Problem:
Problem D: Long Distance Taxi

A taxi driver, Nakamura, was so delighted because he got a passenger who wanted to go to a
city thousands of kilometers away. However, he had a problem. As you may know, most taxis in
Japan run on liquefied petroleum gas (LPG) because it is cheaper than gasoline. There are more
than 50,000 gas stations in the country, but less than one percent of them sell LPG. Although
the LPG tank of his car was full, the tank capacity is limited and his car runs 10 kilometer per
liter, so he may not be able to get to the destination without filling the tank on the way. He
knew all the locations of LPG stations.
Your task is to write a program that finds the best way from the current location to the destination without running out of gas.

Input

The input consists of several datasets, and each dataset is in the following format.

N M cap

src dest

c1,1 c1,2 d1

c2,1 c2,2 d2

.

.

.

cN,1 cN,2 dN

s1

s2

.

.

.

sM

The first line of a dataset contains three integers (N, M, cap), where N is the number of roads
(1 ≤ N ≤ 3000),M is the number of LPG stations (1≤ M ≤ 300), and cap is the tank capacity
(1 ≤ cap ≤ 200) in liter. The next line contains the name of the current city (src) and the name
of the destination city (dest). The destination city is always different from the current city.
The following N lines describe roads that connect cities. The road i (1 ≤ i ≤ N) connects two
different cities ci,1 and ci,2 with an integer distance di (0 < di ≤ 2000) in kilometer, and he can
go from either city to the other. You can assume that no two different roads connect the same
pair of cities. The columns are separated by a single space. The next M lines (s1,s2,...,sM) indicate the names of the cities with LPG station.
You can assume that a city with LPG station has at least one road.

The name of a city has no more than 15 characters. Only English alphabet ('A' to 'Z' and 'a'
to 'z', case sensitive) is allowed for the name.

A line with three zeros terminates the input.

Output

For each dataset, output a line containing the length (in kilometer) of the shortest possible
journey from the current city to the destination city. If Nakamura cannot reach the destination,
output "-1" (without quotation marks). You must not output any other characters.
The actual tank capacity is usually a little bit larger than that on the specification sheet, so
you can assume that he can reach a city even when the remaining amount of the gas becomes
exactly zero. In addition, you can always fill the tank at the destination so you do not have to
worry about the return trip.

Sample Input

6 3 34
Tokyo Kyoto
Tokyo Niigata 335
Tokyo Shizuoka 174
Shizuoka Nagoya 176
Nagoya Kyoto 195
Toyama Niigata 215
Toyama Kyoto 296
Nagoya
Niigata
Toyama
6 3 30
Tokyo Kyoto
Tokyo Niigata 335
Tokyo Shizuoka 174
Shizuoka Nagoya 176
Nagoya Kyoto 195
Toyama Niigata 215
Toyama Kyoto 296
Nagoya
Niigata
Toyama
0 0 0

