题目链接:http://acm.sdut.edu.cn/sdutoj/problem.php?action=showproblem&problemid=2493
题意:给定一个无向图,N个点,M条边,有一个天使可以让其中的一条边的权值减半。求最短路。
解题思路:用两次最短路算法,dis1和dis2存储的分别为s和e到其他点的权值未减半前的最短路。然后枚举每条边就可以了。
Min_Cost = Min(Min_Cost,dis1[edge[i].u] + edge[i].w/2 + dis2[edge[i].v]);
#include <iostream> #include <cstdio> #include <cmath> #include <cstring> #include <algorithm> #define LL long long #define Max(a,b) ((a) > (b) ? (a) : (b)) #define Min(a,b) ((a) < (b) ? (a) : (b)) using namespace std; const LL INF = (1<<30); struct E { int u,v,w; }edge[100010]; LL dis1[1010],dis2[1010]; void dij(int s,int n,int m,LL *dis) { bool mark; int i ,j; for(i = 0;i <= n; ++i) { dis[i] = INF; } dis[s] = 0; for(i = 0;i < n; ++i) { mark = true; for(j = 0;j < m; ++j) { if(dis[edge[j].u] < dis[edge[j].v] - edge[j].w) { dis[edge[j].v] = dis[edge[j].u] + edge[j].w; mark = false; } } if(mark) break; } } int main() { int n,m; int s,e; int i; LL Min_Cost; while(scanf("%d %d",&n,&m) != EOF) { for(i = 0;i < m; ++i) { scanf("%d %d %d",&edge[i].u,&edge[i].v,&edge[i].w); } for(i = 0;i < m; ++i) { edge[i+m] = edge[i]; s = edge[i+m].u; edge[i+m].u = edge[i+m].v; edge[i+m].v = s; } scanf("%d %d",&s,&e); dij(s,n,m*2,dis1); dij(e,n,m*2,dis2); Min_Cost = INF; for(i = 0;i < m*2; ++i) { Min_Cost = Min(Min_Cost,dis1[edge[i].u] + edge[i].w/2+dis2[edge[i].v]); } if(Min_Cost == INF) { cout<<"No solution"<<endl; } else { cout<<Min_Cost<<endl; } } return 0; }