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?

Solution1：Extra 行Mark数组 + 列Mark数组

思路：
Time Complexity: O(MN) Space Complexity: O(M + N)

Solution2：本身第一行／第一列作为行Mark数组 + 列Mark数组

思路： 将本身第一行／第一列作为行Mark数组 + 列Mark数组，额外两个变量first_row_mark / first_col_mark 作为第一行/第一列的mark。

Time Complexity: O(MN) Space Complexity: O(1)

Solution1 Code：

class Solution {
    public void setZeroes(int[][] matrix) {
        boolean[] row_mark = new boolean[matrix.length];
        boolean[] col_mark = new boolean[matrix[0].length];
        
        // when matrix[row][col] == 0, mark it on row_mark or col_mark.
        for(int row = 0; row < matrix.length; row++) {
            for(int col = 0; col < matrix[0].length; col++) {
                if(matrix[row][col] == 0) {
                    row_mark[row] = true;
                    col_mark[col] = true;
                }
            }
        }
        
        // set row or col to 0 based on mark arrays.
        
        for(int i = 0; i < row_mark.length; i++) {
            if(row_mark[i] == true) {
                for(int j = 0; j < matrix[0].length; j++) {
                    matrix[i][j] = 0;
                }
            }
        }
        for(int i = 0; i < col_mark.length; i++) {
            if(col_mark[i] == true) {
                for(int j = 0; j < matrix.length; j++) {
                    matrix[j][i] = 0;
                }
            }
        }
    }
}

Solution2 Code：

public class Solution {
    public void setZeroes(int[][] matrix) {
        
        boolean first_row_mark = false, first_col_mark= false;
        
        // when matrix[row][col] == 0, mark it on row_mark(first row here) or col_mark(first column here).
        for(int row = 0; row < matrix.length; row++) {
            for(int col = 0; col < matrix[0].length; col++) {
                if(matrix[row][col] == 0) {
                    if(row == 0) first_row_mark = true;
                    else if(col == 0) first_col_mark = true;
                    matrix[0][col] = 0;
                    matrix[row][0] = 0;
                }
            }
        }
        
        for(int row = 1; row < matrix.length; row++) {
            for(int col = 1; col < matrix[0].length; col++) {
                if(matrix[row][0] == 0 || matrix[0][col] == 0) {
                    matrix[row][col] = 0;
                }
            }
        }
        if(first_row_mark) {
            for(int j = 0; j < matrix[0].length; j++) {
                matrix[0][j] = 0;
            }
        }
        if(first_col_mark) {
            for(int i = 0; i < matrix.length; i++) {
                matrix[i][0] = 0;
            }
        } 
    }
}