最短路径——floyd（多源最短路径）

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <queue>
#include <malloc.h>

using namespace std;

const int VERTEX_NUM = 20;
const int INFINITY = 0x7fffffff;

bool vis[VERTEX_NUM];
int dist[VERTEX_NUM][VERTEX_NUM]; 

class Graph {
public:
	int vexNum;
	int edgeNum;
	int vex[VERTEX_NUM];
	int arc[VERTEX_NUM][VERTEX_NUM];
};

void createGraph(Graph &G)
{
	cout << "please input vexNum and edgeNum: ";
	cin >> G.vexNum >> G.edgeNum;
	for (int i = 0; i != G.vexNum; ++i) {
		cout << "please input no" << i+1 << " vertex: ";
		cin >>  G.vex[i];				// 自定义顶点序号
	}
	for (int i = 0; i != G.vexNum; ++i) {
		for (int j = 0; j != G.vexNum; ++j) {
			if (i == j)	G.arc[i][j] = 0;
			else	G.arc[i][j] = INFINITY;
		}
	}
	for (int k = 0; k != G.edgeNum; ++k) {
		cout << "please input the vertex of edge(vi, vj) and weight: ";
		int i, j, w;
		cin >> i >> j >> w;
		G.arc[i][j] = w;
		G.arc[j][i] = G.arc[i][j];
	}
}

// Floyd算法
void floyd(Graph &G)
{
	memset(dist, INFINITY, VERTEX_NUM);
	for (int k = 0; k != G.vexNum; ++k) {
		for (int i = 0; i != G.vexNum; ++i) {
			for (int j = 0; j != G.vexNum; ++j) {
				if (G.arc[i][j] > G.arc[i][k] + G.arc[k][j] && G.arc[i][k] < INFINITY && G.arc[k][j] < INFINITY) {
					G.arc[i][j] = G.arc[i][k] + G.arc[k][j];
				}
			}
		}
	}
}

int main()
{
	Graph G;
	createGraph(G);
	floyd(G);
	for (int i = 0; i != G.vexNum; ++i) {
		for (int j = 0; j != G.vexNum; ++j) {
			if (i == j) continue;
			cout << "源点" << i << "到点" << j << "的距离为" << G.arc[i][j] << endl;
		}
	}
	return 0;
}

时间复杂度：O(n³)

测试及结果：