LeetCode 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.

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?

一开始想到了空间O(m + n)的算法，用一个数组arr[m+n]记录某行或者某列是否需要设为0，遍历一遍数组，若num[i][j]==0，则对应的赋值arr[i]=0,arr[m+j]=0即可。

没想到constant的方法，上网搜一番之后发现：
没有必要新开一个arr[m+n]数组，其实遍历num[i][j]==0后，直接将num[i][0]与num[0][j]设为0即可~~确实啊！！！

不过对于首行和首列，这样直接改变它们的值会影响它们原本的值，而首行与首列是否set为0又是由它们原本的值决定的，因此一开始先扫一遍首行与首列，确定它们是否需要set，再扫描i=[2...m]与j=[2...n]，判断其他行与列。

代码：

    public void setZeroes(int[][] matrix) {
        if (matrix.length == 0) return;
        int m = matrix.length, n = matrix[0].length;
        boolean row = false, col = false;
        
        // Check first row & col
        if (matrix[0][0] == 0) {
            row = true;
            col = true;
        } else {
            for (int i = 1; i < m; i++) {
                if (matrix[i][0] == 0) {
                    col = true; 
                    matrix[0][0] = 0;
                    break;
                } 
            }
            
            for (int j = 1; j < n; j++) {
                if (matrix[0][j] == 0) {
                    row = true; 
                    matrix[0][0] = 0;
                    break;
                }             
            }
        }
        
        // Check other rows & cols
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                if (matrix[i][j] == 0) {
                    matrix[i][0] = 0;
                    matrix[0][j] = 0;
                }
            }
        }
        
        // Assign rows
        for (int i = 1; i < m; i++) {
            if (matrix[i][0] == 0) {
                for (int j = 1; j < n; j++) matrix[i][j] = 0;
            }
        }
        
        // Assign cols
        for (int j = 1; j < n; j++) {
            if (matrix[0][j] == 0) {
                for (int i = 1; i < m; i++) matrix[i][j] = 0;
            }
        }
        
        // Assign first row & col
        if (col) {
            for (int i = 1; i < m; i++) matrix[i][0] = 0;
        }
        if (row) {
            for (int j = 1; j < n; j++) matrix[0][j] = 0;
        }
        
    }