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Problem Brief

Calculate the Max Value

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Amazon’s engineering team is developing a tool designed to minimize the size of an n x n grid named matrix, based on a compression ratio described by the array limit. Their challenge is to compute the highest possible sum of exactly x elements from the matrix while adhering to the following conditions:

  • For every row i (where 0 ≤ i < n), the count of elements picked from that row must not surpass limit[i].
  • If it turns out impossible to pick exactly x elements, the function should return -1.

    • Your task is to assist by computing the largest possible sum achievable under these restrictions.

    Input Parameters:

  • limit[n]: A list where each entry specifies the maximum count of numbers allowed to be chosen from the respective row in matrix.
  • matrix[n][n]: A two-dimensional square grid containing integer values.
  • x: The exact total count of elements that need to be picked.

    • Returns:

  • A long integer representing the maximum achievable sum when choosing exactly x elements following the constraints.
  • Return -1 if selecting exactly x elements is not feasible.

    • 1Example 1

    Input
    limit = [1, 2, 1], matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], x = 2
    Output
    15
    Explanation
    The top selections from each row, respecting the limit constraints, are as follows: Row 0: Choose 3 (since limit[0] = 1 allows only one pick) Row 1: Pick 5 and 6 (as limit[1] = 2 permits two selections) Row 2: Choose 9 (since limit[2] = 1 restricts to a single selection) However, only x = 2 items can be chosen in total. The most optimal selection strategy is to pick 6 from Row 1 and 9 from Row 2, maximizing the sum.

    Constraints

    Limits and guarantees your solution can rely on.

    • 1 ≤ n ≤ 50
    • 1 ≤ limit[i] ≤ n
    • 1 ≤ matrix[i][j] ≤ 10^4
    • 1 ≤ x ≤ n * n
    public long findMaxValue(int[] factor, int[][] data, int x) {
  // write your code here
}
    Input

    limit

    [1, 2, 1]

    matrix

    [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

    x

    2

    Output

    15

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