3402: Minimum Operations to Make Columns Strictly Increasing

title: "3402: Minimum Operations to Make Columns Strictly Increasing"
tags:
  - Array
  - Greedy
  - Matrix

You are given a m x n matrix grid consisting of non-negative integers.

In one operation, you can increment the value of any grid[i][j] by 1.

Return the minimum number of operations needed to make all columns of grid strictly increasing.

Example 1:

Input: grid = [[3,2],[1,3],[3,4],[0,1]]

Output: 15

Explanation:

To make the 0^th column strictly increasing, we can apply 3 operations on grid[1][0], 2 operations on grid[2][0], and 6 operations on grid[3][0].
To make the 1^st column strictly increasing, we can apply 4 operations on grid[3][1].

Example 2:

Input: grid = [[3,2,1],[2,1,0],[1,2,3]]

Output: 12

Explanation:

To make the 0^th column strictly increasing, we can apply 2 operations on grid[1][0], and 4 operations on grid[2][0].
To make the 1^st column strictly increasing, we can apply 2 operations on grid[1][1], and 2 operations on grid[2][1].
To make the 2^nd column strictly increasing, we can apply 2 operations on grid[1][2].

Constraints: