Sync LeetCode submission Runtime - 241 ms (88.96%), Memory - 83.7 MB (25.23%)

Author: jimit105

3657-check-if-grid-can-be-cut-into-sections/README.md

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+<p>You are given an integer <code>n</code> representing the dimensions of an <code>n x n</code><!-- notionvc: fa9fe4ed-dff8-4410-8196-346f2d430795 --> grid, with the origin at the bottom-left corner of the grid. You are also given a 2D array of coordinates <code>rectangles</code>, where <code>rectangles[i]</code> is in the form <code>[start<sub>x</sub>, start<sub>y</sub>, end<sub>x</sub>, end<sub>y</sub>]</code>, representing a rectangle on the grid. Each rectangle is defined as follows:</p>
+
+<ul>
+	<li><code>(start<sub>x</sub>, start<sub>y</sub>)</code>: The bottom-left corner of the rectangle.</li>
+	<li><code>(end<sub>x</sub>, end<sub>y</sub>)</code>: The top-right corner of the rectangle.</li>
+</ul>
+
+<p><strong>Note </strong>that the rectangles do not overlap. Your task is to determine if it is possible to make <strong>either two horizontal or two vertical cuts</strong> on the grid such that:</p>
+
+<ul>
+	<li>Each of the three resulting sections formed by the cuts contains <strong>at least</strong> one rectangle.</li>
+	<li>Every rectangle belongs to <strong>exactly</strong> one section.</li>
+</ul>
+
+<p>Return <code>true</code> if such cuts can be made; otherwise, return <code>false</code>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">n = 5, rectangles = [[1,0,5,2],[0,2,2,4],[3,2,5,3],[0,4,4,5]]</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">true</span></p>
+
+<p><strong>Explanation:</strong></p>
+
+<p><img alt="" src="https://assets.leetcode.com/uploads/2024/10/23/tt1drawio.png" style="width: 285px; height: 280px;" /></p>
+
+<p>The grid is shown in the diagram. We can make horizontal cuts at <code>y = 2</code> and <code>y = 4</code>. Hence, output is true.</p>
+</div>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">n = 4, rectangles = [[0,0,1,1],[2,0,3,4],[0,2,2,3],[3,0,4,3]]</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">true</span></p>
+
+<p><strong>Explanation:</strong></p>
+
+<p><img alt="" src="https://assets.leetcode.com/uploads/2024/10/23/tc2drawio.png" style="width: 240px; height: 240px;" /></p>
+
+<p>We can make vertical cuts at <code>x = 2</code> and <code>x = 3</code>. Hence, output is true.</p>
+</div>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">n = 4, rectangles = [[0,2,2,4],[1,0,3,2],[2,2,3,4],[3,0,4,2],[3,2,4,4]]</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">false</span></p>
+
+<p><strong>Explanation:</strong></p>
+
+<p>We cannot make two horizontal or two vertical cuts that satisfy the conditions. Hence, output is false.</p>
+</div>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>3 &lt;= n &lt;= 10<sup>9</sup></code></li>
+	<li><code>3 &lt;= rectangles.length &lt;= 10<sup>5</sup></code></li>
+	<li><code>0 &lt;= rectangles[i][0] &lt; rectangles[i][2] &lt;= n</code></li>
+	<li><code>0 &lt;= rectangles[i][1] &lt; rectangles[i][3] &lt;= n</code></li>
+	<li>No two rectangles overlap.</li>
+</ul>

3657-check-if-grid-can-be-cut-into-sections/solution.py

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+# Approach: Line Sweep
+
+# Time: O(n log n)
+# Space: O(n)
+
+class Solution:
+    def checkValidCuts(self, n: int, rectangles: List[List[int]]) -> bool:
+        # Check if valid cuts can be made in a specific dimension
+        def _check_cuts(rectangles, dim):
+            gap_count = 0
+            rectangles.sort(key=lambda rect: rect[dim])
+
+            furthest_end = rectangles[0][dim + 2]
+            
+            for i in range(1, len(rectangles)):
+                rect = rectangles[i]
+                if furthest_end <= rect[dim]:
+                    gap_count += 1
+
+                furthest_end = max(furthest_end, rect[dim + 2])
+
+            return gap_count >= 2
+
+        return _check_cuts(rectangles, 0) or _check_cuts(rectangles, 1)
+
+