Sj , a , ai , aj , A , Ai , Aj , B , Bi , Bj , C , Ci , Cj ) { - - var i , j , p , q , n , halfk ; - - n = Sj - Si ; - - k = aj - ai - 1 ; - - halfk = 2 + ( k - 1 ) / 2 ; - - // We fill A and B for example with S = [ 1 , 2 , 3 ] and a = [ t , u , v , w , x , y ] - - // ----------------------------------------------------------------------- - // A += | v * 1 | v * 2 | v * 3 | v * 1 | v * 2 | v * 3 | v * 1 | v * 2 | v * 3 | - // ----------------------------------------------------------------------- - // ----------------------------------------------------------------------- - // A += | w * 1 | w * 1 | w * 1 | w * 2 | w * 2 | w * 2 | w * 3 | w * 3 | w * 3 | - // ----------------------------------------------------------------------- - - for ( j = 2 , i = 1 ; j < halfk ; ++j , i *= n ) { - - for ( p = Ai , q = 0 ; p < Aj ; ++p , q = ( ( q + 1 ) / i | 0 ) % n ) { - - A[p] += a[ai + j] * S[Si + q] ; - - } - - } - - // ----------------------------------------------------------------------- - // B += | x * 1 | x * 2 | x * 3 | x * 1 | x * 2 | x * 3 | x * 1 | x * 2 | x * 3 | - // ----------------------------------------------------------------------- - // ----------------------------------------------------------------------- - // B += | y * 1 | y * 1 | y * 1 | y * 2 | y * 2 | y * 2 | y * 3 | y * 3 | y * 3 | - // ----------------------------------------------------------------------- - - for ( i = 1 ; j <= k ; ++j , i *= n ) { - - for ( p = Bi , q = 0 ; p < Bj ; ++p , q = ( ( q + 1 ) / i | 0 ) % n ) { - - B[p] += a[ai + j] * S[Si + q] ; - - } - - } - - // We fill C - - // ----------------------------------- - // C <- | u * 1 + t | u * 2 + t | u * 3 + t | - // ----------------------------------- - - for ( q = 0 ; q < n ; ++q ) { - - C[Ci + q] = a[ai + 1] * S[Si + q] + a[ai] ; - - } - -} ; - -exports.oddkldtto3sum = oddkldtto3sum; diff --git a/kldt/evenkldtto2sum.html b/kldt/evenkldtto2sum.html new file mode 100644 index 0000000..6a1cec8 --- /dev/null +++ b/kldt/evenkldtto2sum.html @@ -0,0 +1,52 @@ +kldt/evenkldtto2sum

js/src/kldt/evenkldtto2sum.js

Transforms an instance of the one-set version of kLDT with k >= 4 even into +a two-set version of 2SUM.

Parameters:

S must be a set.
(is the input set for the kLDT problem)
+
a must be a coefficients.
(is the array of coefficients)
+
A must be a set.
(is one of the input set for 2SUM)
+
B must be a set.
(is one of the input set for 2SUM notes: - n = Sj - Si - k = aj - ai - 1 - a_0 = a[ai] - A and B must be of size n^(k/2) each - B must be initialized to 0 ... 0)
+

var evenkldtto2sum = function ( S , Si , Sj , a , ai , aj , A , Ai , Aj , B , Bi , Bj ) { + + var i , j , p , q , n , halfk ; + + n = Sj - Si ; + + k = aj - ai - 1 ; + + halfk = 1 + k / 2 ;

We fill A and B for example with S = [ 1 , 2 , 3 ] and a = [ t , v , w , x , y ]

  -----------------------------------------------------------------------

A <- | t | t | t | t | t | t | t | t | t |

for ( p = Ai ; p < Aj ; ++p ) { + + A[p] = a[ai] ; + + }

  -----------------------------------------------------------------------

A += | v 1 | v 2 | v 3 | v 1 | v 2 | v 3 | v 1 | v 2 | v * 3 |

  -----------------------------------------------------------------------

A += | w 1 | w 1 | w 1 | w 2 | w 2 | w 2 | w 3 | w 3 | w * 3 |

for ( j = 1 , i = 1 ; j < halfk ; ++j , i *= n ) { + + for ( p = Ai , q = 0 ; p < Aj ; ++p , q = ( ( q + 1 ) / i | 0 ) % n ) { + + A[p] += a[ai + j] * S[Si + q] ; + + } + + }

