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.IO;
using System.Threading;
using System.Text;
using System.Diagnostics;
using static util;
using P = pair<int, int>;
using Number = System.Int32;

class Program {
    static void Main(string[] args) {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        var solver = new Solver(sw);
        // var t = new Thread(solver.solve, 1 << 26); // 64 MB
        // t.Start();
        // t.Join();
        solver.solve();
        sw.Flush();
    }
}

class Solver {
    StreamWriter sw;
    Scan sc;
    void Prt(string a) => sw.WriteLine(a);
    void Prt<T>(IEnumerable<T> a) => Prt(string.Join(" ", a));
    void Prt(params object[] a) => Prt(string.Join(" ", a));
    public Solver(StreamWriter sw) {
        this.sw = sw;
        this.sc = new Scan();
    }

    public void solve() {
        int n, m, s;
        sc.Multi(out n, out m, out s);
        var edge = new List<P>[n];
        for (int i = 0; i < n; i++)
        {
            edge[i] = new List<P>();
        }
        for (int i = 0; i < m; i++)
        {
            int u, v, c;
            sc.Multi(out u, out v, out c);
            edge[u].Add(new P(c, v));
        }
        var dist = ShortestPath.Dijkstra(edge, s, M);
        foreach (var item in dist)
        {
            if (item == M) Prt("INF");
            else Prt(item);
        }
    }
}

class pair<T, U> : IComparable<pair<T, U>> {
    public T v1;
    public U v2;
    public pair() : this(default(T), default(U)) {}
    public pair(T v1, U v2) { this.v1 = v1; this.v2 = v2; }
    public int CompareTo(pair<T, U> a) {
        int c = Comparer<T>.Default.Compare(v1, a.v1);
        return c != 0 ? c : Comparer<U>.Default.Compare(v2, a.v2);
    }
    public override string ToString() => v1 + " " + v2;
    public void Deconstruct(out T a, out U b) { a = v1; b = v2; }
}
static class util {
    public static readonly int M = 1000000007;
    // public static readonly int M = 998244353;
    public static readonly long LM = 1L << 60;
    public static readonly double eps = 1e-11;
    public static void DBG(string a) => Console.Error.WriteLine(a);
    public static void DBG<T>(IEnumerable<T> a) => DBG(string.Join(" ", a));
    public static void DBG(params object[] a) => DBG(string.Join(" ", a));
    public static void Assert(bool cond) { if (!cond) throw new Exception(); }
    public static pair<T, U> make_pair<T, U>(T v1, U v2) => new pair<T, U>(v1, v2);
    public static int CompareList<T>(IList<T> a, IList<T> b) where T : IComparable<T> {
        for (int i = 0; i < a.Count && i < b.Count; i++)
            if (a[i].CompareTo(b[i]) != 0) return a[i].CompareTo(b[i]);
        return a.Count.CompareTo(b.Count);
    }
    public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w;
    static readonly int[] dd = { 0, 1, 0, -1 };
    // static readonly string dstring = "RDLU";
    public static P[] adjacents(int i, int j)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1])).ToArray();
    public static P[] adjacents(int i, int j, int h, int w)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1]))
                                         .Where(p => inside(p.v1, p.v2, h, w)).ToArray();
    public static P[] adjacents(this P p) => adjacents(p.v1, p.v2);
    public static P[] adjacents(this P p, int h, int w) => adjacents(p.v1, p.v2, h, w);
    public static Dictionary<T, int> compress<T>(this IEnumerable<T> a)
        => a.Distinct().OrderBy(v => v).Select((v, i) => new { v, i }).ToDictionary(p => p.v, p => p.i);
    public static Dictionary<T, int> compress<T>(params IEnumerable<T>[] a) => compress(a.Aggregate(Enumerable.Union));
    public static T[] inv<T>(this Dictionary<T, int> dic) {
        var res = new T[dic.Count];
        foreach (var item in dic) res[item.Value] = item.Key;
        return res;
    }
    public static void swap<T>(ref T a, ref T b) where T : struct { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) where T : struct { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a) {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}

