3148. Maximum Difference Score in a Grid

Description

You are given an m x n matrix grid consisting of positive integers. You can move from a cell in the matrix to any other cell that is either to the bottom or to the right (not necessarily adjacent). The score of a move from a cell with the value c1 to a cell with the value c2 is c2 - c1.

You can start at any cell, and you have to make at least one move.

Return the maximum total score you can achieve.

 

Example 1:

Input: grid = [[9,5,7,3],[8,9,6,1],[6,7,14,3],[2,5,3,1]]

Output: 9

Explanation: We start at the cell (0, 1), and we perform the following moves:
- Move from the cell (0, 1) to (2, 1) with a score of 7 - 5 = 2.
- Move from the cell (2, 1) to (2, 2) with a score of 14 - 7 = 7.
The total score is 2 + 7 = 9.

Example 2:

Input: grid = [[4,3,2],[3,2,1]]

Output: -1

Explanation: We start at the cell (0, 0), and we perform one move: (0, 0) to (0, 1). The score is 3 - 4 = -1.

 

Constraints:

• m == grid.length
• n == grid[i].length
• 2 <= m, n <= 1000
• 4 <= m * n <= 105
• 1 <= grid[i][j] <= 105

 

Solutions

Solution: Dynamic Programming

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

 

JavaScript

/**
 * @param {number[][]} grid
 * @return {number}
 */
const maxScore = function (grid) {
  const m = grid.length;
  const n = grid[0].length;
  let dp = [];
  let result = Number.MIN_SAFE_INTEGER;

  for (let row = 0; row < m; row++) {
    const current = [];

    for (let col = 0; col < n; col++) {
      const value = grid[row][col];
      let min = value;

      if (row > 0) {
        result = Math.max(result, value - dp[col]);
        min = Math.min(min, dp[col]);
      }
      if (col > 0) {
        result = Math.max(result, value - current[col - 1]);
        min = Math.min(min, current[col - 1]);
      }
      current.push(min);
    }
    dp = current;
  }
  return result;
};