  -----------------------------------------------------------------------

B += | x 1 | x 2 | x 3 | x 1 | x 2 | x 3 | x 1 | x 2 | x * 3 |

  -----------------------------------------------------------------------

B += | y 1 | y 1 | y 1 | y 2 | y 2 | y 2 | y 3 | y 3 | y * 3 |

for ( i = 1 ; j <= k ; ++j , i *= n ) { + + for ( p = Bi , q = 0 ; p < Bj ; ++p , q = ( ( q + 1 ) / i | 0 ) % n ) { + + B[p] += a[ai + j] * S[Si + q] ; + + } + + } + +} ; + +exports.evenkldtto2sum = evenkldtto2sum;

\ No newline at end of file diff --git a/kldt/oddkldtto3sum.html b/kldt/oddkldtto3sum.html new file mode 100644 index 0000000..4649240 --- /dev/null +++ b/kldt/oddkldtto3sum.html @@ -0,0 +1,54 @@ +kldt/oddkldtto3sum

js/src/kldt/oddkldtto3sum.js

Transforms an instance of the one-set version of kLDT with k >= 3 odd into +a three-set version of 3SUM.

Parameters:

S must be a set.
(is the input set for the kLDT problem)
+
a must be a coefficients.
(is the array of coefficients)
+
A must be a set.
(is one of the input set for 3SUM)
+
B must be a set.
(is one of the input set for 3SUM)
+
C must be a set.
(is one of the input set for 3SUM notes: - n = Sj - Si - k = aj - ai - 1 - a_0 = a[ai] - A and B must be of size n^((k-1)/2) each - A and B must be initialized to 0 ... 0 - C must be of size n)
+

var oddkldtto3sum = function ( S , Si , Sj , a , ai , aj , A , Ai , Aj , B , Bi , Bj , C , Ci , Cj ) { + + var i , j , p , q , n , halfk ; + + n = Sj - Si ; + + k = aj - ai - 1 ; + + halfk = 2 + ( k - 1 ) / 2 ;

We fill A and B for example with S = [ 1 , 2 , 3 ] and a = [ t , u , v , w , x , y ]

  -----------------------------------------------------------------------

A += | v 1 | v 2 | v 3 | v 1 | v 2 | v 3 | v 1 | v 2 | v * 3 |

  -----------------------------------------------------------------------

A += | w 1 | w 1 | w 1 | w 2 | w 2 | w 2 | w 3 | w 3 | w * 3 |

for ( j = 2 , i = 1 ; j < halfk ; ++j , i *= n ) { + + for ( p = Ai , q = 0 ; p < Aj ; ++p , q = ( ( q + 1 ) / i | 0 ) % n ) { + + A[p] += a[ai + j] * S[Si + q] ; + + } + + }

  -----------------------------------------------------------------------

B += | x 1 | x 2 | x 3 | x 1 | x 2 | x 3 | x 1 | x 2 | x * 3 |

  -----------------------------------------------------------------------

B += | y 1 | y 1 | y 1 | y 2 | y 2 | y 2 | y 3 | y 3 | y * 3 |

for ( i = 1 ; j <= k ; ++j , i *= n ) { + + for ( p = Bi , q = 0 ; p < Bj ; ++p , q = ( ( q + 1 ) / i | 0 ) % n ) { + + B[p] += a[ai + j] * S[Si + q] ; + + } + + }

We fill C

  -----------------------------------

C <- | u 1 + t | u 2 + t | u * 3 + t |

for ( q = 0 ; q < n ; ++q ) { + + C[Ci + q] = a[ai + 1] * S[Si + q] + a[ai] ; + + } + +} ; + +exports.oddkldtto3sum = oddkldtto3sum;

\ No newline at end of file diff --git a/minima/clarkson.html b/minima/clarkson.html new file mode 100644 index 0000000..19c68fc --- /dev/null +++ b/minima/clarkson.html @@ -0,0 +1,58 @@ +minima/clarkson

js/src/minima/clarkson.js

Output sensitive inplace algorithm to find the minima set of a set S of +elements according to some partial order.

Uses at most 3nA comparisons where A is the cardinality of the minima set.

For (1), at most nA comparisons are used since we compare each element of S +with each elements of the minima set which is of cardinality at most A +during the execution of the algorithm.

For (2), for each executed loop we +obtain a new minimum and increase the size of the constructed minima set by +1, hence there are at most A loops execution, each of which loops over at +most n elements. (2) uses thus at most nA comparisons.

