[LeetCode] Set Matrix Zeroes-优快云博客

本文链接：https://blog.youkuaiyun.com/zjjee/article/details/41081995

本文详细介绍了如何在不使用额外空间的情况下，将矩阵中某一元素为零的整行和整列设置为零的方法。通过利用矩阵的第一行和第一列作为标记位，实现常量空间复杂度的操作。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

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?

class Solution {
public:
    void setZeroes(vector<vector<int> > &matrix) {
        int m = matrix.size(),n = matrix[0].size();
        vector<bool> col(n,false);
        vector<bool> row(m,false);
        for(int i = 0;i < m;i ++){
            for(int j = 0;j < n;j ++){
                if(matrix[i][j] == 0){
                    col[j] = true;
                    row[i] = true;
                }
            }
        }
        for(int k = 0;k < m;k ++){
            if(row[k] == true){
                for(int q = 0;q < n;q ++)
                        matrix[k][q] = 0;
            }
        }
        for(int k = 0;k < n;k ++){
            if(col[k] == true){
                for(int q = 0;q < m;q ++)
                        matrix[q][k] = 0;
            }
        }
    }
};

可使用第一行，第一列存储标记值，降低空间复杂度

class Solution {
public:
    void setZeroes(vector<vector<int> > &matrix) {
        int m = matrix.size(),n = matrix[0].size();
        bool isColZero = false;
        bool isRowZero = false;
        
        for(int i = 0;i < n;i ++){
            if(matrix[0][i] == 0){
                isColZero = true;
                break;
            }
        }
        for(int i = 0;i < m;i ++){
            if(matrix[i][0] == 0){
                isRowZero = true;
                break;
            }
        }
        for(int i = 0;i < m;i ++){
            for(int j = 0;j < n;j ++){
                if(matrix[i][j] == 0){
                    matrix[0][j] = 0;
                    matrix[i][0] = 0;
                }
            }
        }
        for(int i = 1;i < m;i ++){
            for(int j = 1;j < n;j ++){
                if(matrix[i][0] == 0 || matrix[0][j] == 0)
                    matrix[i][j] = 0;
            }
        }
        if(isRowZero == true){
           for(int q = 0;q < m;q ++)
                matrix[q][0] = 0;
        }
        if(isColZero == true){
            for(int q = 0;q < n;q ++)
                matrix[0][q] = 0;
        }
    }
};