Find Valid Matrix Given Row and Column Sums
You are given two arrays rowSum and colSum of non-negative integers where rowSum[i] is the sum of the elements in the i^th row and colSum[j] is the sum of the elements of the j^th 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 is 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]]The row and column sums match, all matrix elements are non-negative, and another valid matrix could also be returned.
Example 2
Input
rowSum = [5,7,10], colSum = [8,6,8]Output
[[0,5,0],[6,1,0],[2,0,8]]The returned matrix has row sums [5, 7, 10] and column sums [8, 6, 8].
Constraints
- 1 <= rowSum.length, colSum.length <= 500
- 0 <= rowSum[i], colSum[i] <= 10^8
- sum(rowSum) == sum(colSum)
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