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 <iostream>
#include <vector>

using namespace std;

int main() {
	int V,E,r,s,t,din;
	vector<int> d,weight;
	vector<pair<int,int> > edge;
	cin >> V >> E >> r;
	for(int i=0;i<E;i++){
		cin >> s >> t >> din;
		edge.push_back(make_pair(s,t));
		weight.push_back(din);
	}

	for(int i=0;i<V;i++) {
		d.push_back(100000);
	}
	if(d.size()) d[r] = 0;
	if(!d.size()) d.push_back(0);
	for(int i=1;i<V;i++) {
		for(int j=0;j<edge.size();j++) {
			d[edge[j].second] = min(d[edge[j].second],d[edge[j].first]+weight[j]);
		}
	}
	for(int i=0;i<V;i++) {
		if(d[i] == 100000) {
			cout << "INF" << endl;
		} else {
		    cout << d[i] << endl;
		}
	}
}