Set Matrix Zeroes

最新推荐文章于 2020-02-14 21:39:11 发布

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本文详细介绍了两种方法实现矩阵中元素置零的常空间复杂度解决方案，包括利用矩阵自身的首行和首列进行记录的方法，以及使用额外数组记录的方法。文章深入探讨了每种方法的原理、实现细节及其效率对比。

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?

CC上题目1.7

用两个array 来记录, 这种方法 space complexity is o(m+n), 第二种方法实现了 o（1）的space complexity

public class Solution {
    public void setZeroes(int[][] matrix) {
        if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
            return;
        }
        boolean[] row = new boolean[matrix.length];
        boolean[] col = new boolean[matrix[0].length];
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[0].length; j++) {
                if (matrix[i][j] == 0) {
                    row[i] = true;
                    col[j] = true;
                }
            }
        }
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[0].length; j++) {
                if (row[i] || col[j]) {
                    matrix[i][j] = 0;
                }
            }
        }
        
    }
}

这种方法是利用了了matrix 自身。用首行和首列的元素为坐标来记录，这种方法的前提是先记录好首行和首列是否为0

public class Solution {
     // using O(m+n) is easy, to enable O(1), we have to use the space within the matrix   
    public void setZeroes(int[][] matrix) {
        if(matrix == null || matrix.length == 0)
            return;
        
        int rows = matrix.length;
        int cols = matrix[0].length;
        
        boolean empty_row0 = false;
        boolean empty_col0 = false;
        for(int i = 0; i < cols; i++){
            if(matrix[0][i] == 0){
                empty_row0 = true;
                break;
            }
        }
        
        for(int i = 0; i < rows; i++){
            if(matrix[i][0] == 0){
                empty_col0 = true;
                break;
            }
        }
        
        for(int i = 1; i < rows; i++) {
            for(int j =1; j<cols; j++){
                if(matrix[i][j] == 0){
                    matrix[0][j] = 0;
                    matrix[i][0] = 0;
                }
            }
        }
        
        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;
            }
        }
      
        if(empty_row0){
            for(int i = 0; i < cols; i++){
                matrix[0][i] = 0;
            }           
        }
        
        if(empty_col0){
            for(int i = 0; i < rows; i++){
                matrix[i][0] = 0;
            }           
        }

    }
}