Dijkstra算法无法判断含负权边的图的最短路。如果遇到负权,在没有负权回路存在时(负权回路的含义是,回路的权值和为负。)即便有负权的边,也可以采用Bellman-Ford算法正确求出最短路径。
主要是做N次松弛,用变量记录入队列的次数和是否入过队列,如果每次都如队列则判定有负环
#include
#include
#include
#include
#include
#include
using namespace std;
#define maxn 1000
#define INF 1<<30
struct Edge{
int from , to ,val;
Edge(int from,int to,int val) : from(from),to(to),val(val){}
};
int m , n , dest;
int d[maxn],p[maxn];
vector edges;
vector G[maxn];
void init(int n) {
for(int i = 0;i< n;i++) G[i].clear();
edges.clear();
}
void addEdge(int from,int to,int val) {
edges.push_back(Edge(from,to,val));
m = edges.size();
G[from].push_back(m - 1);
}
bool bellman_ford (int s) {
for(int i = 0;i<= m;i++) d[i] = INF;
d[s] = 0;
for(int i = 0;i< n;i++) {
bool change = false;
for(int j = 0; j<= m;j++) {
Edge e = edges[j];
if(d[e.to] > d[e.from] + e.val && d[e.from] < INF) {
d[e.to] = d[e.from] + e.val;
p[e.to] = j;
change = true;
}
}
if(!change) return true;
if(i == n-1 && change)return false;
}
return false;
}
void print(int end) {
Edge e = edges[p[end]];
if(end == 1) {
printf("%d(%d)",e.from,0);
return;
}
if(e.from != end) {
print(e.from);
printf("->%d(%d)",e.to,e.val);
}
}
int main()
{
freopen("in.txt","r",stdin);
while(~scanf("%d%d",&n,&m) && n> 0) {
init(n);
int from,to ,val;
for(int i = 0 ;i< n;i++) {
scanf("%d%d%d",&from,&to,&val);
addEdge(from,to,val);
}
if(bellman_ford(1)) {
print(m);
cout<