# 【图】最短路径Bellman-Ford算法

``````#include<iostream>
using namespace std;

const int max_num = 500;
const int max_len = 10000;
typedef struct Edge{
int begin;//起点
int end;//终点
int weight;//权值
}Edge;
class BellmanFord{
public:
void print_result();
void print_path(int end);
private:
bool bellman_ford();
private:
int node_num;//图的结点数
int edge_num;//图的路径数
int start; //源点
Edge edge[max_num];
int distance[max_num];//结点到源点最小距离
int pre[max_num];//源点到节点的路径
};
cin >> node_num >> edge_num >> start;
for (int i = 1; i <= edge_num; i++){
distance[i] = max_num;
pre[i] = i;
}

distance[start] = 0;
for (int i = 1; i <= edge_num; i++){
cin >> edge[i].begin >> edge[i].end >> edge[i].weight;
if (edge[i].begin == start){//注意这里设置初始情况
distance[edge[i].end] = edge[i].weight;
pre[edge[i].end] = start;
}
}
}
bool BellmanFord::bellman_ford(){
for (int i = 1; i < node_num; i++){
for (int j = 1; j <= edge_num; j++){//松弛计算
if (distance[edge[j].end]>distance[edge[j].begin] + edge[j].weight){
distance[edge[j].end] = distance[edge[j].begin] + edge[j].weight;
pre[edge[j].end] = edge[j].begin;
}
}
}
bool flag = true;
//判断是否有负环路
for (int j = 1; j <= edge_num; j++){
if (distance[edge[j].end]>distance[edge[j].begin] + edge[j].weight){
flag = false;
break;
}
}
return flag;
}
void BellmanFord::print_result(){
if (bellman_ford())
for (int i = 1; i <= node_num; i++){
cout << distance[i] << endl;
print_path(i);
}

else
cout << "有负环" << endl;
}
void BellmanFord::print_path(int end){
int que[max_num];
int count = 1;
que[count] = end;
count++;
int tmp = pre[end];
while (tmp != start){
que[count] = tmp;
count++;
tmp = pre[tmp];
}
que[count] = start;
cout << "源点到顶点"<<end<<"的路径为: ";
for (int i = count; i >= 1; i--)
if (i != 1)
cout << que[i] << " -> ";
else
cout << que[i] << endl;
}

int main(){
BellmanFord bellman_ford;