3548 - Equal Sum Grid Partition II.

Hard

You are given an m x n matrix grid 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:

• Each of the two resulting sections formed by the cut is non-empty.

• The sum of elements in both sections is equal , or can be made equal by discounting at most one single cell in total (from either section).

• If a cell is discounted, the rest of the section must remain connected.

Return true if such a partition exists; otherwise, return false.

Note: A section is connected if every cell in it can be reached from any other cell by moving up, down, left, or right through other cells in the section.

Example 1:

Input: grid = [1,4,2,3]

Output: true

Explanation:

• A horizontal cut after the first row gives sums 1 + 4 = 5 and 2 + 3 = 5, which are equal. Thus, the answer is true.

Example 2:

Input: grid = [1,2,3,4]

Output: true

Explanation:

• A vertical cut after the first column gives sums 1 + 3 = 4 and 2 + 4 = 6.

• By discounting 2 from the right section (6 - 2 = 4), both sections have equal sums and remain connected. Thus, the answer is true.

Example 3:

Input: grid = [1,2,4,2,3,5]

Output: false

Explanation:

• A horizontal cut after the first row gives 1 + 2 + 4 = 7 and 2 + 3 + 5 = 10.

• By discounting 3 from the bottom section (10 - 3 = 7), both sections have equal sums, but they do not remain connected as it splits the bottom section into two parts ([2] and [5]). Thus, the answer is false.

Example 4:

Input: grid = [4,1,8,3,2,6]

Output: false

Explanation:

No valid cut exists, so the answer is false.

Constraints:

• <code>1 <= m == grid.length <= 10⁵</code>

• <code>1 <= n == gridi.length <= 10⁵</code>

• <code>2 <= m * n <= 10⁵</code>

• <code>1 <= gridj<= 10⁵</code>