The running time is dominated by the comparison time and thus the complexity +of this algorihtm is O(nA).

Description and context in

More Output-Sensitive Geometric Algorithms. +-------------------- Kenneth L. Clarkson -

var clarkson = function ( prec , a , i , j ) {

This algorithms reorganizes the input array a as follows

elements that are minima are put at the front of a
other elements are put at the back of a

During the algorithm, a looks like this

| minima set | candidate elements | discarded elements |

i min dis j

var min , dis , k , inc , tmp ; + + min = i ; + dis = j - 1 ;

While there are candidate elements left.

while ( min <= dis ) {

(1) Determine if the right-most candidate should be discarded because it +is dominated by one of the minima elements of the minima set in +construction.

for ( k = i ; k < min && !prec( a[k] , a[dis] ) ; ++k ) ;

If so, discard it.

if ( k < min ) --dis ;

(2) Otherwise, scan the candidates for a minimum. If at this point the +candidate set is not empty, at least one of its elements must be a +minimum. We scan the candidate list to find such a minimum.

else {

Store the current minimum as the left-most candidate.

tmp = a[dis] ; + a[dis] = a[min] ; + a[min] = tmp ;

For each other candidate, right-to-left.

for ( inc = min + 1 ; inc <= dis ; ) {

If the current minimum precedes the right-most candidate, +discard the right-most candidate.

if ( prec( a[min] , a[dis] ) ) --dis ;

Else, if the right-most candidate precedes the current +minimum, we can discard the current minimum and the +right-most candidate becomes the current minimum.

else if ( prec( a[dis] , a[min] ) ) { + tmp = a[dis] ; + a[dis] = a[min] ; + a[min] = tmp ; + --dis ; + }

Otherwise, we save the candidate for the next round.

else { + tmp = a[dis] ; + a[dis] = a[inc] ; + a[inc] = tmp ; + ++inc ; + } + + }

The above loop selects a new minimum from the set of candidates +and places it at position min. We now increase the min +counter to move this minimum from the candidate list to the +minima set.

++min ; + + } + + }

The algorithm returns the outer right bound of the minima set a[i:min].

return min ; + +} ; + +exports.clarkson = clarkson ;

