1605. Find Valid Matrix Given Row and Column Sums

Description

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)

 

Solutions

Solution: Greedy

• Time complexity: O(mn)
• Space complexity: O(mn)

 

JavaScript

/**
 * @param {number[]} rowSum
 * @param {number[]} colSum
 * @return {number[][]}
 */
const restoreMatrix = function (rowSum, colSum) {
  const m = rowSum.length;
  const n = colSum.length;
  const result = new Array(m)
    .fill('')
    .map(_ => new Array(n));

  for (let row = 0; row < m; row++) {
    for (let col = 0; col < n; col++) {
      const value = Math.min(rowSum[row], colSum[col]);

      result[row][col] = value;
      rowSum[row] -= value;
      colSum[col] -= value;
    }
  }
  return result;
};