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++11 (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <queue>
#include <climits>

using namespace std;

int main(int argc, char **argv)
{
        int V, E, r;
        cin >> V >> E >> r;
        vector<vector< pair<int, int>>> A(V);
        for (int i = 0; i < E; i++) {
                int s, t, d;
                cin >> s >> t >> d;
                A[s].push_back({t, d});
        }
        vector<int> d(V, INT_MAX);
        d[r] = 0;
        bool done = false;
        while (!done) {
                done = true;
                for (int i = 0; i < V; i++) {
                        if (d[i] == INT_MAX)
                                continue;
                        for (auto n: A[i]) {
                                int m = d[i] + n.second;
                                if (m < d[n.first]) {
                                        d[n.first] = m;
                                        done = false;
                                }
                        }
                }
        }
        for (int i = 0; i < V; i++) {
                if (d[i] == INT_MAX)
                        cout << "INF";
                else
                        cout << d[i];
                cout << endl;
        }
        return 0;
}