Go: package main

import (
	"container/heap"
	"fmt"
	"runtime"
)

type Node struct {
	NowPosition          int
	DiscountTicketTCount int
	Amount               int
}

type PriorityQueueNode []*Node

func (pq PriorityQueueNode) Len() int {
	return len(pq)
}

func (pq PriorityQueueNode) Less(i, j int) bool {
	return pq[i].Amount < pq[j].Amount
}

func (pq PriorityQueueNode) Swap(i, j int) {
	pq[i], pq[j] = pq[j], pq[i]
}

func (pq *PriorityQueueNode) Push(node interface{}) {
	*pq = append(*pq, node.(*Node))
}

func (pq *PriorityQueueNode) Pop() interface{} {
	old := *pq
	n := len(old)
	item := old[n-1]
	*pq = old[0 : n-1]
	return item
}

type Point struct {
	NextPoint int
	Fee       int
}

type Memo struct {
	NowPoint             int
	DiscountTicketTCount int
}

func main() {
	var c, n, m, s, d int
	var a, b, f int

	for {
		fmt.Scan(&c, &n, &m, &s, &d)
		if c == 0 && n == 0 && m == 0 && s == 0 && d == 0 {
			break
		}
		s--
		d--
		pointMap := make([][]Point, n)
		for i := 0; i < n; i++ {
			pointMap[i] = make([]Point, 0, n)
		}
		for i := 0; i < m; i++ {
			fmt.Scan(&a, &b, &f)
			a--
			b--
			pointMap[a] = append(pointMap[a], Point{NextPoint: b, Fee: f})
			pointMap[b] = append(pointMap[b], Point{NextPoint: a, Fee: f})
		}
		pq := make(PriorityQueueNode, 0, m)
		start := Node{NowPosition: s, DiscountTicketTCount: c, Amount: 0}
		heap.Push(&pq, &start)
		memo := make(map[Memo]int)
		for len(pq) != 0 {
			now := heap.Pop(&pq).(*Node)
			if now.NowPosition == d {
				fmt.Println(now.Amount)
				break
			}
			memo[Memo{NowPoint: now.NowPosition, DiscountTicketTCount: now.DiscountTicketTCount}] = now.Amount
			for _, v := range pointMap[now.NowPosition] {
				next := &Node{v.NextPoint, now.DiscountTicketTCount, now.Amount + v.Fee}
				if memoAmount, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok || (ok && memoAmount > next.Amount) {
					memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}] = next.Amount
					heap.Push(&pq, next)
				}
				if now.DiscountTicketTCount > 0 {
					next = &Node{v.NextPoint, now.DiscountTicketTCount - 1, now.Amount + v.Fee/2}
					if memoAmount, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok || (ok && memoAmount > next.Amount) {
						memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}] = next.Amount
						heap.Push(&pq, next)
					}
				}
			}
		}
		runtime.GC()
	}
}

C++: #include <bits/stdc++.h>
using namespace std;
using ll = long long;
struct line {
    ll a, b, f;
};
using pllll = pair<ll, ll>;
using pl6 = pair<ll, pair<ll, ll>>;
struct edge {
    ll dstb, dstc, cost;
};
int main() {
    
    ll c, n, m, s, d;
    while (cin >> c >> n >> m >> s >> d, c) {

        s--; d--;

        vector<line> l(m, line{0, 0, 0});
        for (ll i = 0; i < m; i++) {
            cin >> l[i].a >> l[i].b >> l[i].f;
            l[i].a--; l[i].b--;
            if (l[i].a > l[i].b) swap(l[i].a, l[i].b);
        }

        sort(l.begin(), l.end(), [](line &i, line &j) -> bool {
                 if (i.a != j.a) return i.a < j.a;
            else if (i.b != j.b) return i.b < j.b;
            else return i.f < j.f;
        });

        // 被った路線はなかったことに
        for (ll i = m; --i; ) {
            if (l[i].a == l[i-1].a && l[i].b == l[i-1].b) {
                l.erase(l.begin() + i);
            }
        }
        m = l.size();

        
        // 無向グラフを構築
        vector<vector<vector<edge>>> g(n, vector<vector<edge>>(c+1));
        for (ll i = m; i--; ) {
            ll a = l[i].a;
            ll b = l[i].b;
            ll f = l[i].f;
            for (ll c0 = c; c0 >= 0; c0--) {
                g[a][c0].push_back(edge{b, c0, f});
                g[b][c0].push_back(edge{a, c0, f});
                if (c0 > 0) {
                    g[a][c0].push_back(edge{b, c0-1, f/2});
                    g[b][c0].push_back(edge{a, c0-1, f/2});
                }
            }
        }

