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.

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?

// 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;
    }
}

// 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;
    }
}