LeetCode: Set Matrix Zeroes 解题报告

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.

click to show follow up.

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?

SOLUTION 1:

题目要求O(1)的空间消耗。

1. 我们可以使用第一行，第一列来作为Flag，记录某一行，某一列是否应该被设置为0.

2. 因为第一行，第一列共用左上角的flag，所以我们需要另外找2个flag来定义第一行，第一列本身是否应该设置为0.

   row1Zero， col1Zero

3. 先扫描首行，首列把首行首列的flag算出。

4. 扫描其他的矩阵，将第一行每一列的flag算出。

5. 设置矩阵中除了首行首列的cells.

6. 设置首行，设置首列。

public class Solution {
    public void setZeroes(int[][] matrix) {
        if (matrix == null || matrix.length == 0 
            || matrix[0].length == 0) {
            return;        
        }
        
        boolean row1Zero = false;
        boolean col1Zero = false;
        
        int rows = matrix.length;
        int cols = matrix[0].length;
        
        // Determine if the first column should be Zero.
        for (int i = 0; i < rows; i++) {
            if (matrix[i][0] == 0) {
                col1Zero = true;
                break;
            }
        }
        
        // Determine if the first row should be Zero.
        for (int i = 0; i < cols; i++) {
            if (matrix[0][i] == 0) {
                row1Zero = true;
                break;
            }
        }
        
        // we use the first row and the first col as the flag to record the 
        // cells whether or not set to 0.
        for (int i = 1; i < rows; i++) {
            for (int j = 1; j < cols; j++) {
                // 注意了，这个矩阵是0和非0，并不是0和1.
                if (matrix[i][j] == 0) {
                    // set the flag in the first line and the first column                
                    matrix[i][0] = 0;
                    matrix[0][j] = 0;
                }
            }
        }
        
        // set the inner cells.
        // Be careful: i, j start from 1.
        for (int i = 1; i < rows; i++) {
            for (int j = 1; j < cols; j++) {
                if (matrix[i][0] == 0
                   || matrix[0][j] == 0) {
                    matrix[i][j] = 0;   
                }
            }
        }
        
        // set the first row.
        if (row1Zero) {
            for (int i = 0; i < cols; i++) {
                matrix[0][i] = 0;
            }    
        }
        
        // set the first col.
        if (col1Zero) {
            for (int i = 0; i < rows; i++) {
                matrix[i][0] = 0;
            }    
        }
        
        return;
    }
}

2014.1230 redo:

把前面三个循环合并，会简单一点儿。

public class Solution {
    public void setZeroes(int[][] matrix) {
        if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
            return;
        }
        
        boolean row1 = false;
        boolean col1 = false;
        
        int rows = matrix.length;
        int cols = matrix[0].length;
        
        // set flags.
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                if (matrix[i][j] != 0) {
                    continue;
                }
                
                // set the flag of a column and a row.
                matrix[0][j] = 0;
                matrix[i][0] = 0;
                
                //  get flag of first row.
                if (i == 0) {
                    row1 = true;
                }
                
                // get flag of first column.
                if (j == 0) {
                    col1 = true;
                }
            }
        }
        
        // set the matrix.
        for (int i = 1; i < rows; i++) {
            for (int j = 1; j < cols; j++) {
                if (matrix[0][j] == 0 || matrix[i][0] == 0) {
                    matrix[i][j] = 0;
                }
            }
        }
        
        // set first column
        if (col1) {
            for (int i = 0; i < rows; i++) {
                // bug 1: can't use matrix[i][j]
                matrix[i][0] = 0;
            }    
        }
        
        // set first row.
        if (row1) {
            for (int i = 0; i < cols; i++) {
                matrix[0][i] = 0;
            }    
        }
    }
}

GitHub Code:

SetZeroes.java