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;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;
using static ShortestPath;

public class A { public static void Main() => (new Solver()).Solve(); }

public class Solver
{
	public void Solve()
	{
		long V = GetLong();
		long E = GetLong();
		long r = GetLong();
		var adj = Range(0, V).Select(_ => new List<Edge<long>>()).ToArray();
		for(long i = 0; i < E; i++)
		{
			long s = GetLong();
			long t = GetLong();
			long d = GetLong();
			adj[s].Add(new Edge<long>(t, d));
		}

		long inf = long.MaxValue / 2;
		var ans = Dijkstra(adj, inf, r, (x, y) => x + y);
		WriteLine(string.Join("\n", ans.Select(x => (x == inf) ? "INF" : $"{x}")));
	}
}

public static class ShortestPath
{
	public struct Edge<T>
	{
		public long To;
		public T Cost;

		public Edge(long to, T cost)
		{
			To = to;
			Cost = cost;
		}
	}

	public static T[] Dijkstra<T>(T[,] cost, T inf, long s, Func<T, T, T> add) where T : IComparable<T>
	{
		long V = cost.GetLength(0);	
		var used = new bool[V];
		var d = Enumerable.Repeat(inf, (int)V).ToArray();
		d[s] = default(T);

		while(true)
		{
			long v = -1;
			for(long u = 0; u < V; u++)
				if(!used[u] && (v == -1 || d[u].CompareTo(d[v]) < 0))
					v = u;

			if(v == -1)
				break;

			used[v] = true;
			for(long u = 0; u < V; u++)
			{
				var tmp = add(d[v], cost[v, u]);
				if(d[u].CompareTo(tmp) > 0)
					d[u] = tmp;
			}
		}
		return d;
	}

	public static T[] Dijkstra<T>(List<Edge<T>>[] adj, T inf, long s, Func<T, T, T> add) where T : IComparable<T>
	{
		Comparison<Tuple<T, long>> comp = ((x, y) => x.Item1.CompareTo(y.Item1));
		var pq = new PriorityQueue<Tuple<T, long>>(adj.Length, comp);

		var d = Enumerable.Repeat(inf, adj.Length).ToArray();
		d[s] = default(T);
		pq.Push(Tuple.Create(d[s], s));
		while(pq.Count > 0)
		{
			var p = pq.Pop();
			long v = p.Item2;
			if(d[v].CompareTo(p.Item1) < 0)
				continue;

			for(long i = 0; i < adj[v].Count; i++)
			{
				var edge = adj[v][(int)i];
				var tmp = add(d[v], edge.Cost);
				if(d[edge.To].CompareTo(tmp) > 0)
				{
					d[edge.To] = tmp;
					pq.Push(Tuple.Create(d[edge.To], edge.To));
				}
			}
		}
		return d;
	}
}

public class PriorityQueue<T>
{
	public long Count { get; private set; } = 0;
	public long MaxSize { get; private set; } = 0;
	private T[] m_heap;
	private Comparison<T> Comp = null;
	
	public PriorityQueue(long maxSize, Comparison<T> comp)
	{
		if(maxSize <= 0)
			throw new Exception();
		MaxSize = maxSize;
		m_heap = new T[maxSize];

		Comp = comp;
	}
	
	public void Push(T x)
	{
		if(Count == MaxSize)
		{
			T[] new_heap = new T[MaxSize << 1];
			Array.Copy(m_heap, new_heap, MaxSize);
			m_heap = new_heap;
			MaxSize <<= 1;
		}
		
		long i = Count++;
		while(i > 0)
		{
			long p = (i - 1)/2;
			if(Comp(m_heap[p], x) <= 0)
				break;
			m_heap[i] = m_heap[p];
			i = p;			
		}
		m_heap[i] = x;		
	}
	
	public T Pop()
	{
		if(Count == 0)
			throw new Exception("Queue is empty.");
		
		T result = m_heap[0];
		T x = m_heap[--Count];
		long i = 0;
		while(i * 2 + 1 < Count)
		{
			long c1 = i * 2 + 1, c2 = i * 2 + 2;
			if(c2 < Count && Comp(m_heap[c2], m_heap[c1]) < 0)
				c1 = c2;
			if(Comp(m_heap[c1], x) >= 0)
				break;
			m_heap[i] = m_heap[c1];
			i = c1;
		}
		m_heap[i] = x;
		
		return result;		
	}
	
	public T Peek() => m_heap[0];
}

public static class MyIO
{
	private static string[] args = new string[0];
	private static int cnt = 0;
	private static IEnumerable<string> getArgs(long N) => Range(0, N).Select(_ => getArg());
	private static string getArg()
	{
		if(cnt == args.Length) { args = Console.ReadLine().Split(); cnt = 0; }
		return args[cnt++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static decimal GetDecimal() => decimal.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(long N) => getArgs(N).Select(int.Parse).ToArray();
	public static long[] GetLongs(long N) => getArgs(N).Select(long.Parse).ToArray();
	public static double[] GetDoubles(long N) => getArgs(N).Select(double.Parse).ToArray();
	public static decimal[] GetDecimals(long N) => getArgs(N).Select(decimal.Parse).ToArray();
	public static string[] GetStrings(long N) => getArgs(N).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) < 0) x = y; }
	public static void chmin<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) > 0)	x = y; }
	public static void swap<T>(ref T x, ref T y) { T tmp = x; x = y; y = tmp; }
	public static long rightShift(long x, long y) => (x >> (int)y);
	public static long leftShift(long x, long y) => (x << (int)y);
	public static bool contains(long s, long x) => (rightShift(s, x) & 1L) == 1L;
	public static long gcd(long x, long y) => (y == 0) ? x : gcd(y, x % y);
	public static long lcm(long x, long y) => (x / gcd(x,y)) * y;	
	public static IEnumerable<int> Range(long start, long count) => Enumerable.Range((int)start, (int)count);
	public static void Sort(this List<string> source) => source.Sort(StringComparer.Ordinal);
}