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)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ConsoleApplication1
{
    class Program
    {
        static int INF = Int32.MaxValue;

        static void Dfs(int wt, int pos, int[] dist, Dictionary<int, int> allDist, int V)
        {
            if (wt >= dist[pos]) return;
            dist[pos] = wt;

            for (int i = 0; i < V; i++)
            {
                if (pos == i) continue;
                var key = pos << 16 | i;
                if (!allDist.ContainsKey(key)) continue;
                Dfs(wt + allDist[key], i, dist, allDist, V);
            }
        }

        public static int[] GetDist(int V, int r, Dictionary<int, int> allDist)
        {
            var dist = new int[V];
            for (int i = 0; i < V; i++) dist[i] = INF;
            Dfs(0, r, dist, allDist, V);
            return dist;
        }

        static void Main(string[] args)
        {
            var str = Console.ReadLine();
            var V = Int32.Parse(str.Split()[0]);
            var E = Int32.Parse(str.Split()[1]);
            var r = Int32.Parse(str.Split()[2]);
            var allDist = new Dictionary<int, int>();

            for (int l = 0; l < E; l++)
            {
                str = Console.ReadLine();
                var s = Int32.Parse(str.Split()[0]);
                var t = Int32.Parse(str.Split()[1]);
                var d = Int32.Parse(str.Split()[2]);
                var key = s << 16 | t;
                if (!allDist.ContainsKey(key)) allDist.Add(key, d);
                else allDist[key] = Math.Min(allDist[key], d);
            }

            var dist = GetDist(V, r, allDist);

            for (int i = 0; i < V; i++)
            {
                Console.WriteLine(dist[i] == INF ? "INF" : string.Format("{0}", dist[i]));
            }
        }
    }
}