LeetCode 3462: Maximum Sum With at Most K Elements Solution

Master LeetCode problem 3462 (Maximum Sum With at Most K Elements), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

3462. Maximum Sum With at Most K Elements

Medium

Array Greedy Sorting Heap (Priority Queue)Matrix

Problem Explanation

Explanation:

To solve this problem, we can use a dynamic programming approach. We will iterate over each row of the matrix grid and for each row, we will maintain a 1D array dp where dp[j] represents the maximum sum of at most j elements taken from that row. We will update dp array for each row based on the elements that can be selected without exceeding the limits.

Initialize a 2D dp array of size n x (k + 1) where dp[i][j] represents the maximum sum of at most j elements taken from the first i rows.
Iterate over each row of the matrix grid.
For each row i, update the dp array based on the elements that can be selected without exceeding the limits[i].
Finally, return the maximum sum from the last row of the dp array. Solution:

Solution Code

class Solution {
    public int maxMatrixSum(int[][] grid, int[] limits, int k) {
        int n = grid.length;
        int m = grid[0].length;
        int[][] dp = new int[n][k + 1];

        for (int i = 0; i < n; i++) {
            int[] tmp = new int[k + 1];
            for (int j = 0; j <= k; j++) {
                dp[i][j] = Integer.MIN_VALUE;
            }

            for (int j = 0; j < m; j++) {
                for (int l = k; l >= 0; l--) {
                    int limit = limits[i];
                    if (l < limit) {
                        dp[i][l + 1] = Math.max(dp[i][l + 1], dp[i][l] + grid[i][j]);
                    }
                    tmp[l] = Math.max(tmp[l], dp[i][l]);
                }
            }
            for (int j = 0; j <= k; j++) {
                dp[i][j] = tmp[j];
            }
        }

        return dp[n - 1][k];
    }
}

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