\ No newline at end of file diff --git a/package.json b/package.json deleted file mode 100644 index 8cba910..0000000 --- a/package.json +++ /dev/null @@ -1,47 +0,0 @@ -{ - "name": "@aureooms/js-algorithms", - "description": "Playground for algorithms in JavaScript", - "homepage": "https://make-github-pseudonymous-again.github.io/js-algorithms", - "main": "js/dist/algorithms.js", - "version": "3.0.7", - "repository": { - "url": "https://github.com/make-github-pseudonymous-again/js-algorithms.git", - "type": "git" - }, - "keywords": [ - "adt", - "algorithm", - "complexity", - "ender", - "javascript", - "js", - "template" - ], - "scripts": { - "build": "./node_modules/.bin/aureooms-node-package-build", - "test": "./node_modules/.bin/aureooms-node-package-test", - "doc": "./node_modules/.bin/groc" - }, - "author": "aureooms", - "devDependencies": { - "@aureooms/js-array": "^4.0.0", - "@aureooms/js-compare": "^1.4.3", - "@aureooms/js-functools": "^2.0.3", - "@aureooms/js-itertools": "^3.0.0", - "@aureooms/js-operator": "^1.0.2", - "@aureooms/js-partition": "^8.0.0", - "@aureooms/js-random": "^2.0.0", - "@aureooms/js-selection": "^9.0.0", - "@aureooms/js-sort": "^7.0.0", - "@aureooms/js-splitting": "^4.0.2", - "aureooms-node-package": "^6.0.1" - }, - "bugs": { - "url": "https://github.com/make-github-pseudonymous-again/js-algorithms/issues" - }, - "dependencies": {}, - "license": "AGPL-3.0", - "spm": { - "main": "js/dist/algorithms.js" - } -} diff --git a/pkg.json b/pkg.json deleted file mode 100644 index 39a1fe2..0000000 --- a/pkg.json +++ /dev/null @@ -1,18 +0,0 @@ -{ - "name": "algorithms", - "code": { - "main": [ - "js", - "dist", - "algorithms.js" - ], - "test": [ - "test", - "js" - ] - }, - "src": "js/src/", - "debug": false, - "out": "js/dist/", - "babel": true -} diff --git a/test/js/index.js b/test/js/index.js deleted file mode 100644 index 869a49d..0000000 --- a/test/js/index.js +++ /dev/null @@ -1,10 +0,0 @@ -var pkg = require('aureooms-node-package'); - - -var opt = { - src : __dirname + '/src/', - exports : module.exports, - base : 0 -}; - -pkg.include(opt); diff --git a/test/js/src/3sum.js b/test/js/src/3sum.js deleted file mode 100644 index a36f2db..0000000 --- a/test/js/src/3sum.js +++ /dev/null @@ -1,75 +0,0 @@ - -var util = require( "util" ); -var array = require( "@aureooms/js-array" ); - -test("3sum", function(){ - - console.log("3sum"); - - var iota = array.iota; - - var n = 100; - - var A = new Array(n); - var B = new Array(n); - var C = new Array(n); - - iota(A, 0, n, -n/2); - iota(B, 0, n, -n/2); - iota(C, 0, n, -n/2); - - var contains = function(a, x) { - var i, y, k; - it : for (i = 0; i < a.length; ++i) { - y = a[i]; - for (k = 0; k < 3; ++k) { - if (x[k] !== y[k]) continue it; - } - return true; - } - return false; - }; - - var _3sum_n3 = function(A, ai, aj, B, bi, bj, C, ci, cj, fn) { - var a, b, c, i, j, k; - for (i = ai; i < aj; ++i) { - a = A[i]; - for (j = bi; j < bj; ++j) { - b = B[j]; - for (k = ci; k < cj; ++k) { - c = C[k]; - if (a + b + c === 0) { - fn(a, b, c); - } - } - } - } - }; - - _3sum_n2 = algorithms._3sum_n2; - - var w = []; - var u = []; - - var __fn__ = function (w) { - return function(a, b, c) { - w.push([a, b, c]); - }; - }; - - var fnw = __fn__(w); - var fnu = __fn__(u); - - - _3sum_n2(A, 0, n, B, 0, n, C, 0, n, fnw); - _3sum_n3(A, 0, n, B, 0, n, C, 0, n, fnu); - - - deepEqual(w.length, u.length, "length check"); - - var k; - for (k = 0; k < w.length; ++k) { - deepEqual(contains(u, w[k]), true, w[k] + " in list"); - } - -}); diff --git a/test/js/src/bdp.js b/test/js/src/bdp.js deleted file mode 100644 index 