        // 拡張Dijkstra
        vector<vector<ll>> dp(n, vector<ll>(c+1, 0x7FFFFFFFLL));
        vector<vector<bool>> determined(n, vector<bool>(c+1, false));
        priority_queue<pl6, vector<pl6>, greater<pl6>> q;
        q.push(pl6(0, pllll(s, c)));
        dp[s][c] = 0;
        while (!q.empty()) {
            pl6 cv = q.top(); q.pop();
            pllll v = cv.second;
            ll vf = dp[v.first][v.second];
            if (determined[v.first][v.second]) continue;
            determined[v.first][v.second] = true;
            for (edge &ed : g[v.first][v.second]) {
                if (determined[ed.dstb][ed.dstc]) continue;
                if (vf + ed.cost < dp[ed.dstb][ed.dstc]) {
                    q.push(pl6(vf + ed.cost, pllll(ed.dstb, ed.dstc)));
                    dp[ed.dstb][ed.dstc] = vf + ed.cost;
                }
            }
        }

        ll ans = 0x7FFFFFFFLL;
        for (ll i = 0; i <= c; i++) {
            ans = min(ans, dp[d][i]);
        }
        cout << ans << endl;

    }

}

C++: #include <cstdio>
#include <cstdlib>
#include <queue>
#include <vector>
#include <utility>
#include <functional>
using namespace std;

#define INF 19980725

/** 割引券の枚数 */
static int c;
#define C 10
/** 町の数 */
static int n;
#define N 100
/** 路線数 */
static int m;
#define M 500
/** 出発地 */
static int s;
/** 目的地 */
static int d;

/** 路線情報 */
static int map[ N ][ N ];

/** 各探索先における状態 */
struct stat
{
  /** 到達先の町 */
  int pos;
  /** 現時点までの費用 */
  int cost;
  /** 割引券の残枚数 */
  int rem;

  stat (
    )
  {
    this->cost = INF;
    this->rem  = 0;
  }
  stat (
    int pos,
    int cost,
    int rem
    )
  {
    this->pos  = pos;
    this->cost = cost;
    this->rem  = rem;
  }
  bool operator> (
    const stat &a
    )
  const
  {
    return ( cost > a.cost
          || ( cost == a.cost && rem < a.rem ) );
  }
};

int
main (
  int   argc,
  char *argv[ ]
  )
{
  for ( ; ; )
  {
    /** 探索キュー */
    priority_queue<stat, vector<stat>, greater<stat> > lis;
    /** s->k への最小費用res[ k ] */
    int res[ N ];
    int i, j;

    /* 基本情報読み込み */
    scanf ( "%d%d%d%d%d", &c, &n, &m, &s, &d );
    if ( !( c | n | m | s | d ) ) break ;
    --s; --d;

    /* 路線情報初期化 */
    for ( i = 0; i < n; ++i )
    for ( j = 0; j < n; ++j )
      map[ i ][ j ] = INF;

    /* 路線情報読み込み */
    for ( i = 0; i < m; ++i )
    {
      int a, b, f;

      scanf ( "%d%d%d", &a, &b, &f );
      --a; --b;
      map[ a ][ b ] =
      map[ b ][ a ] = f;
    }

    /* s->d に対してダイクストラ法を適用 */
    fill ( res, res + n, INF );
    lis.push ( stat ( s, 0, c ) );
    while ( !lis.empty ( ) )
    {
      const stat st = lis.top ( );
      lis.pop ( );

      /* 結果が既に求まっていれば処理しない */
      if ( res[ st.pos ] != INF )
        continue ;
      res[ st.pos ] = st.cost;

      for ( i = 0; i < n; ++i )
      {
        /* st.pos からi への経路が存在しなければ処理しない */
        if ( map[ st.pos ][ i ] == INF )
          continue ;

        /* 隣接する町の探索を予約する．割引券が使えればその探索も予約する． */
        lis.push ( stat ( i, st.cost + map[ st.pos ][ i ], st.rem ) );
        if ( st.rem > 0 )
          lis.push ( stat ( i, st.cost + map[ st.pos ][ i ] / 2, st.rem - 1 ) );
      }
    }
    printf ( "%d\n", res[ d ] );
  }

  return ( EXIT_SUCCESS );
}