算法导论第二十五章-所有结点对的最短路径问题-Cpp代码实现

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这一章就实现了一个Floyd算法。

其中路径的表示没有采用书上的前驱表示，而是用每一对结点中开始结点的后继来表示。

floyd_warshall.h

#pragma once/*************************************************Author:董小歪Date:2016-06-24Description:算法导论第二十五章-所有结点对的最短路径问题-Cpp代码实现**************************************************/#ifndef FLOYD_WARSHALL_H#define FLOYD_WARSHALL_H#include <iostream>#include <vector>using namespace std;class Floyd_Warshall{public:Floyd_Warshall(const vector<vector<int>> &_W);//构造函数vector<vector<int>> floyd_warshall();//Floyd算法void show_path();//显示计算结果void show_vec(const vector<vector<int>> &vec);private:vector<vector<int>> W;//输入邻接矩阵vector<vector<int>> path;//计算路径vector<vector<int>> D;//计算距离};#endif // !FLOYD_WARSHALL_H

floyd_warshall.cpp

#include "floyd-warshall.h"Floyd_Warshall::Floyd_Warshall(const vector<vector<int>> &_W) :W(_W){int n = W.size();path = vector<vector<int>>(n, vector<int>(n, -1));for (int i = 0; i < n; ++i)for (int j = 0; j < n; ++j)if (W[i][j] < INT_MAX)path[i][j] = j;//初始化路径。这里没有按书上的方法，存的是每一个点的后继而不是前驱。}vector<vector<int>> Floyd_Warshall::floyd_warshall(){int n = W.size();D = W;for (int k = 0; k < n; ++k){for (int i = 0; i < n; ++i){for (int j = 0; j < n; ++j){if (D[i][j] > D[i][k] + D[k][j]){D[i][j] = D[i][k] + D[k][j];//发现了更短的距离，取代前者path[i][j] = path[i][k];//更新路径}}}}return D;}void Floyd_Warshall::show_path(){int n = W.size();for (int i = 0; i < n; ++i){for (int j = 0; j < n; ++j){printf("结点%d到结点%d的最短路径是为%d,\t", i, j, D[i][j]);int k = path[i][j];if (k == -1)printf("路径不存在\n");else{printf("(%d", i);while (k != j){printf("->%d", k);k = path[k][j];}printf("->%d)\n", j);}}}}void Floyd_Warshall::show_vec(const vector<vector<int>> &vec){for (int i = 0; i < vec.size(); ++i){for (int j = 0; j < vec[i].size(); ++j){if (vec[i][j] < INT_MAX / 2)cout << vec[i][j] << "\t";elsecout << "∞" << "\t";}cout << endl;}}

测试代码：
main_entrance.cpp

#include "floyd-warshall.h"int main(){vector<vector<int>> W(5, vector<int>(5, INT_MAX / 2));W[0][1] = 3;W[0][2] = 8;W[0][4] = -4;W[1][3] = 1;W[1][4] = 7;W[2][1] = 4;W[3][0] = 2;W[3][2] = -5;W[4][3] = 6;for (int i = 0; i < W.size(); ++i)W[i][i] = 0;Floyd_Warshall fw(W);cout << "初始化的邻接矩阵为：" << endl;fw.show_vec(W);cout << endl << "Floyd计算后的邻接矩阵为：" << endl;fw.show_vec(fw.floyd_warshall());cout << "每两个结点之间的路径：" << endl;fw.show_path();system("pause");}

测试结果:

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