Output for the Sample Input

846
-1

Solution in C# (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Debug;
using SB = System.Text.StringBuilder;
//using System.Numerics;
//using static System.Math;
namespace Program {
    public class Solver {
        //Random rnd = new Random();
        public void Solve() {
            for (; ; )
            {
                var n = ri; var m = ri;
                var cap = ri * 10;
                if (n == 0) return;
                var src = rs;
                var sink = rs;
                Debug.WriteLine(src);
                Debug.WriteLine(sink);
                var from = new string[n];
                var to = new string[n];
                var w = new int[n];
                for (int i = 0; i < n; i++)
                {
                    from[i] = rs;
                    to[i] = rs;
                    w[i] = ri;
                }
                var special = new string[m];
                for (int i = 0; i < m; i++)
                    special[i] = rs;
                var s = new List<string>() { src, sink };
                s.AddRange(from); s.AddRange(to); s.AddRange(special);
                s = s.Distinct().ToList();
                var f = from.Select(x => s.FindIndex(y => y == x)).ToArray();
                var t = to.Select(x => s.FindIndex(y => y == x)).ToArray();
                var sp = new bool[s.Count];
                foreach (var x in special)
                    sp[s.FindIndex(y => y == x)] = true;
                solve(s.Count,
                s.FindIndex(y => y == src),
                s.FindIndex(y => y == sink),
                f, t, w, cap, sp);
            }
        }
        void solve(int n, int src, int sink, int[] f, int[] t, int[] w, int c, bool[] sp) {
            var G = Enumerate(n, x => new List<KeyValuePair<int, int>>());
            for (int i = 0; i < f.Length; i++)
            {
                G[f[i]].Add(new KeyValuePair<int, int>(t[i], w[i]));
                G[t[i]].Add(new KeyValuePair<int, int>(f[i], w[i]));
            }
            var dist = new int[n, c + 1];
            for (int i = 0; i < n; i++)
                for (int j = 0; j <= c; j++)
                    dist[i, j] = 1000000000;
            dist[src, c] = 0;
            var pq = new PriorityQueue<KeyValuePair<int, int>>((l, r) => l.Value.CompareTo(r.Value));
            pq.Enqueue(new KeyValuePair<int, int>(src * 10000 + c, 0));
            while (pq.Any())
            {
                var p = pq.Dequeue();
                var pos = p.Key / 10000;
                var cap = p.Key % 10000;
                if (dist[pos, cap] < p.Value) continue;
                if (pos == sink)
                {
                    Console.WriteLine(p.Value); return;
                }
                //Debug.WriteLine($"{pos} {cap} {p.Value}");
                foreach (var e in G[pos])
                {
                    var to = e.Key;
                    var nc = cap - e.Value;
                    if (nc < 0) continue;
                    if (sp[to]) nc = c;
                    var nw = p.Value + e.Value;
                    if (nc >= 0 && dist[to, nc] > nw)
                    {
                        dist[to, nc] = nw;
                        pq.Enqueue(new KeyValuePair<int, int>(to * 10000 + nc, nw));

                    }
                }
            }
            Console.WriteLine(-1);

        }
        const long INF = 1L << 60;
        int ri { get { return sc.Integer(); } }
        long rl { get { return sc.Long(); } }
        double rd { get { return sc.Double(); } }
        string rs { get { return sc.Scan(); } }
        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());

        static T[] Enumerate<T>(int n, Func<int, T> f) {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f(i);
            return a;
        }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex {
    /*
    static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
        return string.Join(st, ie);
    }*/
    static public void Main() {
        Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Program.Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO {
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer: StreamWriter {
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }

    public class StreamScanner {
        public StreamScanner(Stream stream) { str = stream; }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }

        private byte read() {
            if (isEof) return 0;
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }

        public char Char() {
            byte b = 0;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }
        public string Scan() {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine() {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
}

#endregion
#region BinaryHeap
public class PriorityQueue<T> {
    readonly List<T> heap = new List<T>();
    readonly Comparison<T> compare;
    public PriorityQueue() { compare = Comparer<T>.Default.Compare; }

    public PriorityQueue(Comparison<T> comparison) { compare = comparison; }
    public PriorityQueue(IComparer<T> comparer) { compare = comparer.Compare; }

    public void Enqueue(T item) {
        var pos = heap.Count;
        heap.Add(item);
        while (pos > 0)
        {
            var par = (pos - 1) / 2;
            if (compare(heap[par], item) <= 0)
                break;
            heap[pos] = heap[par];
            pos = par;
        }
        heap[pos] = item;

    }

    public T Dequeue() {
        var ret = heap[0];
        var pos = 0;
        var x = heap[heap.Count - 1];

        while (pos * 2 + 1 < heap.Count - 1)
        {
            var lch = pos * 2 + 1;
            var rch = pos * 2 + 2;
            if (rch < heap.Count - 1 && compare(heap[rch], heap[lch]) < 0) lch = rch;
            if (compare(heap[lch], x) >= 0)
                break;
            heap[pos] = heap[lch];
            pos = lch;
        }
        heap[pos] = x;
        heap.RemoveAt(heap.Count - 1);
        return ret;

    }
    public T Peek() { return heap[0]; }
    public int Count { get { return heap.Count; } }
    public bool Any() { return heap.Count > 0; }

    public T[] Items {
        get {
            var ret = heap.ToArray();
            Array.Sort(ret, compare);
            return ret;
        }
    }
}
#endregion