1594. Maximum Non Negative Product in a Matrix.py

'''
You are given a rows x cols 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 (rows - 1, cols - 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 109 + 7. If the maximum product is negative return -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: -1
Explanation: It's 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: 8
Explanation: Maximum non-negative product is in bold (1 * 1 * -2 * -4 * 1 = 8).
Example 3:

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

Input: grid = [[ 1, 4,4,0],
               [-2, 0,0,1],
               [ 1,-1,1,1]]
Output: 2
Explanation: Maximum non-negative product is in bold (1 * -2 * 1 * -1 * 1 * 1 = 2).
 

Constraints:

1 <= rows, cols <= 15
-4 <= grid[i][j] <= 4
'''

class Solution:
    def maxProductPath(self, grid):
        n = len(grid)
        m = len(grid[0])
        maxp = [[0 for i in range(m)] for j in range(n)]
        minp = [[0 for i in range(m)] for j in range(n)]

        for i in range(n):
            for j in range(m):

                minv = 2**31-1
                maxv = -2**31

                if i==0 and j==0: 
                    maxv = grid[i][j]
                    minv = grid[i][j] 

                if i>0:
                    tmax = max(maxp[i - 1][j] * grid[i][j], minp[i - 1][j] * grid[i][j]); 
                    maxv = max(maxv, tmax)
  
                    tmin = min(maxp[i - 1][j] * grid[i][j], minp[i - 1][j] * grid[i][j]); 
                    minv = min(minv, tmin)

                if (j > 0): 
                    tmax = max(maxp[i][j - 1] * grid[i][j], minp[i][j - 1] * grid[i][j]); 
                    maxv = max(maxv, tmax)
  
                    tmin = min(maxp[i][j - 1] * grid[i][j], minp[i][j - 1] * grid[i][j]); 
                    minv = min(minv, tmin)

                maxp[i][j] = maxv 
                minp[i][j] = minv

        if maxp[-1][-1]>=0:
            return maxp[-1][-1]%(10**9+7)
        else:
            return -1