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++14 (judge verdict: Accepted)

#include <iostream>
#include <algorithm>
#include <vector>
#include <deque>
#include <queue>
#include <list>
#include <stack>
#include <string>
#include <functional>
#include <numeric>
#include <cmath>
#include <iomanip>
#include <map>
#include <set>
#include <cstdlib>
#define INF 100000000
#define _INF -100000000
#define INFLL (long long)1e14
#define _INFLL (long long)-1e14
#define Loop(i, n) for(int i = 0; i < (int)n; i++)
#define Loop1(i, n) for(int i = 1; i <= (int)n; i++)
#define Loopr(i, n) for(int i = (int)n - 1; i >= 0; i--)
#define Loopr1(i, n) for(int i = (int)n; i >= 1; i--)
using namespace std;
typedef long long int ll;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef pair<ll, ll> P;

struct node {
	bool done;
	vi ed, dist;
	int id, from;
	ll d;
	bool operator<(const node & another) const {
		return !(d != another.d ? d < another.d : id < another.id);
	}
};


void dijkstra(vector<node> nodes, int n, int start) {
	priority_queue<node> pq;
	nodes[start].d = 0;
	pq.push(nodes[start]);
	while (pq.size()) {
		node focus = pq.top(); pq.pop();
		if (nodes[focus.id].done) continue;
		Loop(i, focus.ed.size()) {
			if (nodes[focus.ed[i]].done) continue;
			if (focus.d + focus.dist[i] < nodes[focus.ed[i]].d) {
				nodes[focus.ed[i]].d = focus.d + focus.dist[i];
				nodes[focus.ed[i]].from = focus.id;
				pq.push(nodes[focus.ed[i]]);
			}
		}
		nodes[focus.id].done = true;
	}
	Loop(i, n) {
		if (nodes[i].d == INFLL) cout << "INF" << endl;
		else {
			cout << nodes[i].d;
			/*
			stack<int> stk;
			node focus = nodes[i];
			stk.push(i);
			while (focus.from != -1) {
			stk.push(focus.from);
			focus = nodes[focus.from];
			}
			while (stk.size()) {
			cout << " " << stk.top();
			stk.pop();
			}
			*/
			cout << endl;
		}
	}
	return;
}

int main() {
	int v, e, r; cin >> v >> e >> r;
	vector<node> nodes(v + 5);
	Loop(i, v) nodes[i] = { false,{},{}, i, -1, INFLL };
	Loop(i, e) {
		int s, t, d; cin >> s >> t >> d;
		nodes[s].ed.push_back(t);
		nodes[s].dist.push_back(d);
		/*
		nodes[t].ed.push_back(s);
		nodes[t].dist.push_back(d);
		*/
	}
	dijkstra(nodes, v, r);
}