[Luogu 3371] [TEMPLATE] single-source shortest path, luogu3371 single-source shortest path

[Luogu 3371] [TEMPLATE] single-source shortest path, luogu3371 single-source shortest path
Description

For example, a directed graph is provided. output the shortest path length from a certain point to all points.

Input/Output Format

Input Format:

The first line contains three integers, N, M, and S, indicating the number of vertices, the number of directed edges, and the number of the starting point.

Each row in the next M line contains three integers: Fi, Gi, and Wi, indicating the start point, target point, and length of the directed edge of the I.

Output Format:

A row contains N integers separated by spaces. the I-th integer indicates the shortest path length from vertex S to vertex I (if S = I, the shortest path length is 0, if the vertex S cannot reach the vertex I, the shortest path length is 2147483647)

Input and Output sample input sample #1:

4 6 11 2 22 3 22 4 11 3 53 4 31 4 4

Output sample #1:

0 2 4 3

Description

Time-Space limit: 1000 ms, 128 M

Data scale:

For 20% of data: N <= 5, M <= 15

For 40% of data: N <= 100, M <= 10000

For 70% of data: N <= 1000, M <= 100000

For 100% of data: N <= 10000, M <= 500000

Example:

Question:

Dijkstra:

 1 #include<cstdio> 2 #include<iostream> 3 #include<algorithm> 4 #include<cstring> 5 #include<queue> 6 #include<vector> 7 using namespace std; 8 const int INF=0x3f; 9 const int maxn=500050;10 int d[maxn];bool vis[maxn];11 vector<int> G[10004];12 int n,m,sta;13 struct Edge{int u,v,w;}e[maxn];14 struct node{15     int d,u;16     bool operator < (const node &sky) const {17         return sky.d<d;18     }19 };20 void dijkstra(int sta){21     priority_queue<node> q;22     memset(d,INF,sizeof(d)); d[sta]=0;23     q.push((node){0,sta});24     while(!q.empty()){25         node x=q.top();q.pop();26         int u=x.u;27         if(vis[u]) continue;28         for(int i=0;i<G[u].size();i++){29             Edge &edges=e[G[u][i]];30             if(d[edges.v]>d[u]+edges.w){31                 d[edges.v]=d[u]+edges.w;32                 q.push((node){d[edges.v],edges.v});33             }34         }35     }36 }37 int main(){38     scanf("%d%d%d",&n,&m,&sta);39     for(int i=1;i<=m;i++){40         scanf("%d%d%d",&e[i].u,&e[i].v,&e[i].w);41         G[e[i].u].push_back(i);42     }43     dijkstra(sta);44     for(int i=1;i<=n;i++){45         if(d[i]!=0x3f3f3f3f) printf("%d ",d[i]);46         else printf("2147483647 ");47     }48     return 0;49 }

Bellman-Ford:

Not optimized (70 ):

 1 #include<cstdio> 2 #include<iostream> 3 #include<algorithm> 4 #include<cstring> 5 #include<queue> 6 #include<vector> 7 #define maxn 500005 8 using namespace std; 9 int read(){10     int x=0,f=1;char ch=getchar();11     while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}12     while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}13     return x*f;14 }15 int n,m,sta;16 int u[maxn],v[maxn],w[maxn],d[maxn];17 int main(){18     n=read(),m=read(),sta=read();19     for(int i=1;i<=n;i++) d[i]=0x3f3f3f3f;20     d[sta]=0;21     for(int i=1;i<=m;i++) u[i]=read(),v[i]=read(),w[i]=read();22     for(int i=1;i<n;i++){23         for(int j=1;j<=m;j++){24             if(d[v[j]]>d[u[j]]+w[j]){25                 d[v[j]]=d[u[j]]+w[j];26             }27         }28     }29     for(int i=1;i<=n;i++){30         if(d[i]!=0x3f3f3f3f) printf("%d ",d[i]);31         else printf("2147483647 ");32     }33     return 0;34 }

Pruning optimization (100 ):

