Set Matrix Zeroes

Source

• lintcode: 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
Given a matrix

[
  [1,2],
  [0,3]
],
return
[
[0,2],
[0,0]
]

Challenge
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?

Java

public class Solution {
    /**
     * @param matrix: A list of lists of integers
     * @return: Void
     */
    public void setZeroes(int[][] matrix) {
        if(matrix==null || matrix.length==0 || matrix[0].length==0) return;
        int m = matrix.length;
        int n = matrix[0].length;
        boolean[] row = new boolean[m];
        boolean[] col = new boolean[n];
        for(int i=0; i<m; i++){
            for(int j=0; j<n; j++){
                if(matrix[i][j]==0){
                    row[i]=true;
                    col[j]=true;
                }
            }
        }
        for(int i=0; i<m; i++){
            for(int j=0; j<n; j++){
                if(row[i]==true || col[j]==true){
                    matrix[i][j]=0;
                }
            }
        }
    }
}

//O(1) space complexity
public class Solution {
    /**
     * @param matrix: A list of lists of integers
     * @return: Void
     */
    public void setZeroes(int[][] matrix) {
        if(matrix==null || matrix.length==0 || matrix[0].length==0) return;

        int rownum = matrix.length;    
        int colnum = matrix[0].length;     
        boolean hasZeroFirstRow = false, hasZeroFirstColumn = false;    

        // Does first row have zero?    
        for (int j = 0; j < colnum; ++j) {    
            if (matrix[0][j] == 0) {    
                hasZeroFirstRow = true;    
                break;    
            }    
        }    

        // Does first column have zero?    
        for (int i = 0; i < rownum; ++i) {    
            if (matrix[i][0] == 0) {    
                hasZeroFirstColumn = true;    
                break;    
            }    
        }   

        // find zeroes and store the info in first row and column    
        for (int i = 1; i < matrix.length; ++i) {    
            for (int j = 1; j < matrix[0].length; ++j) {    
                if (matrix[i][j] == 0) {    
                    matrix[i][0] = 0;    
                    matrix[0][j] = 0;    
                }    
            }    
        }  

        // set zeroes except the first row and column    
        for (int i = 1; i < matrix.length; ++i) {    
            for (int j = 1; j < matrix[0].length; ++j) {    
                if (matrix[i][0] == 0 || matrix[0][j] == 0) matrix[i][j] = 0;    
            }    
        }  

        // set zeroes for first row and column if needed    
        if (hasZeroFirstRow) {    
            for (int j = 0; j < colnum; ++j) {    
                matrix[0][j] = 0;    
            }    
        }    

        if (hasZeroFirstColumn) {    
            for (int i = 0; i < rownum; ++i) {    
                matrix[i][0] = 0;    
            }    
        }  
    }
}