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.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.UnaryExpression>;

class Program
{
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    static Scan sc = new Scan();
    const int M = 1000000007;
    const double eps = 1e-11;
//    static readonly int[] dd = { 0, 1, 0, -1, 0 };
    static void Main()
    {
        int vn, en, s;
        sc.Multi(out vn, out en, out s);
        var INF = (long)1e16;
        var sp = new ShortestPath<long>(INF);
        var edge = new List<ShortestPath<long>.edge>[vn];
        for (int i = 0; i < vn; i++)
        {
            edge[i] = new List<ShortestPath<long>.edge>();
        }
        for (int i = 0; i < en; i++)
        {
            int a, b, d;
            sc.Multi(out a, out b, out d);
            edge[a].Add(new ShortestPath<long>.edge(b, d));
        }
        var dist = sp.Dijkstra(edge, s);
        foreach (var item in dist)
            Prt(item < INF ? item.ToString() : "INF");

        sw.Flush();
    }

    static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
    static T Max<T>(params T[] a) { return a.Max(); }
    static T Min<T>(params T[] a) { return a.Min(); }
    static void DBG(string a) { Console.WriteLine(a); }
    static void Prt(string a) { sw.WriteLine(a); }
    // static void DBG<T>(IEnumerable<T> a) { DBG(string.Join(" ", a)); }
    // static void DBG(params object[] a) { DBG(string.Join(" ", a)); }
    // static void Prt<T>(IEnumerable<T> a) { Prt(string.Join(" ", a)); }
    // static void Prt(params object[] a) { Prt(string.Join(" ", a)); }

    // for AOJ
    static string Join<T>(string sep, IEnumerable<T> a) { return string.Join(sep, a.Select(x => x.ToString()).ToArray()); }
    static void DBG<T>(IEnumerable<T> a) { DBG(Join(" ", a)); }
    static void DBG(params object[] a) { DBG(Join(" ", a)); }
    static void Prt<T>(IEnumerable<T> a) { Prt(Join(" ", a)); }
    static void Prt(params object[] a) { Prt(Join(" ", a)); }
}
static class ex
{
    public static void swap<T>(this IList<T> a, int i, int j) { 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;
    }
}
static class Operator<T>
{
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) { return Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile(); }
    public static Func<T, T> Lambda(Unary op) { return Expression.Lambda<Func<T, T>>(op(x), x).Compile(); }
}

class Scan
{
    public int Int { get { return int.Parse(Str); } }
    public long Long { get { return long.Parse(Str); } }
    public double Double { get { return double.Parse(Str); } }
    public string Str { get { return Console.ReadLine().Trim(); } }
    public int[] IntArr { get { return StrArr.Select(int.Parse).ToArray(); } }
    public long[] LongArr { get { return StrArr.Select(long.Parse).ToArray(); } }
    public double[] DoubleArr { get { return StrArr.Select(double.Parse).ToArray(); } }
    public string[] StrArr { get { return Str.Split(); } }
    bool eq<T, U>() { return typeof(T).Equals(typeof(U)); }
    T ct<T, U>(U a) { return (T)Convert.ChangeType(a, typeof(T)); }
    T cv<T>(string s) { return 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]); }
    public void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
    { 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]); f = cv<Y>(ar[5]); }
    public void Multi<T, U, V, W, X, Y, Z>(out T a, out U b, out V c, out W d, out X e, out Y f, out Z g)
    { 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]); f = cv<Y>(ar[5]);  g = cv<Z>(ar[6]);}
}
class mymath
{
    public static long Mod = 1000000007;
    public static bool isprime(long a)
    {
        if (a < 2) return false;
        for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
        return true;
    }
    public static bool[] sieve(int n)
    {
        var p = new bool[n + 1];
        for (int i = 2; i <= n; i++) p[i] = true;
        for (int i = 2; i * i <= n; i++) if (p[i]) for (int j = i * i; j <= n; j += i) p[j] = false;
        return p;
    }
    public static List<int> getprimes(int n)
    {
        var prs = new List<int>();
        var p = sieve(n);
        for (int i = 2; i <= n; i++) if (p[i]) prs.Add(i);
        return prs;
    }
    public static long[][] E(int n)
    {
        var ret = new long[n][];
        for (int i = 0; i < n; i++) { ret[i] = new long[n]; ret[i][i] = 1; }
        return ret;
    }
    public static double[][] dE(int n)
    {
        var ret = new double[n][];
        for (int i = 0; i < n; i++) { ret[i] = new double[n]; ret[i][i] = 1; }
        return ret;
    }
    public static long[][] pow(long[][] A, long n)
    {
        if (n == 0) return E(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static double[][] pow(double[][] A, long n)
    {
        if (n == 0) return dE(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static double dot(double[] x, double[] y)
    {
        int n = x.Length;
        double ret = 0;
        for (int i = 0; i < n; i++) ret += x[i] * y[i];
        return ret;
    }
    public static double _dot(double[] x, double[] y)
    {
        int n = x.Length;
        double ret = 0, r = 0;
        for (int i = 0; i < n; i++)
        {
            double s = ret + (x[i] * y[i] + r);
            r = (x[i] * y[i] + r) - (s - ret);
            ret = s;
        }
        return ret;
    }
    public static long dot(long[] x, long[] y)
    {
        int n = x.Length;
        long ret = 0;
        for (int i = 0; i < n; i++) ret = (ret + x[i] * y[i]) % Mod;
        return ret;
    }
    public static T[][] trans<T>(T[][] A)
    {
        int n = A[0].Length, m = A.Length;
        var ret = new T[n][];
        for (int i = 0; i < n; i++) { ret[i] = new T[m]; for (int j = 0; j < m; j++) ret[i][j] = A[j][i]; }
        return ret;
    }
    public static double[] mul(double[][] A, double[] x)
    {
        int n = A.Length;
        var ret = new double[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static long[] mul(long[][] A, long[] x)
    {
        int n = A.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static long[][] mul(long[][] A, long[][] B)
    {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static double[][] mul(double[][] A, double[][] B)
    {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new double[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static long[] add(long[] x, long[] y)
    {
        int n = x.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = (x[i] + y[i]) % Mod;
        return ret;
    }
    public static long[][] add(long[][] A, long[][] B)
    {
        int n = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = add(A[i], B[i]);
        return ret;
    }
    public static long pow(long a, long b)
    {
        if (a >= Mod) return pow(a % Mod, b);
        if (a == 0) return 0;
        if (b == 0) return 1;
        var t = pow(a, b / 2);
        if ((b & 1) == 0) return t * t % Mod;
        return t * t % Mod * a % Mod;
    }
    public static long inv(long a) { return pow(a, Mod - 2); }
    public static long gcd(long a, long b)
    {
        while (b > 0) { var t = a % b; a = b; b = t; }
        return a;
    }
    // a x + b y = gcd(a, b)
    public static long extgcd(long a, long b, out long x, out long y)
    {
        long g = a; x = 1; y = 0;
        if (b > 0) { g = extgcd(b, a % b, out y, out x); y -= a / b * x; }
        return g;
    }
    public static long lcm(long a, long b) { return a / gcd(a, b) * b; }
    public static long comb(int n, int r)
    {
        if (n < 0 || r < 0 || r > n) return 0;
        if (n - r < r) r = n - r;
        if (r == 0) return 1;
        if (r == 1) return n;
        int[] numer = new int[r], denom = new int[r];
        for (int k = 0; k < r; k++) { numer[k] = n - r + k + 1; denom[k] = k + 1; }
        for (int p = 2; p <= r; p++)
        {
            int piv = denom[p - 1];
            if (piv > 1)
            {
                int ofst = (n - r) % p;
                for (int k = p - 1; k < r; k += p) { numer[k - ofst] /= piv; denom[k] /= piv; }
            }
        }
        long ret = 1;
        for (int k = 0; k < r; k++) if (numer[k] > 1) ret = ret * numer[k] % Mod;
        return ret;
    }
}

