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: Accepted)

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

namespace AOJGPL_1_A
{
    class Program
    {
        static void Main(string[] args)
        {
            var VEr = ReadInt();
            int V = VEr[0];
            int E = VEr[1];
            int r = VEr[2];

            List<int>[] edges = new List<int>[V].Select(x => new List<int>()).ToArray();
            List<int>[] distance = new List<int>[V].Select(x => new List<int>()).ToArray();

            for (int i = 0; i < E; i++)
            {
                var input = ReadInt();
                edges[input[0]].Add(input[1]);
                distance[input[0]].Add(input[2]);
            }

            long[] ans = new long[V].Select(x => long.MaxValue).ToArray();
            ans[r] = 0;

            Queue<int> que = new Queue<int>();
            que.Enqueue(r);
            while (que.Count > 0)
            {
                int now = que.Dequeue();

                //決定済みなら行かない
                //if (ans[now] != long.MaxValue && ans[now] != 0) continue;

                for (int i = 0; i < edges[now].Count; i++)
                {
                    long cand = ans[now] + distance[now][i];
                    if (ans[edges[now][i]] > cand)
                    {
                        ans[edges[now][i]] = cand;
                        que.Enqueue(edges[now][i]);
                    }
                }
            }

            foreach (var a in ans)
            {
                if (a == long.MaxValue) Console.WriteLine("INF");
                else Console.WriteLine(a);
            }
            Console.ReadKey();
        }

        static int[] ReadInt()
        {
            int[] ret = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return ret;
        }
        static long[] ReadLong()
        {
            long[] ret = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return ret;
        }
    }
}