Update src/geometry/nearest_points.md

izanbf1803 · adamant-pwn · web-flow · commit 4ce3c84b2950 · 2025-08-23T15:26:40.000+02:00
Better formatting

Co-authored-by: Oleksandr Kulkov &lt;adamant.pwn@gmail.com&gt;
diff --git a/src/geometry/nearest_points.md b/src/geometry/nearest_points.md
@@ -173,7 +173,7 @@ An alternative method arises from a very simple idea to heuristically improve th
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-We will consider only the squares containing at least one point. Denote by $n_1, n_2, \dots, n_k$ the number of points in each of the $k$ remaining squares. Assuming at least two points are in the same or in adjacent squares,  the time complexity is $\Theta(\sum_{i=1}^{k} n_i^2)$.
+We will consider only the squares containing at least one point. Denote by $n_1, n_2, \dots, n_k$ the number of points in each of the $k$ remaining squares. Assuming at least two points are in the same or in adjacent squares,  the time complexity is $\Theta\left(\sum\limits_{i=1}^k n_i^2\right)$.
 
 ??? info "Proof"
 	For the $i$-th square containing $n_i$ points, the number of pairs inside is $\Theta(n_i^2)$. If the $i$-th square is adjacent to the $j$-th square, then we also perform $n_i n_j \le \max(n_i, n_j)^2 \le n_i^2 + n_j^2$ distance comparisons. Notice that each cube has at most $8$ adjacent cubes, so we can bound the sum of all comparisons by $\Theta(\sum_{i=1}^{k} n_i^2)$. $\quad \blacksquare$
