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1594. Maximum Non Negative Product in a Matrix

Difficulty Topics

Description

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 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 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: 8
Explanation: Maximum non-negative product is shown (1 * 1 * -2 * -4 * 1 = 8).

Example 3:

Input: grid = [[1,3],[0,-4]]
Output: 0
Explanation: 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

Solution

maximum-non-negative-product-in-a-matrix.py
class Solution:
    def maxProductPath(self, A: List[List[int]]) -> int:
        M = 1000000007
        row, col = len(A), len(A[0])

        mp = [[0] * col for _ in range(row)] 
        mn = [[0] * col for _ in range(row)] 
        mp[0][0] = mn[0][0] = A[0][0]

        for i in range(1,col):
            mp[0][i] = A[0][i] * mp[0][i-1]
            mn[0][i] = A[0][i] * mp[0][i-1]

        for i in range(1,row):
            mp[i][0] = A[i][0] * mp[i-1][0]
            mn[i][0] = A[i][0] * mp[i-1][0]

        for i in range(1,row):
            for j in range(1,col):
                if A[i][j] > 0:
                    mp[i][j] = max(mp[i-1][j], mp[i][j-1]) * A[i][j]
                    mn[i][j] = min(mn[i-1][j], mn[i][j-1]) * A[i][j]
                else:
                    mp[i][j] = min(mn[i-1][j], mn[i][j-1]) * A[i][j]
                    mn[i][j] = max(mp[i-1][j], mp[i][j-1]) * A[i][j]

        res = mp[row-1][col-1]

        return res%M if res > -1 else -1