【LeetCode】Set Matrix Zeroes

Given a m x n matrix, if an element is 0, set its entire row and column to 0. Do it in-place.

Example 1:

Input: 
[
  [1,1,1],
  [1,0,1],
  [1,1,1]
]
Output: 
[
  [1,0,1],
  [0,0,0],
  [1,0,1]
]

Example 2:

Input: 
[
  [0,1,2,0],
  [3,4,5,2],
  [1,3,1,5]
]
Output: 
[
  [0,0,0,0],
  [0,4,5,0],
  [0,3,1,0]
]

Follow up:

• A straight forward solution using O(mn) space is probably a bad idea.
• A simple improvement uses O(m + n) space, but still not the best solution.
• Could you devise a constant space solution? 

题解：遇到0将当前行列置为0，要求就地常量空间，最常见思路就是用一组变量维护需要置0的行和列但是用一两个是无法实现的，必须o(N)空间，看了答案才发现可以用矩阵第一行和第一列来标记是否为0的状态，也就是看你能否想到用题目中的数组来存储你想要的信息，这里能存储是因为行和列也是要置0的所以标记为0不影响结果，主要注意第一个元素，对第一列额外处理即用一个变量col来判断是否标为0这样就不会和第一行冲突了

class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix) {
        bool isCol=false;
        
        int R=matrix.size(),C=matrix[0].size();
        for (int i = 0; i < R; i++) {

      // Since first cell for both first row and first column is the same i.e. matrix[0][0]
      // We can use an additional variable for either the first row/column.
      // For this solution we are using an additional variable for the first column
      // and using matrix[0][0] for the first row.
      if (matrix[i][0] == 0) {
        isCol = true;
      }

      for (int j = 1; j < C; j++) {
        // If an element is zero, we set the first element of the corresponding row and column to 0
        if (matrix[i][j] == 0) {
          matrix[0][j] = 0;
          matrix[i][0] = 0;
        }
      }
    }

    // Iterate over the array once again and using the first row and first column, update the elements.
    for (int i = 1; i < R; i++) {
      for (int j = 1; j < C; j++) {
        if (matrix[i][0] == 0 || matrix[0][j] == 0) {
          matrix[i][j] = 0;
        }
      }
    }

    // See if the first row needs to be set to zero as well
    if (matrix[0][0] == 0) {
      for (int j = 0; j < C; j++) {
        matrix[0][j] = 0;
      }
    }

    // See if the first column needs to be set to zero as well
    if (isCol) {
      for (int i = 0; i < R; i++) {
        matrix[i][0] = 0;
      }
    }
    }
};