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: Accepted)

#include<queue>
#include<math.h>
#include<cmath>
#include<bitset>
#include<stdio.h>
#include<string>
#include<map>
#include<algorithm>
#include<vector>
#include<iostream>
#include<utility>
using namespace std;
typedef pair<int,int> P;
struct edge{
    int to;
    int cost;
    edge(int t, int w) : to(t), cost(w) { }
};
int main(){
  int i,V,e,r,s,t,d;
  int ds[100010],ns[100010];
  int INF=2000000000;
  priority_queue<P,vector<P>,greater<P> > que;
  vector<vector<edge> > g(100010);
  scanf("%d %d %d\n",&V,&e,&r);
  for(i=0;i<e;i++){
    scanf("%d %d %d\n",&s,&t,&d);
    g[s].push_back(edge(t,d));
  }
  for(i=0;i<V;i++){
    ds[i]=INF,ns[i]=0;
  }
  ds[r]=0,ns[r]=1;
  que.push(P(0,r));
  while(!que.empty()){
    P p=que.top();
    que.pop();
    int v=p.second;
    if(ds[v]<p.first){
      continue;
    }
    for(i=0;i<g[v].size();i++){
      edge us=g[v][i];
      if(ds[us.to]>ds[v]+us.cost && ns[us.to]==0){
        ds[us.to]=ds[v]+us.cost;
        que.push(P(ds[us.to],us.to));
      }
    }
    ns[v]=1;
  }
  for(i=0;i<V;i++){
    if(ds[i]==INF){
      printf("INF\n");
      continue;
    }
    printf("%d\n",ds[i]);
  }
  return 0;
}