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;
using System.Text;

namespace ConsoleApplication1
{
    class Node
    {
        internal int cost;
        internal bool isVisit;
        internal List<Edge> routes;

        public Node()
        {
            cost = int.MaxValue;
            isVisit = false;
            routes = new List<Edge>();
        }
    }

    class Edge : IComparable
    {
        internal int to;
        internal int cost;

        public Edge(int to, int cost)
        {
            this.to = to;
            this.cost = cost;
        }

        public int CompareTo(object obj)
        {
            Edge temp = obj as Edge;
            return this.cost - temp.cost;
        }
    }

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

            Node[] nodeList = Enumerable.Range(0, V).Select(a => new Node()).ToArray();

            for (int i = 0; i < E; i++)
            {
                input = Console.ReadLine().Split(' ');
                int s = int.Parse(input[0]);
                int t = int.Parse(input[1]);
                int d = int.Parse(input[2]);

                nodeList[s].routes.Add(new Edge(t, d));
            }

            Dijkstra(nodeList, r);
        }

        static void Dijkstra(Node[] NL, int start)
        {
            PriorityQueue<Edge> pq = new PriorityQueue<Edge>();

            NL[start].cost = 0;
            pq.Enqueue(new Edge(start, 0));

            while (pq.Count() > 0)
            {
                Edge edge = pq.Dequeue();
                int cur = edge.to;
                NL[cur].isVisit = true;

                if (NL[cur].cost < -edge.cost) continue;

                int outDegree = NL[cur].routes.Count;

                for (int j = 0; j < outDegree; j++)
                {
                    int next = NL[cur].routes[j].to;

                    if (NL[next].isVisit == true) continue;

                    if (NL[next].cost > NL[cur].cost + NL[cur].routes[j].cost)
                    {
                        NL[next].cost = NL[cur].cost + NL[cur].routes[j].cost;
                        pq.Enqueue(new Edge(next, -NL[next].cost));
                    }
                }
            }

            StringBuilder sb = new StringBuilder();
            int len = NL.Length;
            string temp = "";
            for (int i = 0; i < len; i++)
            {
                temp = NL[i].cost == int.MaxValue ? "INF" : NL[i].cost.ToString();
                sb.AppendLine(temp);
            }
            Console.Write(sb);
        }
    }

    class PriorityQueue<T> where T : IComparable
    {
        List<T> heap;
        int size;

        public PriorityQueue()
        {
            heap = new List<T>();
        }

        public void Enqueue(T x)
        {
            heap.Add(x);
            int i = size++;

            while (i > 0)
            {
                int p = (i - 1) / 2;

                if (Compare(heap[p], x) <= 0) break;

                heap[i] = heap[p];
                i = p;
            }
            heap[i] = x;
        }

        public T Dequeue()
        {
            T ret = heap[0];
            T x = heap[--size];

            int i = 0;
            while (i * 2 + 1 < size)
            {
                int a = i * 2 + 1;
                int b = i * 2 + 2;

                if (b < size && Compare(heap[b], heap[a]) < 0)
                    a = b;
                if (Compare(heap[a], x) >= 0)
                    break;

                heap[i] = heap[a];
                i = a;
            }
            heap[i] = x;
            heap.RemoveAt(size);
            return ret;
        }

        public int Count()
        {
            return size;
        }

        private int Compare(T x, T y)
        {
            return y.CompareTo(x);
        }
    }
}