Problem:
Single Source Shortest Path

For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).

Input

An edge-weighted graph G (V, E) and the source r.

|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1

|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

Print the costs of SSSP in the following format.

c0
c1
:
c|V|-1

The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print INF.

Constraints

1 ≤ |V| ≤ 100000

0 ≤ di ≤ 10000

0 ≤ |E| ≤ 500000

There are no parallel edges

There are no self-loops

Sample Input 1

4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5

Sample Output 1

0
1
3
4

Sample Input 2

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5

Sample Output 2

3
0
2
INF

Solution in C (judge verdict: Wrong Answer)

#include<stdio.h>
#include<math.h>
int R=1,C=1,H[1000010]={0};
int N[1000010]={-1000};
//ヒープに入れる
void hin(int a){
  int i=C++;
  for(N[R]=a;a<N[H[i/2]];i/=2)H[i]=H[i/2];
  H[i]=R++;
}
//ヒープから最小値を取り出す
int hout(){
  int rt=H[1],nt=1,i=0,k=H[--C];
  while(nt-i){
    H[i=nt]=k;
    if(i*2  <C&&N[  k  ]>N[H[i*2  ]])H[i]=H[nt=i*2  ];
    if(i*2+1<C&&N[H[nt]]>N[H[i*2+1]])H[i]=H[nt=i*2+1];
  }
  return rt;
}
int CO[100010];
void dijk(int v,int e,int *fr,int *to,int *co,int mi){
  int i,id[100010],ta[100010],nt[100010],f[100010]={0};
  for(i=0;i<v;i++)ta[i]=-1;
  for(i=0;i<v;i++)CO[i]=1000000000;
  for(i=CO[mi]=0;i<e;i++){
    nt[i]=ta[fr[i]];
    ta[fr[i]]=i;
  }
  while(f[mi]-1){
    f[mi]=1;
    for(i=ta[mi];i+1;i=nt[i]){
      if(CO[to[i]]>CO[mi]+co[i])hin(CO[id[R]=to[i]]=CO[mi]+co[i]);
    }
    while(f[mi]&&C-1)mi=id[hout()];
  }
}
int main(){
  int n,m,s,a[100010],b[100010],c[100010],i;
  scanf("%d %d %d",&n,&m,&s);
  for(i=0;i<m;i++)scanf("%d %d %d",&a[i],&b[i],&c[i]);
  dijk(n,m,a,b,c,s);
  for(i=0;i<n;i++)CO[i]-1000000000?printf("%d\n",CO[i]):printf("INF\n");
  return 0;
}