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 Program
    {
        /// <summary>
        /// find the shortest path from start to all destination
        /// works for directed/nondirected graph
        /// </summary>
        public class BellmanFord
        {
            public List<edge> Edge = new List<edge>();
            public int V;   // number of vertex

            public class edge
            {
                public int from, to, cost;
                public edge(int _from, int _to, int _cost)
                {
                    from = _from;
                    to = _to;
                    cost = _cost;
                }
            }

            public BellmanFord(int v)
            {
                V = v;
            }

            /// <summary>
            ///  return shortestPath[V] represents distance from startIndex
            /// </summary>
            public int[] GetShortestPath(int startIndex)
            {
                int[] shortestPath = new int[V];
                var INF = Int32.MaxValue;

                for (int i = 0; i < V; i++) shortestPath[i] = INF;
                shortestPath[startIndex] = 0;
                while (true)
                {
                    bool update = false;
                    foreach (edge e in Edge)
                    {
                        if (shortestPath[e.from] != INF && shortestPath[e.to] > shortestPath[e.from] + e.cost)
                        {
                            shortestPath[e.to] = shortestPath[e.from] + e.cost;
                            update = true;
                        }
                    }
                    if (!update) break;
                }

                return shortestPath;
            }

            /// <summary>
            ///  return true if it has negative close loop
            /// </summary>
            public bool HasNegativeLoop()
            {
                int[] d = new int[V];
                for (int i = 0; i < V; i++)
                {
                    foreach (edge e in Edge)
                    {
                        if (d[e.to] > d[e.from] + e.cost)
                        {
                            d[e.to] = d[e.from] + e.cost;
                            if (i == V - 1) return true;
                        }
                    }
                }
                return false;
            }
        }

        static void Main(string[] args)
        {
            var str = Console.ReadLine().Split();
            var V = Int32.Parse(str[0]);
            var E = Int32.Parse(str[1]);
            var r = Int32.Parse(str[2]);

            var bellmanFord = new BellmanFord(V);

            for (int l = 0; l < E; l++)
            {
                str = Console.ReadLine().Split();
                var s = Int32.Parse(str[0]);
                var t = Int32.Parse(str[1]);
                var d = Int32.Parse(str[2]);
                bellmanFord.Edge.Add(new BellmanFord.edge(s, t, d));
            }

            var dist = bellmanFord.GetShortestPath(r);

            for (int i = 0; i < V; i++)
            {
                Console.WriteLine(dist[i] == Int32.MaxValue ? "INF" : string.Format("{0}", dist[i]));
            }
        }
    }
}