1594. Maximum Non Negative Product in a Matrix

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 modulo109 + 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

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(mn)
• Space complexity: O(mn)

 

JavaScript

/**
 * @param {number[][]} grid
 * @return {number}
 */
const maxProductPath = function (grid) {
  const MODULO = 10 ** 9 + 7;
  const m = grid.length;
  const n = grid[0].length;
  const dpMax = new Array(m)
    .fill('')
    .map(_ => new Array(n).fill(0));
  const dpMin = new Array(m)
    .fill('')
    .map(_ => new Array(n).fill(0));

  for (let row = 0; row < m; row++) {
    for (let col = 0; col < n; col++) {
      const value = grid[row][col];
      const maxUpValue = dpMax[row - 1]?.[col] * value;
      const maxLeftValue = dpMax[row][col - 1] * value;
      const minUpValue = dpMin[row - 1]?.[col] * value;
      const minLeftValue = dpMin[row][col - 1] * value;

      if (row === 0 && col === 0) {
        dpMax[row][col] = dpMin[row][col] = grid[0][0];
      } else if (row === 0) {
        dpMax[row][col] = Math.max(maxLeftValue, minLeftValue);
        dpMin[row][col] = Math.min(maxLeftValue, minLeftValue);
      } else if (col === 0) {
        dpMax[row][col] = Math.max(maxUpValue, minUpValue);
        dpMin[row][col] = Math.min(maxUpValue, minUpValue);
      } else {
        const maxUp = Math.max(maxUpValue, minUpValue);
        const maxLeft = Math.max(maxLeftValue, minLeftValue);
        const minUp = Math.min(maxUpValue, minUpValue);
        const minLeft = Math.min(maxLeftValue, minLeftValue);

        dpMax[row][col] = Math.max(maxUp, maxLeft);
        dpMin[row][col] = Math.min(minUp, minLeft);
      }
    }
  }
  return dpMax[m - 1][n - 1] < 0 ? -1 : dpMax[m - 1][n - 1] % MODULO;
};