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

namespace GPL1A_2{
    public class Program{
        public static void Main(string[] args){
            var sr = new StreamReader();
            //---------------------------------
            var V = sr.Next<int>();
            var E = sr.Next<int>();
            var R = sr.Next<int>();

            var dj = new Dijkstra(V);
            for(var i = 0; i < E; i++){
                dj.AddEdge(sr.Next<int>(), sr.Next<int>(), sr.Next<int>());
            }

            var sb = new StringBuilder();
            foreach(var i in dj.Solve(R)){
                sb.AppendLine(i != int.MaxValue ? i.ToString() : "INF");
            }
            Console.Write(sb);
            //---------------------------------
        }
    }

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

        public class Node : IComparable<Node>{
            public int Id;
            public int Cost;

            public int CompareTo(Node node){
                return Math.Sign(Cost - node.Cost);
            }
        }

        private readonly List<Edge>[] _adj;

        public Dijkstra(int v){
            _adj = new List<Edge>[v];
            for(var i = 0; i < v; i++) _adj[i] = new List<Edge>();
        }

        public void AddEdge(int from, int to, int cost){
            _adj[from].Add(new Edge{To = to, Cost = cost});
        }

        public int[] Solve(int start){
            var v = _adj.Length;
            var used = new bool[v];
            var res = new int[v];

            for(var i = 0; i < v; i++) res[i] = int.MaxValue;
            res[start] = 0;

            var pq = new PriorityQueue<Node>();
            pq.Enqueue(new Node{Id = start, Cost = 0});

            while(pq.Count > 0){
                var stat = pq.Dequeue();
                var from = stat.Id;
                used[from] = true;

                foreach(var edge in _adj[from]){
                    var to = edge.To;
                    var cost = stat.Cost + edge.Cost;

                    if(used[to] || cost > res[to]) continue;
                    res[to] = cost;
                    pq.Enqueue(new Node{Id = to, Cost = cost});
                }
            }
            return res;
        }
    }

    public class PriorityQueue<T> : IEnumerable<T> where T : IComparable<T>{
        private readonly List<T> _list = new List<T>();

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

        IEnumerator<T> IEnumerable<T>.GetEnumerator(){
            return _list.GetEnumerator();
        }

        IEnumerator IEnumerable.GetEnumerator(){
            return _list.GetEnumerator();
        }

        public void Clear(){
            _list.Clear();
        }

        public bool Contains(T value){
            return _list.Contains(value);
        }

        public T Peek(){
            return _list[0];
        }

        public void Enqueue(T value){
            _list.Add(value);
            PushHeap();
        }

        public T Dequeue(){
            var ret = _list[0];
            _list[0] = _list[Count - 1];
            _list.RemoveAt(Count - 1);
            PopHeap();
            return ret;
        }

        private void PushHeap(){
            var i = Count - 1;
            while(i != 0){
                var p = (i - 1) / 2;
                if(_list[i].CompareTo(_list[p]) > 0) return;

                SwapIndex(i, i = p);
            }
        }

        private void PopHeap(){
            var i = 0;
            while(true){
                var l = 2 * i + 1;
                var r = l + 1;

                var maxi = i;
                if(l < Count && _list[maxi].CompareTo(_list[l]) > 0) maxi = l;
                if(r < Count && _list[maxi].CompareTo(_list[r]) > 0) maxi = r;
                if(maxi == i) return;

                SwapIndex(i, i = maxi);
            }
        }

        private void SwapIndex(int left, int right){
            var tmp = _list[left];
            _list[left] = _list[right];
            _list[right] = tmp;
        }
    }

    public class StreamReader{
        private readonly char[] _c = {' '};
        private int _index = -1;
        private string[] _input = new string[0];

        public T Next<T>(){
            if(_index == _input.Length - 1){
                _index = -1;
                while(true){
                    string rl = Console.ReadLine();
                    if(rl == null){
                        if(typeof(T).IsClass) return default(T);
                        return (T)typeof(T).GetField("MinValue").GetValue(null);
                    }
                    if(rl != ""){
                        _input = rl.Split(_c, StringSplitOptions.RemoveEmptyEntries);
                        break;
                    }
                }
            }
            return (T)Convert.ChangeType(_input[++_index], typeof(T), System.Globalization.CultureInfo.InvariantCulture);
        }

        public T[] Next<T>(int x){
            var ret = new T[x];
            for(var i = 0; i < x; ++i) ret[i] = Next<T>();
            return ret;
        }

        public T[][] Next<T>(int y, int x){
            var ret = new T[y][];
            for(var i = 0; i < y; ++i) ret[i] = Next<T>(x);
            return ret;
        }
    }
}