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: Accepted)

object Main{
  class Edge(val from:Int,val to:Int,val cost:Long){}

  // v:????????°
  // s:?§????
  // graph:??£??\?????????
  def dijkstra(v:Int,s:Int,graph:Array[Array[Edge]],inf:Long= Long.MaxValue / 10) : Array[Long] = {
    val d : Array[Long] = Array.fill(v)(inf)
    val que = new scala.collection.mutable.PriorityQueue[Tuple2[Long,Int]]()(Ordering.Tuple2[Long,Int].reverse)
    que += Tuple2(0,s)
    d(s) = 0
    while(que.nonEmpty){
      val (cost,node) = que.dequeue
      if(d(node) >= cost){
        for(e <- graph(node)){
          if(d(e.to) > d(node)+e.cost){
            d(e.to) = d(node)+e.cost
            que+=Tuple2(d(e.to),e.to)
          }
        }
      }
    }
    return d
  }

  def main(args : Array[String]){
    val inf = Long.MaxValue / 10
    val sc = new java.util.Scanner(System.in)
    val v,e,r = sc.nextInt
    val g : Array[Array[Edge]] = Array.fill(v)(Array.empty)

    for(i <- 0 to e-1){
      val s,t,d = sc.nextInt
      g(s) :+= new Edge(s,t,d)
    }

    val res = dijkstra(v,r,g,inf)
    res.foreach(x => if(x==inf) println("INF") else println(x))
  }
}