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: Memory Limit Exceeded)

using System.Collections.Generic;
using System;

public class PriorityQueue<T> where T : IComparable
{
    private IComparer<T> _comparer = null;
    private int _type = 0;
    private T[] _heap;
    private int _sz = 0;
    private int _count = 0;
    /// <summary>
    /// Priority Queue with custom comparer
    /// </summary>
    public PriorityQueue(int maxSize, IComparer<T> comparer)
    {
        _heap = new T[maxSize];
        _comparer = comparer;
    }

    /// <summary>
    /// Priority queue
    /// </summary>
    /// <param name="maxSize">max size</param>
    /// <param name="type">0: asc, 1:desc</param>
    public PriorityQueue(int maxSize, int type = 0)
    {
        _heap = new T[maxSize];
        _type = type;
    }
    private int Compare(T x, T y)
    {
        if (_comparer != null) return _comparer.Compare(x, y);
        return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
    }
    public void Push(T x)
    {
        _count++;
        //node number
        var i = _sz++;
        while (i > 0)
        {
            //parent node number
            var p = (i - 1) / 2;

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

            _heap[i] = _heap[p];
            i = p;
        }
        _heap[i] = x;
    }
    public T Pop()
    {
        _count--;
        T ret = _heap[0];
        T x = _heap[--_sz];

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

            if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

            if (Compare(_heap[a], x) >= 0) break;

            _heap[i] = _heap[a];
            i = a;
        }
        _heap[i] = x;
        return ret;
    }
    public int Count()
    {
        return _count;
    }
    public T Peek()
    {
        return _heap[0];
    }
    public bool Contains(T x)
    {
        for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
        return false;
    }
    public void Clear()
    {
        while (this.Count() > 0) this.Pop();
    }
    public IEnumerator<T> GetEnumerator()
    {
        var ret = new List<T>();
        while (this.Count() > 0)
        {
            ret.Add(this.Pop());
        }
        foreach (var r in ret)
        {
            this.Push(r);
            yield return r;
        }
    }
    public T[] ToArray()
    {
        T[] array = new T[_sz];
        int i = 0;
        foreach (var r in this)
        {
            array[i++] = r;
        }
        return array;
    }
}
public class Node : IComparable
{
    public int id { get; set; }
    public int d { get; set; }
    public int CompareTo(object obj)
    {
        var x = (Node)obj;
        if (this.d > x.d) return 1;
        else if (this.d == x.d) return 0;
        else return -1;
    }
}
public class Hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        var pq = new PriorityQueue<Node>(n+5000, 0);
        var e = int.Parse(line[1]);
        var r = int.Parse(line[2]);
        var a = new int[n, n];
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < n; j++)
                if (i == j) a[i, j] = 0;
                else a[i, j] = -1;
        }
        for (int i = 0; i < e; i++)
        {
            string[] line2 = Console.ReadLine().Trim().Split(' ');
            var s = int.Parse(line2[0]);
            var t = int.Parse(line2[1]);
            var d = int.Parse(line2[2]);
            a[s, t] = d;
        }
        var mind = new int[n];
        for (int i = 0; i < n; i++) mind[i] = 9999999;
        goDijk(pq, a, r, n ,mind);
        foreach (var x in mind)
            if (x == 9999999) Console.WriteLine("INF");
            else Console.WriteLine(x);
    }
    public static void goDijk(PriorityQueue<Node> pq, int[,] a, int r, int n ,int[] mind)
    {
        pq.Push(new Node { id = r, d = 0 });
        while (pq.Count() > 0)
        {
            var targ = pq.Pop();
            var nowd = targ.d;
            var nowid = targ.id;
            if (mind[nowid] < nowd) continue;
            mind[nowid] = nowd;
            for (int i = 0; i < n; i++)
            {
                if (a[nowid, i] != -1 && (nowd + a[nowid, i] < mind[i]))
                    pq.Push(new Node { id = i, d = nowd + a[nowid, i] });
            }
        }




    }
}