85092bf..0000000 --- a/test/js/src/bdp.js +++ /dev/null @@ -1,216 +0,0 @@ - - -var n; - -var itertools = require( "@aureooms/js-itertools" ); -var functools = require( "@aureooms/js-functools" ); -var splitting = require( "@aureooms/js-splitting" ); -var partition = require( "@aureooms/js-partition" ) ; -var selection = require( "@aureooms/js-selection" ) ; -var operator = require( "@aureooms/js-operator" ); -var compare = require( "@aureooms/js-compare" ); -var random = require( "@aureooms/js-random" ); -var array = require( "@aureooms/js-array" ); - -var one = function ( bdp, __f__, a, i, j, di, dj, expected ) { - - ++n; - - random.shuffle( a, i, j ); - - var out = itertools.list( bdp( __f__, a, i, j, di, dj, [] ) ); - - var outputordering = compare.lexicographical( compare.lexicographical( compare.increasing ) ); - - array.sort( outputordering, out ); - array.sort( outputordering, expected ); - - deepEqual( out, expected, n ); - -}; - -var all = function ( name, algo ) { - - n = 0; - - test( name, function ( ) { - - var f, __f__; - - f = function ( i, a, b ) { - return a[i] - b[i]; - }; - - __f__ = functools.curry( f, 3 ); - - one( algo, __f__, [], 0, 0, 1, 1, [] ); - - one( algo, __f__, [ [0] ], 0, 1, 1, 1, [] ); - - one( algo, __f__, [ [1] ], 0, 1, 1, 1, [] ); - - one( algo, __f__, [ [0], [0], [0], [0] ], 0, 4, 1, 1, [] ); - - one( algo, __f__, [ [1], [1], [1], [1] ], 0, 4, 1, 1, [] ); - - one( - algo, - __f__, - [ [0], [0], [1], [1] ], - 0, 4, - 1, 1, - [ - [ [1], [0] ], - [ [1], [0] ], - [ [1], [0] ], - [ [1], [0] ] - ] - ); - - one( - algo, - __f__, - [ [0, 0.5], [0, 1], [1, 1], [1, 0.5] ], - 0, 4, - 1, 2, - [ - [ [1, 1], [0, 1] ], - [ [1, 1], [0, 0.5] ], - [ [1, 0.5], [0, 0.5] ] - ] - ); - - one( - algo, - __f__, - [ [0, 0.5, 1], [0, 1, 2], [1, 1, 1], [1, 0.5, 2] ], - 0, 4, - 1, 3, - [ - [ [1, 1, 1], [0, 0.5, 1] ], - [ [1, 0.5, 2], [0, 0.5, 1] ] - ] - ); - - one( - algo, - __f__, - [ [0, 0.5, 1], [0, 1, 2], [1, 1, 1], [1, 0.5, 2], [1, 1, 1], [1, 0.5, 2] ], - 0, 6, - 1, 3, - [ - [ [1, 1, 1], [0, 0.5, 1] ], - [ [1, 0.5, 2], [0, 0.5, 1] ], - [ [1, 1, 1], [0, 0.5, 1] ], - [ [1, 0.5, 2], [0, 0.5, 1] ] - ] - ); - - - one( - algo, - __f__, - [ [0, 0.5, 1], [0, 1, 2], [1, 1, 1], [1, 0.5, 2], [1, 1, 3], [1, 1, 2] ], - 0, 6, - 1, 3, - [ - [ [1, 1, 1], [0, 0.5, 1] ], - [ [1, 0.5, 2], [0, 0.5, 1] ], - [ [1, 1, 3], [0, 0.5, 1] ], - [ [1, 1, 2], [0, 0.5, 1] ], - [ [1, 1, 3], [0, 1, 2] ], - [ [1, 1, 2], [0, 1, 2] ] - ] - ); - - one( - algo, - __f__, - [ [0, 0.5, 1], [0, 1, 2], [1, 1, 1], [1, 0.5, 2], [1, 1, 3], [0, 105, 1], [0, 1, 20], [1, 1, 2] ], - 0, 8, - 1, 3, - [ - [ [1, 1, 1], [0, 0.5, 1] ], - [ [1, 0.5, 2], [0, 0.5, 1] ], - [ [1, 1, 3], [0, 0.5, 1] ], - [ [1, 1, 2], [0, 0.5, 1] ], - [ [1, 1, 3], [0, 1, 2] ], - [ [1, 1, 2], [0, 1, 2] ] - ] - ); - - one( - algo, - __f__, - [ [0, 0.5, 1], [0, 1, 2], [0, 105, 1], [0, 1, 20], [1, 105, 20], [1, 105, 20], [1, 106, 20] ], - 0, 7, - 1, 3, - [ - [ [1, 105, 20], [0, 0.5, 1] ], - [ [1, 105, 20], [0, 1, 2] ], - [ [1, 105, 20], [0, 105, 1] ], - [ [1, 105, 20], [0, 1, 20] ], - [ [1, 105, 20], [0, 0.5, 1] ], - [ [1, 105, 20], [0, 1, 2] ], - [ [1, 105, 20], [0, 105, 1] ], - [ [1, 105, 20], [0, 1, 20] ], - [ [1, 106, 20], [0, 0.5, 1] ], - [ [1, 106, 20], [0, 1, 2] ], - [ [1, 106, 20], [0, 105, 1] ], - [ [1, 106, 20], [0, 1, 20] ] - ] - ); - - one( - algo, - __f__, - [ [0, 0.5, 1], [0, 1, 2], [0, 105, 1], [0, 1, 20], [1, 105, 20], [1, 105, 20], [1, 106, 20], [0, 107, 1], [0, 107, 1] ], - 0, 9, - 1, 3, - [ - [ [1, 105, 20], [0, 0.5, 1] ], - [ [1, 105, 20], [0, 1, 2] ], - [ [1, 105, 20], [0, 105, 1] ], - [ [1, 105, 20], [0, 1, 20] ], - [ [1, 105, 20], [0, 0.5, 1] ], - [ [1, 105, 20], [0, 1, 2] ], - [ [1, 105, 20], [0, 105, 1] ], - [ [1, 105, 20], [0, 1, 20] ], - [ [1, 106, 20], [0, 0.5, 1] ], - [ [1, 106, 20], [0, 1, 2] ], - [ [1, 106, 20], [0, 105, 1] ], - [ [1, 106, 20], [0, 1, 20] ] - ] - ); - - - }); - -}; - -[ - [ - "algorithms.