1605. Find Valid Matrix Given Row and Column Sums.md

1605. Find Valid Matrix Given Row and Column Sums

---

the third one in Biweekly Contest 36.

---

Difficulty : Medium

Related Topics : Greedy

---

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'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 = 0 == 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]]

Example 3:

Input: rowSum = [14,9], colSum = [6,9,8]
Output: [[0,9,5],
         [6,0,3]]

Example 4:

Input: rowSum = [1,0], colSum = [1]
Output: [[1],
         [0]]

Example 5:

Input: rowSum = [0], colSum = [0]
Output: [[0]]

Constraints:

• 1 <= rowSum.length, colSum.length <= 500
• 0 <= rowSum[i], colSum[i] <= 10^8
• sum(rows) == sum(columns)

---

Solution

• mine
  • Java
    • ``

---

• the most votes

• Runtime: 2 ms, faster than 90.81%, Memory Usage: 47.4 MB, less than 22.90% of Java online submissions

  // O(R * C)time
  // O(R * C)space
  public int[][] restoreMatrix(int[] rowSum, int[] colSum) {
      int m = rowSum.length;
      int n = colSum.length;
      int[][] ans = new int[m][n];
      for (int i = 0; i < m; i++) {
          for (int j = 0; j < n; j++) {
              if (rowSum[i] == 0 || colSum[j] == 0) continue;
              int now = Math.min(rowSum[i], colSum[j]);
              ans[i][j] = now;
              rowSum[i] -= now;
              colSum[j] -= now;
          }
      }
      return ans;
  }
  

---