Problem:
Minimum-Cost Arborescence

Find the sum of the weights of edges of the Minimum-Cost Arborescence with the root r for a given weighted directed graph G = (V, E).

Input

|V| |E| r
s0 t0 w0
s1 t1 w1
:
s|E|-1 t|E|-1 w|E|-1

, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the root of the Minimum-Cost Arborescence.

si and ti represent source and target verticess of i-th directed edge. wi represents the weight of the i-th directed edge.

Output

Print the sum of the weights the Minimum-Cost Arborescence.

Constraints

1 ≤ |V| ≤ 100

0 ≤ |E| ≤ 1,000

0 ≤ wi ≤ 10,000

G has arborescence(s) with the root r

Sample Input 1

4 6 0
0 1 3
0 2 2
2 0 1
2 3 1
3 0 1
3 1 5

Sample Output 1

6

Sample Input 2

6 10 0
0 2 7
0 1 1
0 3 5
1 4 9
2 1 6
1 3 2
3 4 3
4 2 2
2 5 8
3 5 3

Sample Output 2

11

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using SB = System.Text.StringBuilder;
//using System.Threading.Tasks;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
using System.Numerics;
using static System.Math;
using pair = Pair<int, int>;

class Program
{
    static void Main()
    {
        SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    readonly int dom = 998244353;
    bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (b.CompareTo(a) < 0) { a = b; return true; } return false; }

    void solve()
    {
        int N = cin.nextint;
        int M = cin.nextint;
        int r = cin.nextint;

        var MSTA = new MinimumSpanningTreeArborescence();
        var E = MSTA.Input(M, 0);
        WriteLine(MSTA.Run(N, E, r));
    }
}

class MinimumSpanningTreeArborescence
{
    public Edge[] Input(int m, int indexed = 1, bool cost = true)
    {
        var cin = new Scanner();
        var ret = new Edge[m];
        for (int i = 0; i < m; i++)
        {
            int a = cin.nextint - indexed;
            int b = cin.nextint - indexed;
            var c = cost ? cin.nextlong : 1;
            ret[i] = new Edge(a, b, c);
        }
        return ret;
    }
    Edge apply(Edge a, long b) => new Edge(a.from, a.to, a.cost + b);
    long merge(long a, long b) => a + b;
    public long Run(int n, Edge[] E, int root = 0)
    {
        var U = new DisjointSet(n);
        var H = new LazySkewHeap<Edge, long>[n];
        for (int i = 0; i < H.Length; i++)
        {
            H[i] = new LazySkewHeap<Edge, long>(apply, merge);
        }
        foreach (var e in E)
        {
            H[e.to].Enqueue(e);
        }
        var used = new int[n];
        for (int i = 0; i < used.Length; i++)
        {
            used[i] = -1;
        }
        used[root] = root;

        var ret = 0L;
        for (int s = 0; s < n; s++)
        {
            var path = new Stack<int>();
            int u = s;
            while (used[u] == -1)
            {
                used[u] = s;
                path.Push(u);
                if (H[u].Count == 0) return -1;

                var e = H[u].Dequeue();
                ret += e.cost;
                H[u].Add(-e.cost);

                int v = U[e.from];
                if (used[v] != s)
                {
                    u = v;
                    continue;
                }

                var next = new LazySkewHeap<Edge, long>(apply, merge);
                int w = -1;
                do
                {
                    w = path.Pop();
                    next.Meld(H[w]);
                } while (U.Unite(v, w));

                u = U[v];
                H[u] = next;
                used[u] = -1;
            }
        }
        return ret;
    }
}

class LazySkewHeap<T, U> where T : IComparable<T>
{
    static readonly Node nil = new Node(default(T));
    Node root = nil;
    readonly Func<T, U, T> apply;
    readonly Func<U, U, U> merge;

    public LazySkewHeap(Func<T, U, T> apply, Func<U, U, U> merge)
    {
        this.apply = apply;
        this.merge = merge;
    }
    public void Meld(LazySkewHeap<T, U> h)
    {
        root = meld(root, h.root);
        h.root = nil;
    }
    Node meld(Node a, Node b)
    {
        if (a.Count == 0) return b;
        if (b.Count == 0) return a;
        eval(ref a); eval(ref b);
        if (a.Key.CompareTo(b.Key) > 0) swap(ref a, ref b);
        a.Right = meld(a.Right, b);
        swap(ref a.Left, ref a.Right);
        a.Update();
        return a;
    }
    public void Enqueue(T key)
    {
        Node node = new Node(key);
        node.Left = node.Right = nil;
        node.Update();
        root = meld(root, node);
    }
    public T Dequeue()
    {
        T ret = Peek;
        root = meld(root.Left, root.Right);
        return ret;
    }
    public void Add(U x)
    {
        root.Lazy = merge(root.Lazy, x);
    }
    void eval(ref Node t)
    {
        if (t.Left.Count > 0) t.Left.Lazy = merge(t.Left.Lazy, t.Lazy);
        if (t.Right.Count > 0) t.Right.Lazy = merge(t.Right.Lazy, t.Lazy);
        t.Key = apply(t.Key, t.Lazy);
        t.Lazy = default(U);
    }
    public T Peek { get { eval(ref root); return root.Key; } }
    public int Count => root.Count;