class Scan {
    StreamReader sr;
    public Scan() { sr = new StreamReader(Console.OpenStandardInput()); }
    public Scan(string path) { sr = new StreamReader(path); }
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public string Str => sr.ReadLine().Trim();
    public pair<T, U> Pair<T, U>() {
        T a; U b;
        Multi(out a, out b);
        return new pair<T, U>(a, b);
    }
    public P P => Pair<int, int>();
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public string[] StrArr => Str.Split(new[]{' '}, StringSplitOptions.RemoveEmptyEntries);
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>()    ? ct<T, int>(int.Parse(s))
                       : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>()   ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    public void Multi<T>(out T a) => a = cv<T>(Str);
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
}


static class ShortestPath {
    public static void WarshallFloyd(Number[][] g) {
        int n = g.Length;
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j)
                for (int k = 0; k < n; ++k)
                    g[j][k] = Math.Min(g[j][k], g[j][i] + g[i][k]);
    }

    class Heap {
        int n;
        Number[] values;
        int[] keys, indices;
        public Heap(int n, int s, Number inf) {
            this.n = 1;
            values = new Number[n];
            keys = new int[n];
            indices = new int[n];
            for (int i = 0; i < n; i++) {
                values[i] = inf;
                keys[i] = -1;
                indices[i] = -1;
            }
            values[s] = 0;
            keys[0] = s;
            indices[s] = 0;
        }

        void Update(int i, Number val) {
            if (indices[i] == -1) {
                keys[n] = i;
                indices[i] = n;
                ++n;
            }
            values[i] = val;
            int p = indices[i];
            while (p > 0) {
                int par = p - 1 >> 1;
                if (values[keys[par]] > val) {
                    keys[p] = keys[par];
                    indices[keys[p]] = p;
                    p = par;
                }
                else break;
            }
            keys[p] = i;
            indices[i] = p;
        }
        int Pop() {
            --n;
            int ret = keys[0];
            indices[ret] = -1;
            int i = keys[n];
            keys[n] = -1;
            Number val = values[i];
            if (n == 0) return ret;
            int p = 0;
            while ((p << 1 | 1) < n) {
                int ch = p << 1 | 1;
                if (ch < n - 1 && values[keys[ch]] > values[keys[ch + 1]]) ++ch;
                if (val > values[keys[ch]]) {
                    keys[p] = keys[ch];
                    indices[keys[p]] = p;
                    p = ch;
                }
                else break;
            }
            keys[p] = i;
            indices[i] = p;
            return ret;
        }
        public Number[] Run(List<pair<Number, int>>[] edges) {
            while (n > 0) {
                int p = Pop();
                foreach (var e in edges[p])
                    if (values[e.v2] > values[p] + e.v1)
                        Update(e.v2, values[p] + e.v1);
            }
            return values;
        }
    }

    public static Number[] Dijkstra(List<pair<Number, int>>[] edges, int s, Number inf) => new Heap(edges.Length, s, inf).Run(edges);

    // public static Number[] Dijkstra(List<pair<Number, int>>[] edges, int s, out long[] cnt, long Mod) {
    //     int n = edges.Length;
    //     var dist = new Number[n];
    //     var q = new PriorityQueue<pair<Number, int>>(){ rev = true };
    //     for (int i = 0; i < n; ++i) dist[i] = Inf;
    //     dist[s] = 0;
    //     q.Push(new pair<Number, int>(dist[s], s));
    //     cnt = new long[n];
    //     cnt[s] = 1;
    //     while (q.Count > 0) {
    //         var p = q.Pop();
    //         if (dist[p.v2] < p.v1) continue;
    //         foreach (var e in edges[p.v2]) {
    //             Number d = p.v1 + e.v1;
    //             if (dist[e.v2] > d) {
    //                 dist[e.v2] = d;
    //                 cnt[e.v2] = cnt[p.v2];
    //                 q.Push(new pair<Number, int>(d, e.v2));
    //             }
    //             else if (dist[e.v2] == d) cnt[e.v2] = (cnt[e.v2] + cnt[p.v2]) % Mod;
    //         }
    //     }
    //     return dist;
    // }
}