面试经典150题 P73 矩阵置零

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时间轴

时间轴

2025-11-17

init

矩阵

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题目：

P73 矩阵置零

https://leetcode.cn/problems/set-matrix-zeroes/?envType=study-plan-v2&envId=top-interview-150

最开始我是这样写的，但是用哈希表存储效率很低。

#include <vector>
#include <unordered_set>

using std::vector;
using std::unordered_set;

class Solution {
    public:
	void setZeroes(vector<vector<int> > &matrix)
	{
		unordered_set<int> iuset;
		unordered_set<int> juset;
		int i, j, m = matrix.size(), n = matrix[0].size();
		for (i = 0; i < m; i++) {
			for (j = 0; j < n; j++) {
				if (matrix[i][j] == 0) {
					iuset.insert(i);
					juset.insert(j);
				}
			}
		}
		for (i = 0; i < m; i++) {
			if (iuset.count(i)) { // 这一行都为0
				std::fill(matrix[i].begin(), matrix[i].end(), 0);
				continue;
			}
			for (j = 0; j < n; j++) {
				if (juset.count(j)) {
					matrix[i][j] = 0;
				}
			}
		}
	}
};

可以改成数组形式记录：

class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix) {
        int m = matrix.size();
        int n = matrix[0].size();
        vector<int> row(m), col(n);

        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (!matrix[i][j]) {
                    row[i] = col[j] = true;
                }
            }
        }
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (row[i] || col[j]) {
                    matrix[i][j] = 0;
                }
            }
        }
    }
};

如果要再节省空间的话，可以找到数组中第一个为 0 的元素，用它的行列数组当作记录为 0 的行/列。最后再把它置零。

leetcode hot 100 rewrite:

#include <vector>
using std::vector;

class Solution {
    public:
        void setZeroes(vector<vector<int> > &matrix)
        {
                int i, j, m = matrix.size(), n = matrix[0].size();
                int flagi, flagj;
                bool fflag = false;

                for (i = 0; i < m; i++) {
                        for (j = 0; j < n; j++) {
                                if (matrix[i][j] == 0) {
                                        flagi = i;
                                        flagj = j;
                                        fflag = true;
                                        break;
                                }
                        }
                        if (fflag)
                                break;
                }
                if (!fflag) // 没有一个0
                        return;

                for (i = 0; i < m; i++) {
                        if (matrix[i][flagj] != 0) {
                                // if matrix[i][flagj] == 0 it means row(行)i is 0
                                matrix[i][flagj] = -1;
                        }
                }

                for (j = 0; j < n; j++) {
                        if (matrix[flagi][j] != 0) {
                                // if matrix[flagi][j] == 0 it means column(行)j is 0
                                matrix[flagi][j] = -1;
                        }
                }

                for (i = 0; i < m; i++) {
                        if (i == flagi)
                                continue;
                        for (j = 0; j < n; j++) {
                                if (j == flagj)
                                        continue;
                                if (matrix[i][j] == 0) {
                                        matrix[flagi][j] = 0; // tag as column j is 0
                                        matrix[i][flagj] = 0; // tag as row i is 0
                                }
                        }
                }
                for (i = 0; i < m; i++) {
                        if (matrix[i][flagj] == 0) {
                                // i 行都是 0
                                if (i == flagi)
                                        continue;
                                for (j = 0; j < n; j++) {
                                        if (j == flagj)
                                                continue;
                                        matrix[i][j] = 0;
                                }
                        }
                }

                for (j = 0; j < n; j++) {
                        if (matrix[flagi][j] == 0) {
                                // 第j列都是0
                                if (j == flagj)
                                        continue;
                                for (i = 0; i < m; i++) {
                                        if (i == flagi)
                                                continue;
                                        matrix[i][j] = 0;
                                }
                        }
                }

                for (i = 0; i < m; i++)
                        matrix[i][flagj] = 0;

                for (j = 0; j < n; j++)
                        matrix[flagi][j] = 0;
        }
};

#include <stdio.h>
int main()
{
        Solution S;
        vector<vector<int> > matrix = { { 1, 1, 1 }, { 1, 0, 1 }, { 1, 1, 1 } };
        S.setZeroes(matrix);
        for (vector<int> &vec : matrix) {
                for (int val : vec) {
                        printf("%d ", val);
                }
                printf("\n");
        }
}