    class Node
    {
        public T Key;
        public Node(T Key) { this.Key = Key; }
        public U Lazy { get; set; }
        public int Count { get; private set; }
        public void Update() { Count = 1 + Left.Count + Right.Count; }
        public Node Left, Right;
    }
    void swap(ref Node a, ref Node b)
    {
        Node t = a;
        a = b;
        b = t;
    }
}

class Edge : IComparable<Edge>
{
    public int from, to, id; public long cost;
    public Edge(int from, int to, long cost, int id = -1)
    {
        this.from = from;
        this.to = to;
        this.cost = cost;
        this.id = id;
    }
    public int CompareTo(Edge e) => cost.CompareTo(e.cost);
    public override string ToString() => $"{from} {to} {cost}";
}

/// <OriginalAuthor>camypaper</OriginalAuthor>
class DisjointSet
{
    readonly int[] par;
    readonly byte[] rank;
    /// <summary>
    /// 0 から <paramref name="N"/>-1 までの番号がついた <paramref name="N"/> 個の要素からなる集合を作成します．
    /// </summary>
    /// <param name="N">要素数</param>
    /// <remarks>このコンストラクタは O(N) で実行されます．</remarks>
    public DisjointSet(int N)
    {
        par = new int[N];
        rank = new byte[N];
        for (int i = 0; i < N; i++) par[i] = -1;
    }
    /// <summary>
    /// 指定した要素が属する集合の代表値を取得します．
    /// </summary>
    /// <param name="id">調べたい要素の 0-indexed での番号</param>
    /// <returns>指定した要素が属する集合の代表値</returns>
    /// <remarks>最悪計算量 O(α(N)) で実行されます．</remarks>
    public int this[int id]
    {
        get
        {
            if (par[id] < 0) return id;
            return par[id] = this[par[id]];
        }
    }
    /// <summary>
    /// 指定した 2 つの要素が属する集合同士を 1 つに統合することを試みます．
    /// </summary>
    /// <param name="x">最初の要素の 0-indexed での番号</param>
    /// <param name="y">2 つ目の要素の 0-indexed での番号</param>
    /// <returns>統合に成功したならば true，そうでなければ false．</returns>
    /// <remarks>最悪計算量 O(α(N)) で実行されます．</remarks>
    public bool Unite(int x, int y)
    {
        x = this[x]; y = this[y];
        if (x == y) return false;
        if (rank[x] < rank[y]) { var tmp = x; x = y; y = tmp; }
        par[x] += par[y];
        par[y] = x;
        if (rank[x] == rank[y])
            rank[x]++;
        return true;
    }
    /// <summary>
    /// 指定した要素が属する集合のサイズを取得します．
    /// </summary>
    /// <param name="x">指定する要素の 0-indexed での番号</param>
    /// <returns>集合のサイズ</returns>
    /// <remarks>最悪計算量 O(α(N)) で実行されます．</remarks>
    public int Size(int x) => -par[this[x]];

    /// <summary>
    /// 指定した 2 つの要素が属する集合が同じかどうかを判定する．計算量 O(α(N))．
    /// </summary>
    /// <param name="x">最初の要素の 0-indexed での番号</param>
    /// <param name="y">2 つ目の要素の 0-indexed での番号</param>
    /// <returns>同じならば true，そうでなければ false．</returns>
    /// <remarks>最悪計算量 O(α(N)) で実行されます．</remarks>
    public bool Same(int x, int y) => this[x] == this[y];
}

static class Ex
{
    public static void join<T>(this IEnumerable<T> values, string sep = " ") => WriteLine(string.Join(sep, values));
    public static string concat<T>(this IEnumerable<T> values) => string.Concat(values);
    public static string reverse(this string s) { var t = s.ToCharArray(); Array.Reverse(t); return t.concat(); }

    public static int lower_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) < 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    public static int upper_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) <= 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}

class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f; public U s;
    public Pair(T f, U s) { this.f = f; this.s = s; }
    public int CompareTo(Pair<T, U> a) => f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    public override string ToString() => $"{f} {s}";
}

class Scanner
{
    string[] s; int i;
    readonly char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan => ReadLine().Split();
    public int[] scanint => Array.ConvertAll(scan, int.Parse);
    public long[] scanlong => Array.ConvertAll(scan, long.Parse);
    public double[] scandouble => Array.ConvertAll(scan, double.Parse);
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint => int.Parse(next);
    public long nextlong => long.Parse(next);
    public double nextdouble => double.Parse(next);
}