矩阵相关算法

矩阵旋转90度

给定一个 n × n 的二维矩阵 matrix 表示一个图像，请你将图像顺时针旋转 90 度。

#include <iostream>
#include <vector>using namespace std;void rotate(vector<vector<int>>& matrix) {int n = matrix.size();// 第一步：转置矩阵for (int i = 0; i < n; ++i) {for (int j = i + 1; j < n; ++j) {swap(matrix[i][j], matrix[j][i]);}}// 第二步：反转每一行for (int i = 0; i < n; ++i) {std::reverse(matrix[i].begin(), matrix[i].end());}
}int main() {vector<vector<int>> matrix = {{1, 2, 3},{4, 5, 6},{7, 8, 9}};rotate(matrix);// 输出结果for (const auto& row : matrix) {for (const auto& elem : row) {cout << elem << " ";}cout << endl;}return 0;
}

螺旋矩阵

将一个矩阵中的元素按照从右到左，从上到下，从右到左，从下到上依次输出

#include <iostream>
#include <vector>using namespace std;vector<int> spiralOrder(const vector<vector<int>>& matrix) {vector<int> result;if (matrix.empty()) return result;int top = 0, bottom = matrix.size() - 1;int left = 0, right = matrix[0].size() - 1;while (top <= bottom && left <= right) {// 从左到右遍历上边界for (int i = left; i <= right; i++) {result.push_back(matrix[top][i]);}top++;// 从上到下遍历右边界for (int i = top; i <= bottom; i++) {result.push_back(matrix[i][right]);}right--;//防止上面top++越界if (top <= bottom) {// 从右到左遍历下边界for (int i = right; i >= left; i--) {result.push_back(matrix[bottom][i]);}bottom--;}//防止上面right--越界if (left <= right) {// 从下到上遍历左边界for (int i = bottom; i >= top; i--) {result.push_back(matrix[i][left]);}left++;}}return result;
}int main() {vector<vector<int>> matrix = {{1, 2, 3},{4, 5, 6},{7, 8, 9}};vector<int> result = spiralOrder(matrix);// 输出结果for (int num : result) {cout << num << " ";}cout << endl;return 0;
}