class ShortestPath<T> where T : struct, IComparable<T>
{
    T Inf;
    public ShortestPath(T inf) { Inf = inf; }
    T min(T a, T b) { return a.CompareTo(b) > 0 ? b : a; }
    T Add(T a, T b) { return Operator<T>.Add(a, b); }
    public T[][] WarshallFloyd(T[][] g)
    {
        var d = Copy(g);
        int n = d.Length;
        for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j) for (int k = 0; k < n; ++k) d[j][k] = min(d[j][k], Add(d[j][i], d[i][k]));
        return d;
    }
    T[][] Copy(T[][] g)
    {
        int n = g.Length;
        var ret = new T[n][];
        for (int i = 0; i < n; ++i)
        {
            ret[i] = new T[n];
            for (int j = 0; j < n; ++j)
            {
                if (i != j && g[i][j].Equals(default(T))) ret[i][j] = Inf;
                else ret[i][j] = g[i][j];
            }
        }
        return ret;
    }

    public struct edge : IComparable<edge>
    {
        public int to;
        public T cost;
        public edge(int t, T c) { to = t; cost = c; }
        public int CompareTo(edge a) { return cost.CompareTo(a.cost); }
    }

    public T[] Dijkstra(List<edge>[] edges, int s)
    {
        int n = edges.Length;
        var dist = new T[n];
        var q = new PriorityQueue<edge>(){ rev = true };
        for (int i = 0; i < n; ++i) dist[i] = Inf;
        dist[s] = default(T);
        q.Push(new edge(s, dist[s]));
        while (q.Count > 0)
        {
            var p = q.Pop();
            foreach (var e in edges[p.to])
            {
                T d = Add(p.cost, e.cost);
                if (dist[e.to].CompareTo(d) > 0)
                {
                    dist[e.to] = d;
                    q.Push(new edge(e.to, d));
                }
            }
        }
        return dist;
    }
}

// the greatest element pops
class PriorityQueue<T> where T : IComparable<T>
{
    List<T> buf;
    public bool rev = false;
    public PriorityQueue() { buf = new List<T>(); }
    int cmp(int i, int j) { return buf[i].CompareTo(buf[j]) * (rev ? -1 : 1); }
    void swap(int i, int j) { var t = buf[i]; buf[i] = buf[j]; buf[j] = t; }
    public void Push(T elem)
    {
        int n = buf.Count;
        buf.Add(elem);
        while (n > 0)
        {
            int i = (n - 1) >> 1;
            if (cmp(n, i) > 0) swap(i, n);
            n = i;
        }
    }
    public T Pop()
    {
        T ret = buf[0];
        int n = buf.Count - 1;
        buf[0] = buf[n];
        buf.RemoveAt(n);
        for (int i = 0, j; (j = (i << 1) + 1) < n; i = j)
        {
            if (j != n - 1 && cmp(j, j + 1) < 0) ++j;
            if (cmp(i, j) < 0) swap(i, j);
        }
        return ret;
    }
    public T Top { get { return buf[0]; } }
    public int Count { get { return buf.Count; } }
}