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.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
static string[] inputvv = Console.ReadLine().Split(' ');//Splitで区切り文字を指定して複数個受け取る。
static long n = long.Parse(inputvv[0]);
static long e = long.Parse(inputvv[1]);
static long startV = long.Parse(inputvv[2]);
static List<long[]>[] nextList = new List<long[]>[n];//頂点番号ごとの隣接リスト。距離、隣接頂点番号
static long[] colors = new long[n];//最短距離未確定の頂点が0、確定で2
static long[] distances = new long[n];//各頂点への最短距離
static long[] distanceMemos = new long[2];//キューから捨てた最短距離と頂点番号

	static void Main()
	{
    for(long i = 0; i < n; i++)
    {
      nextList[i] = new List<long[]>();//リストの宣言が必要
    }
    
    for(long j = 0; j < e; j++)
    {
      long[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
      long[] nextMemo = new long[2];
      nextMemo[1] = nums[1];//隣接頂点番号
      nextMemo[0] = nums[2];//距離
      nextList[nums[0]].Add(nextMemo);//隣接リストの作成
    }
    
    Dijkstra();
	}

  static void Dijkstra()//O((|頂点数|+|辺数|)log頂点数)で各頂点への最短距離を求める
  {
    List<long[]> distanceList = new List<long[]>();//優先度付きキュー
    for(long i = 0; i < n; i++)
    {
      distances[i] = long.MaxValue;//最短距離を無限とおく
    }

    long[] newDistance = new long[2];

    //スタート地点を決める
    newDistance[1] = startV;//スタート地点番号
    distances[startV] = 0;
    colors[startV] = 1;

    newDistance[0] = 0;//スタートからスタートまでの距離0
    distanceList.Add(newDistance);

    while(distanceList.Count() != 0)
    {
      distanceList = PopHeap(distanceList);
      long minVertex = distanceMemos[1];//最短頂点の番号
      colors[minVertex] = 2;
      if(distances[minVertex] < distanceMemos[0]) continue;//最小値が最短でないなら無視

      for(long i = 0; i < nextList[minVertex].Count(); i++)
      {
        long v = nextList[minVertex][(int)i][1];
        if(colors[v] == 2) continue;
        if(distances[v] > distances[minVertex] + nextList[minVertex][(int)i][0])
        {
          distances[v] = distances[minVertex] + nextList[minVertex][(int)i][0];
          long[] newDistanceSub = new long[2];
          newDistanceSub[0] = distances[v];
          newDistanceSub[1] = v;
          distanceList = PushHeap(distanceList, newDistanceSub);
          colors[v] = 1;
        }
      }
    }

    for(long i = 0; i < n; i++)
    {
      Console.WriteLine((distances[i] == long.MaxValue? "INF" : distances[i].ToString()));
        //全頂点について最短距離の出力。到達不可能な頂点は-1を出力。
    }
    
  }

  //引数は、昇順にソート済みのリスト
  static List<long[]> PushHeap(List<long[]> nums, long[] addNums)//現在のヒープnumsにaddNumを追加
  {
    int n = nums.Count;
    nums.Add(addNums);

    while (n > 0)
    {
      int i = (n-1)/2;
      if (nums[n][0] < nums[i][0])//親のほうが大きいなら入れ替え。
      {
        long tmp = nums[n][0];
        long tmpSub = nums[n][1];
        nums[n][0] = nums[i][0];
        nums[n][1] = nums[i][1];
        nums[i][0] = tmp;
        nums[i][1] = tmpSub;
      }
      n = i;
    }
    return nums;
  }

  static List<long[]> PopHeap(List<long[]> nums)//ヒープnumsからポップ
  {
    int n = nums.Count - 1;
    distanceMemos[0] = nums[0][0];//捨てる値の保存
    distanceMemos[1] = nums[0][1];
    nums[0][0] = nums[n][0];//最小値である根を削除してリストの最後を持ってくる
    nums[0][1] = nums[n][1];
    nums.RemoveAt(n);

    for (int i = 0, j; (j = 2*i+1) < n; )
    {
      if ((j != n-1) && (nums[j][0] > nums[j+1][0]))// ２つの子のうち、値の小さい方を選ぶ
        j++;
      if (nums[i][0] > nums[j][0])//子が親より小さいなら入れ替え
      {
        long tmp = nums[j][0];
        long tmpSub = nums[j][1];
        nums[j][0] = nums[i][0];
        nums[j][1] = nums[i][1];
        nums[i][0] = tmp;
        nums[i][1] = tmpSub;
      }
      i = j;
    }
    return nums;
  }
  
}