hdu1688 Sightseeing（次短路）

题目链接：

hdu1688

题意：

给你n个点，m条有向边，问你从s走到t点最短路加上最短路权值加一的路径条数

数据范围：

2≤n≤1000,1≤m≤10000，1≤s,t≤n,s≠t，且没有自环

题解：

我们相当于求最短路和次短路，注意这里的次短路是权值的次短。然后注意处理最小和次小的关系！！

代码：

#include<cstdio>
#include<cstring>
#include<iostream>
#include<sstream>
#include<algorithm>
#include<vector>
#include<bitset>
#include<set>
#include<queue>
#include<stack>
#include<map>
#include<cstdlib>
#include<cmath>
#define PI 2*asin(1.0)
#define LL long long
#define pb push_back
#define pa pair<int,int>
#define clr(a,b) memset(a,b,sizeof(a))
#define lson lr<<1,l,mid
#define rson lr<<1|1,mid+1,r
#define bug(x) printf("%d++++++++++++++++++++%d\n",x,x)
#define key_value ch[ch[root][1]][0]
const int  MOD = 1000000007;
const int N = 1000 + 15;
const int maxn = 1e4+ 14;
const int letter = 130;
const int INF = 1e9;
const double pi=acos(-1.0);
const double eps=1e-8;
using namespace std;
inline int read()
{
int x=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
return x*f;
}
int n,m,s,t,head
,tot;
int dis
[2],vis
[2],path
[2];
struct edges{
int to,next,val;
}e[maxn];
void add(int u,int v,int val){
e[tot].val=val,e[tot].to=v,e[tot].next=head[u],head[u]=tot++;
}
struct node{
int x,val,mark;
node(){}
node(int x,int val,int mark):x(x),val(val),mark(mark){}
bool operator < (const node &p) const{
return val>p.val;
}
};
priority_queue<node>pq;
void dijstra(int s,int t){
while(!pq.empty()) pq.pop();
for(int i=1;i<=n;i++) dis[i][0]=dis[i][1]=INF;
clr(vis,0),clr(path,0);
dis[s][0]=0;
path[s][0]=1;
pq.push(node(s,0,0));
while(!pq.empty()){
node now=pq.top();
pq.pop();
int x=now.x,mark=now.mark;
if(vis[x][now.mark]) continue;
vis[x][now.mark]=1;
for(int i=head[x];i!=-1;i=e[i].next){

int to=e[i].to,val=e[i].val;
if(dis[x][mark]+val<dis[to][0]){
if(dis[to][0]!=INF){
dis[to][1]=dis[to][0];
path[to][1]=path[to][0];
pq.push(node(to,dis[to][1],1));
}
dis[to][0]=dis[x][mark]+val;
path[to][0]=path[x][mark];
pq.push(node(to,dis[to][0],0));
}
else if(dis[x][mark]+val==dis[to][0]){
path[to][0]+=path[x][mark];
}
else if(dis[x][mark]+val<dis[to][1]){
dis[to][1]=dis[x][mark]+val;
path[to][1]=path[x][mark];
pq.push(node(to,dis[to][1],1));
}
else if(dis[x][mark]+val==dis[to][1]){
path[to][1]+=path[x][mark];
}
}
}
///for(int i=1;i<=n;i++) printf("i = %d %d %d\n",i,dis[i][0],dis[i][1]);
int ans=path[t][0];
if(dis[t][0]==dis[t][1]-1) ans+=path[t][1];
printf("%d\n",ans);
}
int main(){
int T,u,v,w;
scanf("%d",&T);
while(T--){
clr(head,-1),tot=0;
scanf("%d%d",&n,&m);
for(int i=0;i<m;i++){
scanf("%d%d%d",&u,&v,&w);
add(u,v,w);
}
scanf("%d%d",&s,&t);
dijstra(s,t);
}
return 0;
}