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: Runtime Error)



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

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

class Graph[T : Numeric] {

  def dijkstra(graph : ArrayBuffer[ArrayBuffer[(Int, T)]], source : Int) : ArrayBuffer[Option[T]] = {
    val pq = new mutable.PriorityQueue[(T, Int)]()
    val ret = new ArrayBuffer[Option[T]]() ++ Range(0, graph.size).map(x => None)

    ret.update(source, Some(0.asInstanceOf[T]))
    pq.enqueue((0.asInstanceOf[T], source))

    while (! (pq.isEmpty)) {
      val (dis, node) = pq.dequeue()
      for ((n, e) <- graph(node)) {
        val ndis = implicitly[Numeric[T]].plus(dis, e)
        ret(n) match {
          case None => ret.update(n, Some(ndis)); pq.enqueue((ndis, n))
          case Some(x) => if (x > ndis) { ret.update(n, Some(ndis)); pq.enqueue((ndis, n))}
        }
      }
    }
    ret
  }
}

object Main {
  def main(args: Array[String]) {
    val in = io.Source.createBufferedSource(System.in)
    //val in = io.Source.fromFile("src/main/resources/test.in")

    val data = in.getLines().toList
    val info = data.head.split("\\s+").map(_.toInt).toList
    val edges = data.drop(1).map {x => x.split("\\s+").map(_.toInt)}
    val graph = new ArrayBuffer[ArrayBuffer[(Int, Int)]]()
    for (_ <- Range(0, info.head)) graph += new ArrayBuffer[(Int, Int)]()

    for (e <- edges) {
      val tmp = e.toList
      graph(tmp.head) += Tuple2(tmp.tail.head, tmp.last)
    }
    val g = new Graph[Int]
    val ret = g.dijkstra(graph, info.last)
    for (n <- Range(0, info.head)) {
      ret(n) match {
        case None => println("INF")
        case Some(x) => println(x)
      }
    }
  }
}