HDU 3416 Marriage Match IV (求最短路的条数,最大流)
2016-08-09 10:42
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Marriage Match IV
题目链接:
http://acm.hust.edu.cn/vjudge/contest/122685#problem/QDescription
Do not sincere non-interference。Like that show, now starvae also take part in a show, but it take place between city A and B. Starvae is in city A and girls are in city B. Every time starvae can get to city B and make a data with a girl he likes. But there are two problems with it, one is starvae must get to B within least time, it's said that he must take a shortest path. Other is no road can be taken more than once. While the city starvae passed away can been taken more than once.
So, under a good RP, starvae may have many chances to get to city B. But he don't know how many chances at most he can make a data with the girl he likes . Could you help starvae?
Input
The first line is an integer T indicating the case number.(1<=T<=65)For each case,there are two integer n and m in the first line ( 2<=n<=1000, 0<=m<=100000 ) ,n is the number of the city and m is the number of the roads.
Then follows m line ,each line have three integers a,b,c,(1<=a,b<=n,0<c<=1000)it means there is a road from a to b and it's distance is c, while there may have no road from b to a. There may have a road from a to a,but you can ignore it. If there are two roads from a to b, they are different.
At last is a line with two integer A and B(1<=A,B<=N,A!=B), means the number of city A and city B.
There may be some blank line between each case.
Output
Output a line with a integer, means the chances starvae can get at most.Sample Input
3 7 8 1 2 1 1 3 1 2 4 1 3 4 1 4 5 1 4 6 1 5 7 1 6 7 1 1 7 6 7 1 2 1 2 3 1 1 3 3 3 4 1 3 5 1 4 6 1 5 6 1 1 6 2 2 1 2 1 1 2 2 1 2
Sample Output
21
1
Hint
题意:
求最短路的条数.要求这些路径互相没有相同的边.
题解:
由于要求同一条边不能出现在两条最短路中.所以直接标记出最短路中的边,对这些边跑一次最大流即可. (这里直接用了sap模版)
若这个题没有不共边的要求,就直接对最短路中的边dfs即可.
HDU1142-A Walk Through the Forest
题解:http://www.cnblogs.com/Sunshine-tcf/p/5752205.html
代码:
#include <iostream> #include <cstdio> #include <cstring> #include <cmath> #include <algorithm> #include <queue> #include <map> #include <set> #include <vector> #define LL long long #define eps 1e-8 #define maxn 501000 #define mod 1000000007 #define inf 0x3f3f3f3f #define IN freopen("in.txt","r",stdin); using namespace std; int n, m; typedef pair<int,int> pii; priority_queue<pii,vector<pii>,greater<pii> > q; bool vis[maxn]; int edges, u[maxn], v[maxn], w[maxn]; int first[maxn], _next[maxn]; int dist[maxn]; int pre1[maxn]; void add_edge(int s, int t, int val) { u[edges] = s; v[edges] = t; w[edges] = val; _next[edges] = first[s]; first[s] = edges++; } void dijkstra(int s) { memset(pre1, -1, sizeof(pre1)); memset(vis, 0, sizeof(vis)); for(int i=1; i<=n; i++) dist[i]=inf; dist[s] = 0; while(!q.empty()) q.pop(); q.push(make_pair(dist[s], s)); while(!q.empty()) { pii cur = q.top(); q.pop(); int p = cur.second; if(vis[p]) continue; vis[p] = 1; for(int e=first[p]; e!=-1; e=_next[e]) if(dist[v[e]] > dist[p]+w[e]){ dist[v[e]] = dist[p] + w[e]; q.push(make_pair(dist[v[e]], v[e])); pre1[v[e]] = p; } } } //最大流SAP struct Node { int to,_next,cap; }edge[maxn]; int tol; int head[maxn]; int gap[maxn],dis[maxn],pre[maxn],cur[maxn]; void init() { tol=0; memset(head,-1,sizeof(head)); } void addedge(int u,int v,int w,int rw=0) { edge[tol].to=v;edge[tol].cap=w;edge[tol]._next=head[u];head[u]=tol++; edge[tol].to=u;edge[tol].cap=rw;edge[tol]._next=head[v];head[v]=tol++; } int sap(int start,int end,int nodenum) { memset(dis,0,sizeof(dis)); memset(gap,0,sizeof(gap)); memcpy(cur,head,sizeof(head)); int u=pre[start]=start,maxflow=0,aug=-1; gap[0]=nodenum; while(dis[start]<nodenum) { loop: for(int &i=cur[u];i!=-1;i=edge[i]._next) { int v=edge[i].to; if(edge[i].cap&&dis[u]==dis[v]+1) { if(aug==-1||aug>edge[i].cap) aug=edge[i].cap; pre[v]=u; u=v; if(v==end) { maxflow+=aug; for(u=pre[u];v!=start;v=u,u=pre[u]) { edge[cur[u]].cap-=aug; edge[cur[u]^1].cap+=aug; } aug=-1; } goto loop; } } int mindis=nodenum; for(int i=head[u];i!=-1;i=edge[i]._next) { int v=edge[i].to; if(edge[i].cap&&mindis>dis[v]) { cur[u]=i; mindis=dis[v]; } } if((--gap[dis[u]])==0)break; gap[dis[u]=mindis+1]++; u=pre[u]; } return maxflow; } int main(void) { //IN; int t; cin >> t; int ca = 1; while(t--) { memset(first, -1, sizeof(first)); edges = 0; cin >> n >> m; while(m--) { int u,v,w; scanf("%d %d %d", &u, &v, &w); if(u == v) continue; add_edge(u, v, w); } int s, t; cin >> s >> t; dijkstra(s); init(); for(int e=0; e<edges; e++) { //判断是否是最短路上的边 if(dist[v[e]] == dist[u[e]]+w[e]) { addedge(u[e], v[e], 1); } } int paths = sap(s, t, n); printf("%d\n", paths); } return 0; }
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