POJ 3255 - Roadblocks（次短路）

Roadblocks Time Limit: 2000MS   Memory Limit: 65536K Total Submissions: 16533   Accepted: 5829 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 intersection N. 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 Line 1: Two space-separated integers: N and R  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 Line 1: The length of the second shortest path between node 1 and node N Sample Input 4 4 1 2 100 2 4 200 2 3 250 3 4 100 Sample Output 450 Hint Two routes: 1 -> 2 -> 4 (length 100+200=300) and 1 -> 2 -> 3 -> 4 (length 100+250+100=450) Source USACO 2006 November Gold

题意：

要绝对意义的次短路，一定要比最短路短

#include <string>
#include <string.h>
#include <iostream>
#include <queue>
#include <math.h>
#include <stdio.h>
#include <algorithm>
using namespace std;
#define LL long long
const int maxn = 200000+55;
const int inf = 0x3f3f3f3f;
int n,m;
int head[5555],nxt[maxn],to[maxn],sz=0,w[maxn];
int dis[5555][2];
typedef pair<int, int> pi;
void dij()
{
for(int i=1;i<=n;i++) dis[i][0]=dis[i][1]=inf;
priority_queue&l
e824
t;pi,vector<pi>,greater<pi> >q;
q.push(make_pair(0, 1));
while(!q.empty()){
int now=q.top().first;
int u=q.top().second;
q.pop();
if(dis[u][1]<now) continue;
for(int i=head[u];~i;i=nxt[i]){
int v=to[i];
int ww=w[i];
if(now+ww<dis[v][0]){
dis[v][1]=now+ww;
swap(dis[v][1], dis[v][0]);
q.push(make_pair(dis[v][0], v));
}else if(now+ww<dis[v][1]&&now+ww>dis[v][0]){
dis[v][1]=now+ww;
q.push(make_pair(dis[v][1],v));
}
}
}
printf("%d\n",dis
[1]);
}
int main()
{
scanf("%d %d",&n,&m);
for(int i=1;i<=n;i++) head[i]=-1;
for(int i=1;i<=m;i++){
int u,v,ww;
scanf("%d %d %d",&u,&v,&ww);
nxt[sz]=head[u],to[sz]=v,w[sz]=ww,head[u]=sz++;
nxt[sz]=head[v],to[sz]=u,w[sz]=ww,head[v]=sz++;
}
dij();

return 0;
}