equal-sum-grid-partition-i

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Algorithms

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 either one horizontal or one vertical cut on the grid such that:

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

Return <code>true</code> if such a partition exists; otherwise return <code>false</code>.

&nbsp;
Example 1:

<div class="example-block">
Input: grid = [[1,4],[2,3]]

Output: true

Explanation:

<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;" />

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>.
</div>

Example 2:

<div class="example-block">
Input: grid = [[1,3],[2,4]]

Output: false

Explanation:

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

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= m == grid.length &lt;= 105</code></li>
	<li><code>1 &lt;= n == grid[i].length &lt;= 105</code></li>
	<li><code>2 &lt;= m * n &lt;= 105</code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 105</code></li>
</ul>