一、单源最短路
1、正权
dijkstra
2、任意权
2、1 bellman-ford
2、2 spfa
二、任意点之间最短路
floyd
三、最短路的应用：差分约束系统
参考模板
http://www.toposort.com/blog/shortest-path.html
贴一个新的最新的 spfa模板:
1 #include <iostream> 2 #include <cstdio> 3 #include <cstring> 4 #include <cstdlib> 5 #include <cmath> 6 #include <queue> 7 #include <algorithm> 8 #include <vector> 9 #define LL __int64 10 const int maxm = 2e6 + 10; 11 const int maxn = 5e5 + 10; 12 const int INF = 1<<28; 13 using namespace std; 14 int cnt, head[maxn], d[maxn], vis[maxn], n, m; 15 16 struct node 17 { 18 int v, w, next; 19 }edge[2*maxm]; 20 21 void add(int u, int v, int w) 22 { 23 edge[cnt].v = v; 24 edge[cnt].w = w; 25 edge[cnt].next = head[u]; 26 head[u] = cnt++; 27 }; 28 29 void spfa(int s) 30 { 31 queue<int>q; 32 int i, u, v; 33 for(i = 0; i <= n; i++) 34 d[i] = INF; 35 d[s] = 0; 36 37 q.push(s); 38 39 vis[s] = 1; 40 while(!q.empty()) 41 { 42 u = q.front(); 43 q.pop(); 44 vis[u] = 0; 45 for(i = head[u]; i != -1; i = edge[i].next) 46 { 47 v=edge[i].v; 48 if(d[u] + edge[i].w < d[v]) 49 { 50 d[v] = d[u] + edge[i].w; 51 if(!vis[v]) 52 { 53 vis[v] = 1; 54 q.push(v); 55 } 56 } 57 } 58 } 59 }; 60 int main() 61 { 62 int i; 63 int a, b, w; 64 int s, t; 65 while(~scanf("%d%d", &n, &m)) 66 { 67 cnt = 0; 68 memset(head, -1, sizeof(head)); 69 memset(vis, 0, sizeof(vis)); 70 for(i = 0; i < m; i++) 71 { 72 scanf("%d%d%d", &a, &b, &w); 73 add(a, b, w); 74 add(b, a, w); 75 } 76 scanf("%d%d", &s, &t); 77 spfa(s); 78 printf("%d\n", d[t]); 79 } 80 }