1594. Maximum Non Negative Product in a Matrix

Medium

730

36

You are given a `m x n`

matrix `grid`

. Initially, you are located at the top-left corner `(0, 0)`

, and in each step, you can only **move right or down** in the matrix.

Among all possible paths starting from the top-left corner `(0, 0)`

and ending in the bottom-right corner `(m - 1, n - 1)`

, find the path with the **maximum non-negative product**. The product of a path is the product of all integers in the grid cells visited along the path.

Return the *maximum non-negative product modulo *

`10`^{9} + 7

. `-1`

.Notice that the modulo is performed after getting the maximum product.

**Example 1:**

Input:grid = [[-1,-2,-3],[-2,-3,-3],[-3,-3,-2]]Output:-1Explanation:It is not possible to get non-negative product in the path from (0, 0) to (2, 2), so return -1.

**Example 2:**

Input:grid = [[1,-2,1],[1,-2,1],[3,-4,1]]Output:8Explanation:Maximum non-negative product is shown (1 * 1 * -2 * -4 * 1 = 8).

**Example 3:**

Input:grid = [[1,3],[0,-4]]Output:0Explanation:Maximum non-negative product is shown (1 * 0 * -4 = 0).

**Constraints:**

`m == grid.length`

`n == grid[i].length`

`1 <= m, n <= 15`

`-4 <= grid[i][j] <= 4`

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