 1 #include<cstdio> 2 #include<iostream> 3 #include<algorithm> 4 #include<cstring> 5 #include<queue> 6 #include<vector> 7 #define maxn 500005 8 using namespace std; 9 int read(){10     int x=0,f=1;char ch=getchar();11     while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}12     while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}13     return x*f;14 }15 int n,m,sta;16 int u[maxn],v[maxn],w[maxn],d[maxn];17 int main(){18     n=read(),m=read(),sta=read();19     for(int i=1;i<=n;i++) d[i]=0x3f3f3f3f;20     d[sta]=0;21     for(int i=1;i<=m;i++) u[i]=read(),v[i]=read(),w[i]=read();22     for(int i=1;i<n;i++){23         bool flag=0;24         for(int j=1;j<=m;j++){25             if(d[v[j]]>d[u[j]]+w[j]){26                 flag=true;27                 d[v[j]]=d[u[j]]+w[j];28             }29         }30         if(!flag) break;31     }32     for(int i=1;i<=n;i++){33         if(d[i]!=0x3f3f3f3f) printf("%d ",d[i]);34         else printf("2147483647 ");35     }36     return 0;37 }

Spfa:

Adjacent table version:

 1 #include<cstdio> 2 #include<iostream> 3 #include<algorithm> 4 #include<cstring> 5 #include<queue> 6 #include<vector> 7 #define maxn 10005 8 using namespace std; 9 int read(){10     int x=0,f=1;char ch=getchar();11     while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}12     while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}13     return x*f;14 }15 struct edge{int v,w;};16 vector<edge>G[maxn];17 int d[maxn],n,m,sta;18 bool inq[maxn];19 void add(int u,int v,int w){G[u].push_back((edge){v,w});}20 void spfa(int sta){21     memset(d,-1,sizeof(d));22     d[sta]=0;23     memset(inq,0,sizeof(inq));24     queue<int> q;25     q.push(sta);26     while(!q.empty()){27         int k=q.front(); q.pop();28         inq[k]=0;29         for(int i=0;i<G[k].size();i++){30             edge &e=G[k][i];31             if(d[e.v]==-1||d[k]+e.w<d[e.v]){32                 d[e.v]=d[k]+e.w;33                 if(!inq[e.v]){34                     inq[e.v]=1;35                     q.push(e.v);36                 }37             }38         }39     }40 }41 int main(){42     n=read(),m=read(),sta=read();43     int u,v,w;44     for(int i=1;i<=m;i++){45         u=read(),v=read(),w=read();46         add(u,v,w);47     }48     spfa(sta);49     for(int i=1;i<=n;i++){50         if(d[i]==-1) printf("2147483647 ");51         else printf("%d ",d[i]);52     }53     return 0;54 }

Forward star version:

 1 #include<cstdio> 2 #include<iostream> 3 #include<algorithm> 4 #include<cstring> 5 #include<queue> 6 #include<vector> 7 #define maxn 10005 8 #define maxm 500005 9 using namespace std;10 int n,m,sta,last[maxn],cnt,inq[maxn],d[maxn];11 int read(){12     int x=0,f=1;char ch=getchar();13     while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}14     while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}15     return x*f;16 }17 struct edge{int to,next,cost;}e[maxm];18 void add(int x,int y,int z){e[++cnt].to=y;e[cnt].next=last[x];last[x]=cnt;e[cnt].cost=z;}19 void spfa(int sta){20     memset(d,-1,sizeof(d)); d[sta]=0;21     memset(inq,0,sizeof(inq));22     queue<int> q;23     q.push(sta);24     while(!q.empty()){25         int k=q.front(); q.pop();26         inq[k]=0;27         for(int i=last[k];i;i=e[i].next){28             int v=e[i].to;29             if(d[v]==-1||d[v]>d[k]+e[i].cost){30                 d[v]=d[k]+e[i].cost;31                 if(!inq[v]){32                     inq[v]=1;33                     q.push(v);34                 }35             }36         }37     }38 }39 int main(){40     n=read(),m=read(),sta=read();41     int u,v,w;42     for(int i=1;i<=m;i++){43         u=read(),v=read(),w=read();44         add(u,v,w);45     }46     spfa(sta);47     for(int i=1;i<=n;i++){48         if(d[i]==-1) printf("2147483647 ");49         else printf("%d ",d[i]);50     }51     return 0;52 }