> For the complete documentation index, see [llms.txt](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/array/73.-set-matrix-zeroes.md).

# 73. 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**](https://en.wikipedia.org/wiki/In-place_algorithm).

**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?

```cpp
// Constant space method
void setZeroes(vector<vector<int>>& matrix) { // time: O(m * n); space: O(1)
    // Use the 1st row to record each column, and 
    // the 1st column to record each row
    // matrix[0][0] is overlapped, representing the row_0
    // Need another variable col_0 to record the first column
    int col_0 = 1, m = matrix.size(), n = matrix[0].size();
    
    // Loop through all elements to set states in the first row and the first column
    for (int i = 0; i < m; ++i) {
        if (matrix[i][0] == 0) col_0 = 0;
        for (int j = 1; j < n; ++j) {
            if (matrix[i][j] == 0) matrix[i][0] = matrix[0][j] = 0;
        }
    }
    
    // Use the first row and column to set zero from bottom right
    for (int i = m - 1; i >= 0; --i) {
        for (int j = n - 1; j >= 1; --j) {
            if (matrix[i][0] == 0 || matrix[0][j] == 0) matrix[i][j] = 0;
        }
        if (!col_0) matrix[i][0] = 0;
    }
}
```

```cpp
// Constant space method
void setZeroes(vector<vector<int>>& matrix) { // time: O(m * n); space: O(1)
    // Input validation
    if (matrix.empty() || matrix[0].empty()) return;
    
    // Use the 1st row to record each column, and 
    // the 1st column to record each row
    // matrix[0][0] is not used to store any info
    // Need another variable row_0 and col_0 to record the first row and column
    int row_0 = 1, col_0 = 1, m = matrix.size(), n = matrix[0].size();
    
    // Loop through all elements to set states in the first row and the first column
    for (int i = 0; i < m; ++i) {
        if (matrix[i][0] == 0) col_0 = 0;
    }
    for (int j = 0; j < n; ++j) {
        if (matrix[0][j] == 0) row_0 = 0;
    }
    for (int i = 1; i < m; ++i) {
        for (int j = 1; j < n; ++j) {
            if (matrix[i][j] == 0) 
                matrix[i][0] = matrix[0][j] = 0;
        }
    }
    
    // Use the first row and column to set zero
    for (int i = 1; i < m; ++i) {
        for (int j = 1; j < n; ++j) {
            if (matrix[i][0] == 0 || matrix[0][j] == 0) 
                matrix[i][j] = 0;
        }
    }
    if (!row_0) {
        for (int j = 0; j < n; ++j) matrix[0][j] = 0;
    }
    if (!col_0) {
        for (int i = 0; i < m; ++i) matrix[i][0] = 0;
    }
}
```