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 Scala (judge verdict: Wrong Answer)

/**
 * Created by m00nlight on 7/30/15.
 */

import scala.collection.mutable
import scala.math.Ordering.Implicits._
import scala.collection.mutable.HashMap

class Graph[N : Ordering, E : Numeric] {

  def dijkstra(graph : Map[N, List[(N, E)]], source : N): HashMap[N, E] = {
    val pq = new mutable.PriorityQueue[(E, N)]()
    val ret = new HashMap[N, E]()
    ret += Tuple2(source, 0.asInstanceOf[E])
    pq.enqueue((0.asInstanceOf[E], source))

    while (! (pq.isEmpty)) {
      val (dis, node) = pq.dequeue()
      val updated = graph.get(node) match {
        case None => List()
        case Some(xs) => xs.filter {
          case (n, e) => {
            ret.get(n) == None || (dis < implicitly[Numeric[E]].plus(ret.get(n).get, e))
          }
        }
      }

      val tmp = updated.map {x => (x._1, implicitly[Numeric[E]].plus(dis, x._2))}
      ret ++= tmp
      for (x <- tmp) pq.enqueue((x._2, x._1))
    }
    ret
  }

  def buildGraph(edges : List[(N, N, E)]) : Map[N, List[(N, E)]]  = {
    edges.groupBy(_._1).map {
      case (k, v) => (k, v.map {x => (x._2, x._3)})
    }
  }
}


object Main {
  def main(args: Array[String]) {
    //val in = io.Source.fromFile("src/test.in")
    val in = io.Source.createBufferedSource(System.in)
    val xs = in.getLines().toList.map{ x => x.split("\\s+").map(_.toInt)}.map {x => (x.head, x.tail.head, x.last)}
    val graph = new Graph[Int, Int]()
    val res = graph.dijkstra(graph.buildGraph(xs.tail), xs.head._3)
    for (x <- Range(0, xs.head._1)) {
      res.get(x) match {
        case None => println("INF")
        case Some(x) => println(x)
      }
    }
  }
}