三种
1.Floyd复杂度高，可求多源最短路，可有负边权，本质是DP
2.SPFA复杂度容易被坑，单源最短路，可有负边权
3.dijkstra复杂度好，单源最短路，无负边权
SPFA容易被卡数据，一般用dijkstra
1 #include<cstdio> 2 #include<algorithm> 3 #include<vector> 4 #include<queue> 5 #define N 10002 6 #define M 1000002 7 #define inf 2147483647 8 using namespace std; 9 struct edge 10 { 11 int v,w; 12 edge(){} 13 edge(int _v,int _w):v(_v),w(_w) 14 {} 15 }; 16 int n,m,s; 17 bool inq[N]; 18 long long dis[N]; 19 queue<int>q; 20 vector<edge>e[N]; 21 int cnt[N]; 22 void add(int u,int v,int w) 23 { 24 e[u].push_back(edge(v,w)); 25 } 26 int main() 27 { 28 scanf("%d%d%d",&n,&m,&s); 29 for(int i=1,u,v,w;i<=m;i++) 30 { 31 scanf("%d%d%d",&u,&v,&w); 32 add(u,v,w); 33 } 34 for(int i=1;i<=n;i++) dis[i]=inf; 35 q.push(s); 36 inq[s]=1; 37 dis[s]=0; 38 //O(km) k<=4 SPFA 39 while(!q.empty()) 40 { 41 int t=q.front(); 42 inq[t]=0; 43 q.pop(); 44 for(int i=0;i<e[t].size();i++) 45 { 46 if(dis[t]+e[t][i].w<dis[e[t][i].v]) 47 { 48 dis[e[t][i].v]=dis[t]+e[t][i].w; 49 if(!inq[e[t][i].v]) q.push(e[t][i].v),inq[e[t][i].v]=1; 50 } 51 } 52 } 53 for(int i=1;i<=n;i++) printf("%lld ",dis[i]); 54 return 0; 55 }
SPFA
#include <cstdio> #include <algorithm> using namespace std; const int N = 2005; const int M = 2e5 + 5; double dis[N]; bool vis[N]; struct edge { int to, next; double w; } e[M]; int head[N], cnt; int n, m; void add(int u, int v, double w) { e[++cnt].w = w; e[cnt].to = v; e[cnt].next = head[u]; head[u] = cnt; } void dijkstra(int x) { for (int i = 1; i <= n; i++) dis[i] = 0; dis[x] = 1; for (int i = 1; i <= n; i++) { int p = 0; for (int j = 1; j <= n; j++) { if (!vis[j]) if (p == 0 || dis[j] > dis[p]) p = j; } vis[p] = 1; for (int j = head[p]; j; j = e[j].next) if (!vis[e[j].to] && dis[p] * e[j].w > dis[e[j].to]) dis[e[j].to] = dis[p] * e[j].w; } } int main() { scanf("%d%d", &n, &m); for (int i = 1, u, v, w; i <= m; i++) { scanf("%d%d%d", &u, &v, &w); add(u, v, 1 - w / 100.00); add(v, u, 1 - w / 100.0); } int p, q; scanf("%d%d", &p, &q); dijkstra(p); printf("%.8lf ", 100 / dis[q]); return 0; }
dijkstra