原文链接: https://leetcode-cn.com/problems/find-valid-matrix-given-row-and-column-sums

英文原文

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]]

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] <= 108
• sum(rows) == sum(columns)

中文题目

给你两个非负整数数组 rowSum 和 colSum ，其中 rowSum[i] 是二维矩阵中第 i 行元素的和， colSum[j] 是第 j 列元素的和。换言之你不知道矩阵里的每个元素，但是你知道每一行和每一列的和。

请找到大小为 rowSum.length x colSum.length 的任意 非负整数 矩阵，且该矩阵满足 rowSum 和 colSum 的要求。

请你返回任意一个满足题目要求的二维矩阵，题目保证存在 至少一个 可行矩阵。

 

示例 1：

输入：rowSum = [3,8], colSum = [4,7]
输出：[[3,0],
      [1,7]]
解释：
第 0 行：3 + 0 = 3 == rowSum[0]
第 1 行：1 + 7 = 8 == rowSum[1]
第 0 列：3 + 1 = 4 == colSum[0]
第 1 列：0 + 7 = 7 == colSum[1]
行和列的和都满足题目要求，且所有矩阵元素都是非负的。
另一个可行的矩阵为：[[1,2],
                  [3,5]]

示例 2：

输入：rowSum = [5,7,10], colSum = [8,6,8]
输出：[[0,5,0],
      [6,1,0],
      [2,0,8]]

示例 3：

输入：rowSum = [14,9], colSum = [6,9,8]
输出：[[0,9,5],
      [6,0,3]]

示例 4：

输入：rowSum = [1,0], colSum = [1]
输出：[[1],
      [0]]

示例 5：

输入：rowSum = [0], colSum = [0]
输出：[[0]]

 

提示：

• 1 <= rowSum.length, colSum.length <= 500
• 0 <= rowSum[i], colSum[i] <= 108
• sum(rows) == sum(columns)

通过代码

高赞题解

解题思路

将第$i$行第$j$列设为$\min(row[i], col[j])$，同时更新$row[i]$和$col[j]$即可。

为什么这一贪心策略是正确的呢？

其实很简单。我们首先考虑第一行，显然有$row[0]\leq\sum_j col[j]$，因此在经过上述操作后，一定能使得$row[0]=0$。同时，因为每次我们取得是$\min(row[0], col[j])$，所以操作后，一定仍满足$\forall j,col[j]\geq0$。这样，我们就把原问题变成了$N-1$行，$M$列的新问题。依次类推，我们就一定能够得到一组可行解。

时间复杂度$O(NM)$。

代码

class Solution {
public:
    vector<vector<int>> restoreMatrix(vector<int>& rowSum, vector<int>& colSum) {
        int n = rowSum.size(), m = colSum.size();
        vector<vector<int>> ans(n, vector<int>(m));
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < m; ++j) {
                ans[i][j] = min(rowSum[i], colSum[j]);
                rowSum[i] -= ans[i][j];
                colSum[j] -= ans[i][j];
            }
        }
        return ans;
    }
};

统计信息

通过次数	提交次数	AC比率
3689	4999	73.8%

提交历史

提交时间	提交结果	执行时间	内存消耗	语言