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: Time Limit Exceeded)

#include <map>
#include <vector>
#include <iostream>

void calcShortestPath(std::map<int, std::map<int, int> > &path,
				      std::vector<long long> &shortestPath, int V, int E, int r);

const int INF = 99999;

int main()
{
	using namespace std;
	
	int V, E, r; // ????????°???????????°????§??????????
	cin >> V >> E >> r;
	
	map<int, map<int, int> > path;
	vector<long long> shortestPath;
	shortestPath.assign(V, INF);
	for (int i = 0; V > i; ++i) {
		path[i][i] = 0;
	}
	for (int i = 0; E > i; ++i) {
		int s, t, d; // ???????§??????????????????????????????????
		cin >> s >> t >> d;
		path[s][t] = d;
	}
	calcShortestPath(path, shortestPath, V, E, r);
	
	for (int i = 0; V > i; ++i) {
		if (INF != shortestPath[i]) {
			cout << shortestPath[i] << endl;
		}
		else {
			cout << "INF" << endl;
		}
	}
	
	return 0;
}

void calcShortestPath(std::map<int, std::map<int, int> > &path,
			std::vector<long long> &shortestPath, int V, int E, int r)
{
	for (int mid = 0; V > mid; ++mid) {
		for (int start = 0; V > start; ++start) {
			for (int goal = 0; V > goal; ++goal) {
				if (((path.end() != path.find(start)) && (path[start].end() != path[start].find(mid))) && 
					((path.end() != path.find(mid)) && (path[mid].end() != path[mid].find(goal)))) {
					int tmp = path[start][mid] + path[mid][goal];
					if((r == start) && (shortestPath[goal] > tmp)) {
						shortestPath[goal] = tmp;
					}
					if((path.end() != path.find(start)) && (path[start].end() != path[start].find(goal))) {
						if(path[start][goal] > tmp) {
							path[start][goal] = tmp;
						}
					}
					else {
						path[start][goal] = tmp;
					}
				}
			}
		}
	}
}