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.Linq;
using System.Collections.Generic;

namespace ForPaiza
{
    class Program
    {
        static void Main(string[] args)
        {
            var buffer = Console.ReadLine().Split();
            var V = int.Parse(buffer[0]);
            var E = int.Parse(buffer[1]);
            var r = int.Parse(buffer[2]);

            var entryList = new List<Entry>();
            for(var i = 0; i < E; i += 1)
            {
                buffer = Console.ReadLine().Split();
                var s = int.Parse(buffer[0]);
                var t = int.Parse(buffer[1]);
                var d = int.Parse(buffer[2]);

                entryList.Add(new Entry(s, t, d));
            }

            var graph = Enumerable.Range(0, V).Select(x => new Node(x, entryList.Where(y => y.start == x).ToList())).ToArray();

            /*
            foreach (var node in graph)
            {
                Console.Write("{0} {1} : ", node.nodeNum, node.cost);
                foreach (var link in node.linkData)
                {
                    Console.Write("node {0} cost {1}", link.end, link.cost);
                }
                Console.WriteLine();
            }
            */
            var openNodeSet = new HashSet<Node>();
            var closeNodeSet = new HashSet<Node>();
            
            openNodeSet.Add(graph[r]);
            graph[r].cost = 0;

            while (openNodeSet.Count != 0)
            {
                var nowNode = openNodeSet.Where(x => x.cost == openNodeSet.Min(y => y.cost)).First();

                openNodeSet.Remove(nowNode);
                closeNodeSet.Add(nowNode);
                foreach(var entry in nowNode.linkData)
                {
                    var linkNode = graph[entry.end];
                    if(!closeNodeSet.Contains(linkNode))
                    {
                        openNodeSet.Add(linkNode);
                        linkNode.cost = Math.Min(linkNode.cost, nowNode.cost + entry.cost);
                    }
                }
            }

            foreach(var node in graph)
            {
                var message = (node.cost == int.MaxValue) ? "INF" : node.cost.ToString();
                Console.WriteLine(message);
            }
        }

        class Entry
        {
            public int start;
            public int end;
            public int cost;

            public Entry(int s, int t, int d)
            {
                start = s;
                end = t;
                cost = d;
            }
        }

        class Node
        {
            public readonly int nodeNum;
            public int cost;
            public List<Entry> linkData;

            public Node(int num)
            {
                nodeNum = num;
                cost = int.MaxValue;
            }

            public Node(int num, List<Entry> _linkData)
            {
                nodeNum = num;
                cost = int.MaxValue;
                linkData = new List<Entry>(_linkData);
            }
        }
    }
}