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] <= 108

• sum(rowSum) == sum(colSum)

有點像中學的幾元一次方程組了，就是但是求解的方式不太一樣，就是每次先找到這個行列和的最小值，讓這個元素等于這個值，然后行之和減去這個值，列之和減去這個值，一旦行之和或者列之和為0了，就i++ 或者j++;

即可。

Runtime:?1 ms, faster than?100.00%?of?Java?online submissions for?Find Valid Matrix Given Row and Column Sums.

Memory Usage:?50.8 MB, less than?27.05%?of?Java?online submissions for?Find Valid Matrix Given Row and Column Sums.