Sync LeetCode submission Runtime - 77 ms (86.34%), Memory - 198.6 MB (88.95%)

Author: koralkulacoglu

LeetCode/3763-separate-squares-i/README.md

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+<p>You are given a 2D integer array <code>squares</code>. Each <code>squares[i] = [x<sub>i</sub>, y<sub>i</sub>, l<sub>i</sub>]</code> represents the coordinates of the bottom-left point and the side length of a square parallel to the x-axis.</p>
+
+<p>Find the <strong>minimum</strong> y-coordinate value of a horizontal line such that the total area of the squares above the line <em>equals</em> the total area of the squares below the line.</p>
+
+<p>Answers within <code>10<sup>-5</sup></code> of the actual answer will be accepted.</p>
+
+<p><strong>Note</strong>: Squares <strong>may</strong> overlap. Overlapping areas should be counted <strong>multiple times</strong>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">squares = [[0,0,1],[2,2,1]]</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">1.00000</span></p>
+
+<p><strong>Explanation:</strong></p>
+
+<p><img alt="" src="https://assets.leetcode.com/uploads/2025/01/06/4062example1drawio.png" style="width: 378px; height: 352px;" /></p>
+
+<p>Any horizontal line between <code>y = 1</code> and <code>y = 2</code> will have 1 square unit above it and 1 square unit below it. The lowest option is 1.</p>
+</div>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">squares = [[0,0,2],[1,1,1]]</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">1.16667</span></p>
+
+<p><strong>Explanation:</strong></p>
+
+<p><img alt="" src="https://assets.leetcode.com/uploads/2025/01/15/4062example2drawio.png" style="width: 378px; height: 352px;" /></p>
+
+<p>The areas are:</p>
+
+<ul>
+	<li>Below the line: <code>7/6 * 2 (Red) + 1/6 (Blue) = 15/6 = 2.5</code>.</li>
+	<li>Above the line: <code>5/6 * 2 (Red) + 5/6 (Blue) = 15/6 = 2.5</code>.</li>
+</ul>
+
+<p>Since the areas above and below the line are equal, the output is <code>7/6 = 1.16667</code>.</p>
+</div>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= squares.length &lt;= 5 * 10<sup>4</sup></code></li>
+	<li><code>squares[i] = [x<sub>i</sub>, y<sub>i</sub>, l<sub>i</sub>]</code></li>
+	<li><code>squares[i].length == 3</code></li>
+	<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>9</sup></code></li>
+	<li><code>1 &lt;= l<sub>i</sub> &lt;= 10<sup>9</sup></code></li>
+	<li>The total area of all the squares will not exceed <code>10<sup>12</sup></code>.</li>
+</ul>

LeetCode/3763-separate-squares-i/solution.cpp

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+class Solution {
+public:
+    double separateSquares(vector<vector<int>>& squares) {
+        auto goUp = [&](double y) {
+            double above=0, below=0;
+            for (vector<int>& square : squares) {
+                double yi = square[1], li = square[2];
+                double h_below = min(li, max(0.0, y - yi));
+                below += h_below * li;
+                above += (li - h_below) * li;
+            }
+            return above > below;
+        };
+
+        double l=0, r=2e9;
+        while (r - l > 1e-5) {
+            double m = l + (r - l) / 2;
+            if (goUp(m)) l = m;
+            else r = m;
+        }
+
+        return r;
+    }
+};