1605. Find Valid Matrix Given Row and Column Sums

Problem

You are given two arrays rowSum and colSum of non-negative integers where rowSum[i] is the sum of the elements in the ith row and colSum[j] is the sum of the elements of the jth column of a 2D matrix. In other words, you do not know the elements of the matrix, but you do know the sums of each row and column.

Find any matrix of non-negative integers of size rowSum.length x colSum.length that satisfies the rowSum and colSum requirements.

Return **a 2D array representing *any* matrix that fulfills the requirements**. It's guaranteed that **at least one **matrix that fulfills the requirements exists.

  Example 1:

Input: rowSum = [3,8], colSum = [4,7]
Output: [[3,0],
         [1,7]]
Explanation: 
0th row: 3 + 0 = 3 == rowSum[0]
1st row: 1 + 7 = 8 == rowSum[1]
0th column: 3 + 1 = 4 == colSum[0]
1st column: 0 + 7 = 7 == colSum[1]
The row and column sums match, and all matrix elements are non-negative.
Another possible matrix is: [[1,2],
                             [3,5]]

Example 2:

Input: rowSum = [5,7,10], colSum = [8,6,8]
Output: [[0,5,0],
         [6,1,0],
         [2,0,8]]

  Constraints:

• 1 <= rowSum.length, colSum.length <= 500

• 0 <= rowSum[i], colSum[i] <= 10^8

• sum(rows) == sum(columns)

Solution (Java)

class Solution {
    public int[][] restoreMatrix(int[] rowSum, int[] colSum) {
        int[][] ans = new int[rowSum.length][colSum.length];
        for (int i = 0; i < rowSum.length; i++) {
            for (int j = 0; j < colSum.length; j++) {
                if (rowSum[i] != 0 && colSum[j] != 0) {
                    ans[i][j] = Math.min(rowSum[i], colSum[j]);
                    rowSum[i] -= ans[i][j];
                    colSum[j] -= ans[i][j];
                }
            }
        }
        return ans;
    }
}

Explain:

nope.

Complexity:

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