Maximum Non Negative Product in a Matrix
You are given an 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. If the maximum product is negative, return -1.
Notice that the modulo is performed after getting the maximum product.
Example 1
-1 -2 -3 -2 -3 -3 -3 -3 -2
Input
grid = [[-1,-2,-3],[-2,-3,-3],[-3,-3,-2]]Output
-1It is not possible to get non-negative product in the path from (0, 0) to (2, 2), so return -1.
Example 2
1 -2 1 1 -2 1 3 -4 1
Input
grid = [[1,-2,1],[1,-2,1],[3,-4,1]]Output
8The maximum non-negative product is 1 * 1 * -2 * -4 * 1 = 8.
Constraints
- m == grid.length
- n == grid[i].length
- 1 <= m, n <= 15
- -4 <= grid[i][j] <= 4