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: Runtime Error)

#pragma warning disable

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.Serialization.Formatters.Binary;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
using System.Numerics;
using System.Collections;
using System.Timers;

static class MainClass
{
    public static void Main(string[] args)
    {
        var VEr = Console.ReadLine().SplittedStringToInt32List();
        var v = VEr[0];
        var e = VEr[1];
        var r = VEr[2];
        var ls = new List<Edge>();
        for (int i = 0; i < e; i++)
        {
            var item = Console.ReadLine().SplittedStringToInt32List();
            var edge = new Edge() { Cost = item[2], From = item[0], To = item[1] };
            ls.Add(edge);
        }
        InitializeDijkstra(v, e, ls);
        SearchShortestDistance(r);
        for (int i = 0; i < v; i++)
        {
            var omomi = ShortestDistances[i];
            if (omomi == INF)
                Console.WriteLine("INF");
            else
                Console.WriteLine(omomi);
        }

        Console.ReadLine();
    }



    public class DjkEdge
    {
        public int To;
        public int Cost;
    }

    public class Edge
    {
        public int To;
        public int From;
        public int Cost;
    }

    public class ComparablePair : IComparable<ComparablePair>
    {
        public int ShortestDistance;
        public int Number;

        public int CompareTo(ComparablePair other)
        {
            return ShortestDistance.CompareTo(other.ShortestDistance);
        }
    }

    public static int V;
    public static List<DjkEdge>[] Edges;
    public static int[] ShortestDistances;

    public static void InitializeDijkstra(int e,int v, List<Edge> es)
    {
        Edges = new List<DjkEdge>[e];
        for (int i = 0; i < e; i++)
        {
            Edges[i] = new List<DjkEdge>();
        }
        ShortestDistances = new int[v];
        V = v;
        foreach (var item in es)
        {
            Edges[item.From].Add(new DjkEdge() { Cost = item.Cost, To = item.To });
        }
    }

    public static void SearchShortestDistance(int s)
    {
        var queue = new PriorityQueue<ComparablePair>();
        for (int i = 0; i < V; i++)
        {
            ShortestDistances[i] = INF;
        }
        ShortestDistances[s] = 0;
        queue.Push(new ComparablePair() { Number = s, ShortestDistance = 0 });
        while (queue.Count != 0)
        {
            var p = queue.Pop();
            int v = p.Number;
            if (ShortestDistances[v] < p.ShortestDistance)
            {
                continue;
            }
            for (int i = 0; i < Edges[v].Count(); i++)
            {
                var e = Edges[v][i];
                if (ShortestDistances[e.To] > ShortestDistances[v] + e.Cost)
                {
                    ShortestDistances[e.To] = ShortestDistances[v] + e.Cost;
                    queue.Push(new ComparablePair() { ShortestDistance = ShortestDistances[e.To], Number = e.To });
                }
            }
        }
    }


    class PriorityQueue<T> where T : IComparable<T>
    {
        List<T> buffer;

        public PriorityQueue() { buffer = new List<T>(); }
        public PriorityQueue(int capacity) { buffer = new List<T>(capacity); }

        static void PushHeap(List<T> array, T elem)
        {
            int n = array.Count;
            array.Add(elem);

            while (n != 0)
            {
                int i = (n - 1) / 2;
                if (array[n].CompareTo(array[i]) > 0)
                {
                    T tmp = array[n]; array[n] = array[i]; array[i] = tmp;
                }
                n = i;
            }
        }


        static void PopHeap(List<T> array)
        {
            int n = array.Count - 1;
            array[0] = array[n];
            array.RemoveAt(array.Count - 1);

            for (int i = 0, j; (j = 2 * i + 1) < n;)
            {
                if ((j != n - 1) && (array[j].CompareTo(array[j + 1]) < 0))
                    j++;
                if (array[i].CompareTo(array[j]) < 0)
                {
                    T tmp = array[j]; array[j] = array[i]; array[i] = tmp;
                }
                i = j;
            }
        }


        public void Push(T elem)
        {
            PushHeap(this.buffer, elem);
        }


        public T Pop()
        {
            var data = buffer[0];
            PopHeap(buffer);
            return data;
        }

        public int Count
        {
            get { return buffer.Count; }
        }
    }

    #region ライブラリ
    public static long ToInt64(this string str) => long.Parse(str);
    public static int ToInt32(this string str) => int.Parse(str);
    public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
    public static List<string> SplittedStringToList(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).ToList();
    public static List<int> SplittedStringToInt32List(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => int.Parse(x)).ToList();
    public static List<BigInteger> SplittedStringToBigInteger(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => BigInteger.Parse(x)).ToList();

    public const int INF = int.MaxValue / 2;
    #endregion
}