leetcode-problemset/leetcode-cn/problem (English)/等和矩阵分割 I(English) [equal-sum-grid-partition-i].html

<p>You are given an <code>m x n</code> matrix <code>grid</code> of positive integers. Your task is to determine if it is possible to make <strong>either one horizontal or one vertical cut</strong> on the grid such that:</p>

<ul>
	<li>Each of the two resulting sections formed by the cut is <strong>non-empty</strong>.</li>
	<li>The sum of the elements in both sections is <strong>equal</strong>.</li>
</ul>

<p>Return <code>true</code> if such a partition exists; 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">grid = [[1,4],[2,3]]</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/2025/03/30/lc.png" style="width: 200px;" /><img alt="" src="https://assets.leetcode.com/uploads/2025/03/30/lc.jpeg" style="width: 200px; height: 200px;" /></p>

<p>A horizontal cut between row 0 and row 1 results in two non-empty sections, each with a sum of 5. Thus, the answer is <code>true</code>.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[1,3],[2,4]]</span></p>

<p><strong>Output:</strong> <span class="example-io">false</span></p>

<p><strong>Explanation:</strong></p>

<p>No horizontal or vertical cut results in two non-empty sections with equal sums. Thus, the answer is <code>false</code>.</p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= m == grid.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= n == grid[i].length &lt;= 10<sup>5</sup></code></li>
	<li><code>2 &lt;= m * n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 10<sup>5</sup></code></li>
</ul>