[Leetcode 61] 73 Set Matrix Zeros

Problem:

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

Follow up:

Did you use extra space?
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?

Analysis:

The simplest way is to have a copy of the given matrix and then find 0's indexes in the aux matrix and set the rows and columns to 0 in original matrix. This requires sapce O(mn)

Next method is the scan through the matrix, keep record of rows and columns that need to be set to 0. This requires space O(m+n)

After referencing the online resource, find the following constant space solution.

To use constant space to solve a problem, either 1). use constant variables to solve the problem or 2). make use of the current space to solve the problem. In this problem is the second case.

1. scan the first row and first column to remember whether need to set them to zero.

2. scan the rest part of the matrix, if a position (x, y) is zero. Set (x, 0) and (0, y) to zero.

3. scan again the first row and first column to set rows and columns to 0s.

4. process the first row and first column according to step 1.

Code:

class Solution {
public:
    void setZeroes(vector<vector<int> > &matrix) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int m = matrix.size();
        int n = matrix[0].size();
        bool setFirstRow = false, setFirstCol = false;
        
        for (int i=0; i<n; i++)
            if (matrix[0][i] == 0) {
                setFirstRow = true;
                break;
            }
            
        for (int i=0; i<m; i++)
            if (matrix[i][0] == 0) {
                setFirstCol = true;
                break;
            }
        
        for (int i=1; i<m; i++)
            for (int j=1; j<n; j++) {
                if (matrix[i][j] == 0) {
                    matrix[0][j] = 0;
                    matrix[i][0] = 0;
                }
            }
            
        for (int i=1; i<n; i++) {
            if (matrix[0][i] == 0) {
                for (int j=1; j<m; j++) 
                    matrix[j][i] = 0;
            }
        }    
        
        
        for (int i=1; i<m; i++) {
            if (matrix[i][0] == 0) {
                for (int j=1; j<n; j++)
                    matrix[i][j] = 0;
            }
        }
        
        if (setFirstRow) {
            for (int i=0; i<n; i++)
                matrix[0][i] = 0;
        }
        
        if (setFirstCol) {
            for (int i=0; i<m; i++)
                matrix[i][0] = 0;
        }
    }
};