__bdpdc__", - algorithms.__bdpdc__( - selection.single( partition.hoare ) , // select, - functools.curry( function ( i, v, a ) { // __eq__, - return + ( v === a[i] ); - }, 3 ), - functools.curry( function ( i, v, a ) { // __ne__, - return + ( v !== a[i] ); - }, 3 ), - operator.itemgetter( 0 ), // color, - splitting.hoare, // split, - array.swapranges // swap - ) - ], - - [ - "algorithms.__bdpdn2__", - algorithms.__bdpdn2__( - operator.itemgetter( 0 ), // color, - splitting.hoare // split - ) - ] - -].forEach( functools.partial( functools.star, [all] ) ); diff --git a/test/js/src/birthdays.js b/test/js/src/birthdays.js deleted file mode 100644 index 8e81841..0000000 --- a/test/js/src/birthdays.js +++ /dev/null @@ -1,25 +0,0 @@ - -var compare = algorithms.__absepsilon__( 1e-4 ); - -var run = function ( k, n, days, expected ) { - - var computed; - - computed = algorithms.samebirthday( k, n, days ); - - equal( compare( computed, expected ), 0, k + ", " + n + ", " + days + " : " + computed ); - -}; - - -test( "birthdays", function () { - - run( 1, 3, 365, 1 - ( 364 / 365 * 364 / 365 ) ); - run( 2, 3, 365, 1 - ( 364 / 365 * 363 / 365 ) ); - run( 10, 10, 365, 0.1169 ); - run( 23, 23, 365, 0.5073 ); - run( 50, 50, 365, 0.9704 ); - run( 100, 100, 365, 1 - 3.072e-7 ); - run( 365, 365, 365, 0.9999 ); - -} ); diff --git a/test/js/src/iter.js b/test/js/src/iter.js deleted file mode 100644 index 86113bd..0000000 --- a/test/js/src/iter.js +++ /dev/null @@ -1,24 +0,0 @@ - -var array = require( "@aureooms/js-array" ); - -test( "iter", function () { - - var f, b, fe, be, n; - - f = []; - b = []; - fe = []; - be = []; - - n = 10; - - array.iota( fe, 0, n, 0 ); - array.reversed( fe, be ); - - algorithms.fiter( 0, n, f.push.bind(f) ); - algorithms.biter( 0, n, b.push.bind(b) ); - - deepEqual( f, fe, "forward" ); - deepEqual( b, be, "backward" ); - -}); diff --git a/test/js/src/ksum/sortxy.js b/test/js/src/ksum/sortxy.js deleted file mode 100644 index a099062..0000000 --- a/test/js/src/ksum/sortxy.js +++ /dev/null @@ -1,76 +0,0 @@ - -var util = require( "util" ) ; -var array = require( "@aureooms/js-array" ) ; - -test( "sortxy" , function ( ) { - - var n , X , Y , v , w , k , __fn__ , contains , compare ; - - console.log( "sortxy" ); - - n = 20 ; - - X = array.alloc( n ) ; - Y = array.alloc( n ) ; - - array.iota( X , 0 , n , 0 ) ; - array.iota( Y , 0 , n , 1000 ) ; - - contains = function ( a , x ) { - - var i , y , k ; - - it : for ( i = 0 ; i < a.length ; ++i ) { - - y = a[i] ; - - for ( k = 0 ; k < 4 ; ++k ) { - - if ( x[k] !== y[k] ) { - continue it ; - } - - } - - return true ; - } - - return false ; - - } ; - - v = [] ; - w = [] ; - - __fn__ = function ( w ) { - - return function ( a , b , c , d ) { - w.push( [ a , b , c , d ] ) ; - } ; - - } ; - - - compare = function ( a , b , c , d ) { - return a + b - c - d ; - } ; - - - algorithms.sortxy_n3( compare , X , Y , 0 , n - 1 , 0 , n - 1 , 0 , n - 1 , 0 , n - 1 , __fn__( v ) ) ; - algorithms.sortxy_n4( compare , X , Y , 0 , n - 1 , 0 , n - 1 , 0 , n - 1 , 0 , n - 1 , __fn__( w ) ) ; - - - for ( k = 0 ; k < w.length ; ++k ) { - - if ( w[k][0] > w[k][2] ) { - continue ; - } - - if ( w[k][0] === w[k][2] && w[k][1] <= w[k][3] ) { - continue ; - } - - deepEqual( contains( v , w[k] ), true, w[k] + " in list" ) ; - } - -} ) ;