3462: Maximum Sum With at Most K Elements

Problem Statement

You are given a 2D integer matrix grid of size n x m, an integer array limits of length n, and an integer k. The task is to find the maximum sum of at most k elements from the matrix grid such that:

  • The number of elements taken from the ith row of grid does not exceed limits[i].

Return the maximum sum.

Example 1:

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

Output: 7

Explanation:

  • From the second row, we can take at most 2 elements. The elements taken are 4 and 3.
  • The maximum possible sum of at most 2 selected elements is 4 + 3 = 7.

Example 2:

Input: grid = [[5,3,7],[8,2,6]], limits = [2,2], k = 3

Output: 21

Explanation:

  • From the first row, we can take at most 2 elements. The element taken is 7.
  • From the second row, we can take at most 2 elements. The elements taken are 8 and 6.
  • The maximum possible sum of at most 3 selected elements is 7 + 8 + 6 = 21.

Constraints:

  • n == grid.length == limits.length
  • m == grid[i].length
  • 1 <= n, m <= 500
  • 0 <= grid[i][j] <= 105
  • 0 <= limits[i] <= m
  • 0 <= k <= min(n * m, sum(limits))

Code Solution