| Time Limit: 2000MS | Memory Limit: 65536K | |
| Total Submissions: 15645 | Accepted: 5504 |
Description
Bessie has moved to a small farm and sometimes enjoys returning to visit one of her best friends. She does not want to get to her old home too quickly, because she likes the scenery along the way. She has decided to take the second-shortest rather than the shortest path. She knows there must be some second-shortest path.
The countryside consists of R (1 ≤ R ≤ 100,000) bidirectional roads, each linking two of the N (1 ≤ N ≤ 5000) intersections, conveniently numbered 1..N. Bessie starts at intersection 1, and her friend (the destination) is at intersectionN.
The second-shortest path may share roads with any of the shortest paths, and it may backtrack i.e., use the same road or intersection more than once. The second-shortest path is the shortest path whose length is longer than the shortest path(s) (i.e., if two or more shortest paths exist, the second-shortest path is the one whose length is longer than those but no longer than any other path).
Input
Lines 2..R+1: Each line contains three space-separated integers: A, B, and D that describe a road that connects intersections A and B and has length D (1 ≤ D ≤ 5000)
Output
Sample Input
4 4 1 2 100 2 4 200 2 3 250 3 4 100
Sample Output
450
Hint
Source
#include <ctype.h> #include <cstdio> #include <vector> #include <queue> #define BUF 100000010 #define M 100005 #define N 5005 char Buf[BUF],*buf=Buf; struct Edge { int next,to,w; }; Edge edge1[M<<1],edge2[M<<1]; using namespace std; int n,r,cnt,dis[N],head1[N],head2[N]; bool vis[N]; struct node { int to,g; bool operator<(node a)const { return g+dis[to]>a.g+dis[a.to]; } }; struct Node { int x,y; bool operator<(Node a)const { return y>a.y; } }; inline void Read(register int &x) { for(x=0;!isdigit(*buf);++buf); for(;isdigit(*buf);x=x*10+*buf-'0',++buf); } inline void ins(int u,int v,int w) { edge1[++cnt].next=head1[u]; edge1[cnt].to=v; edge1[cnt].w=w; head1[u]=cnt; edge2[cnt].next=head2[v]; edge2[cnt].to=u; edge2[cnt].w=w; head2[v]=cnt; edge1[++cnt].next=head1[v]; edge1[cnt].to=u; edge1[cnt].w=w; head1[v]=cnt; edge2[cnt].next=head2[u]; edge2[cnt].to=v; edge2[cnt].w=w; head2[u]=cnt; } void dij(int s) { for(int i=1;i<n;++i) dis[i]=0x7fffffff; priority_queue<Node>q; dis[s]=0; Node a; a.x=s; a.y=dis[s]; q.push(a); for(Node now;!q.empty();) { now=q.top(); q.pop(); if(vis[now.x]) continue; vis[now.x]=1; for(register int i=head2[now.x];i;i=edge2[i].next) { int v=edge2[i].to; if(dis[v]>dis[now.x]+edge2[i].w) { dis[v]=dis[now.x]+edge2[i].w; Node tmp; tmp.x=v; tmp.y=dis[v]; q.push(tmp); } } } } int Astar(register int s,register int t) { priority_queue<node>q; node a; a.to=s;a.g=0; q.push(a); register int ct=0; for(node now;!q.empty();) { now=q.top();q.pop(); if(now.to==t) ct++; if(ct==2) return now.g; for(register int i=head1[now.to];i;i=edge1[i].next) { int v=edge1[i].to; node tmp; tmp.to=v;tmp.g=now.g+edge1[i].w; q.push(tmp); } } return 0; } void write(register int x) { if(x>9) write(x/10); putchar(x%10+'0'); } int Main() { #define MINE #ifdef MINE freopen("block.in","r",stdin); freopen("block.out","w",stdout); fread(buf,1,BUF,stdin); #endif Read(n); Read(r); for(register int x,y,z;r--;) { Read(x); Read(y); Read(z); ins(x,y,z); } dij(n); write(Astar(1,n)); return 0; } int sb=Main(); int main(int argc,char *argv[]) {;}
2. spfa
#include <ctype.h> #include <cstdio> #include <vector> #include <queue> #define M 100005 #define N 5005 struct Edge { int next,from,to,w; Edge (int next=0,int from=0,int to=0,int w=0) :next(next),from(from),to(to),w(w) {} }edge[M<<1]; using namespace std; int n,r,cnt,dis1[N],dis2[N],head[N]; bool vis[N]; inline void Read(int &x) { bool f=0; register char ch=getchar(); for(x=0;!isdigit(ch);ch=getchar()) if(ch=='-') f=1; for(;isdigit(ch);x=x*10+ch-'0',ch=getchar()); x=f?-x:x; } void ins(int u,int v,int w) { edge[++cnt]=Edge(head[u],u,v,w); head[u]=cnt; edge[++cnt]=Edge(head[v],v,u,w); head[v]=cnt; } void spfa(int s,int *dis) { queue<int>q; q.push(s); for(int i=1;i<=n;++i) dis[i]=0x7fffffff; dis[s]=0; vis[s]=1; for(int now;!q.empty();) { now=q.front(); q.pop(); vis[now]=0; for(int i=head[now];i;i=edge[i].next) { int v=edge[i].to; if(dis[v]>dis[now]+edge[i].w) { dis[v]=dis[now]+edge[i].w; if(!vis[v]) { vis[v]=1; q.push(v); } } } } } int main() { Read(n); Read(r); for(int x,y,z;r--;) { Read(x); Read(y); Read(z); ins(x,y,z); } spfa(1,dis1); spfa(n,dis2); int Min=dis1[n],ans=0x7fffffff,dist; for(int i=1;i<=cnt;++i) { int u=edge[i].from,v=edge[i].to; dist=dis1[u]+edge[i].w+dis2[v]; if(dist>Min&&dist<ans) ans=dist; } printf("%d\n",ans); return 0; }