1605 - Find Valid Matrix Given Row and Column Sums\.

Medium

You are given two arrays rowSum and colSum of non-negative integers where rowSum[i] is the sum of the elements in the <code>i^th</code> row and colSum[j] is the sum of the elements of the <code>j^th</code> 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:

0^th row: 3 + 0 = 3 == rowSum0

1^st row: 1 + 7 = 8 == rowSum1

0^th column: 3 + 1 = 4 == colSum0

1^st column: 0 + 7 = 7 == colSum1

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

• <code>0 <= rowSumi, colSumi<= 10⁸</code>

• sum(rows) == sum(columns)