How hard is LeetCode 1594. Maximum Non Negative Product in a Matrix?

LeetCode 1594. Maximum Non Negative Product in a Matrix is rated Medium on LeetCode.

What topics does LeetCode 1594. Maximum Non Negative Product in a Matrix cover?

LeetCode 1594. Maximum Non Negative Product in a Matrix is tagged Array, Dynamic Programming and Matrix on LeetCode.

Maximum Non Negative Product in a Matrix — LeetCode 1594 Python Solution

MediumArrayDynamic ProgrammingMatrix

Problem: #1594
Pattern: Matrix and Grid
Reading time: 4 min
Source: leetcode.com

The problem

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.

Example

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.

Python solution

Python

class Solution:
    def maxProductPath(self, grid: List[List[int]]) -> int:
        m, n = len(grid), len(grid[0])
        mod = 10**9 + 7
        dp = [[[grid[0][0]] * 2 for _ in range(n)] for _ in range(m)]
        for i in range(1, m):
            dp[i][0] = [dp[i - 1][0][0] * grid[i][0]] * 2
        for j in range(1, n):
            dp[0][j] = [dp[0][j - 1][0] * grid[0][j]] * 2
        for i in range(1, m):
            for j in range(1, n):
                v = grid[i][j]
                if v >= 0:
                    dp[i][j][0] = min(dp[i - 1][j][0], dp[i][j - 1][0]) * v
                    dp[i][j][1] = max(dp[i - 1][j][1], dp[i][j - 1][1]) * v
                else:
                    dp[i][j][0] = max(dp[i - 1][j][1], dp[i][j - 1][1]) * v
                    dp[i][j][1] = min(dp[i - 1][j][0], dp[i][j - 1][0]) * v
        ans = dp[-1][-1][1]
        return -1 if ans < 0 else ans % mod

Complexity

Measure	Complexity
Time	O(n·m) (typical)
Space	O(n·m) or optimized auxiliary

Pattern: Matrix and Grid

Treat a 2-D grid as a graph whose neighbours are the four adjacent cells. LeetCode 1594. Maximum Non Negative Product in a Matrix is filed here because LeetCode tags it Matrix, which is the vocabulary this hub collects.

The matrix and grid guide has the Python template for the pattern and the 216 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 1594. Maximum Non Negative Product in a Matrix?: LeetCode 1594. Maximum Non Negative Product in a Matrix is rated Medium on LeetCode.
What topics does LeetCode 1594. Maximum Non Negative Product in a Matrix cover?: LeetCode 1594. Maximum Non Negative Product in a Matrix is tagged Array, Dynamic Programming and Matrix on LeetCode.