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 <iostream>
#include <algorithm>

  using namespace std;

  const int INF = 1000000000;

  int c, n, m, s, d;
  int visited[100][11];
  int edge[100][100];

  void dfs(int p, int rem, int cost){
    if(visited[p][rem] < cost) return;
    visited[p][rem] = cost;
    if(p == d) return;
    for(int i=0;i<n;i++){
      if(edge[p][i] == INF) continue;
      if(rem > 0 ) dfs(i, rem-1, cost+(edge[p][i]/2));
      dfs(i, rem, cost+edge[p][i]);
    }
  }


 main(){
    while(cin >> c >> n >> m >> s >> d && (c || n || m || s || d)){
      fill(edge[0], edge[100], INF);
      fill(visited[0], visited[100], INF);
      --s; --d;
      for(int i=0;i<m;i++){
         int a, b, f;
         cin >> a >> b >> f;
         --a; --b;
         edge[a][b] = edge[b][a] = f;
      }

      dfs(s, c, 0);
      int ans = INF;
      for(int i=0;i<c;i++){
         ans = min(ans, visited[d][i]);
      }

      cout << ans << endl;
    }

    return 0;
}

C++: #include <bits/stdc++.h>

using namespace std;

#define llong long long 
typedef pair<int, int> P;

typedef struct data{
	int now;
	int time;
	int dep;

	bool operator > (const data& right) const{
		return dep == right.dep ? time > right.time : dep > right.dep;
	}

}data;

int c, n, m, s, d;
vector<P> edges[101];
int cost[101][11];
priority_queue<data, vector<data>, greater<data> > q;

void solve(){
	data D;
	D.now = s;
	D.time = 0;
	D.dep = 0;
	q.push(D);

	while(!q.empty()){
		data nd = q.top(); q.pop();
		int nowp = nd.now;
		int nowtime = nd.time;
		int nowdep = nd.dep;

		if(cost[nowp][nowdep] < nowtime) continue;

		for(int i = 0; i < edges[nowp].size(); i++){
			P edge = edges[nowp][i];
			if(cost[edge.first][nowdep] > cost[nowp][nowdep] + edge.second){
				data in;
				in.now = edge.first;
				in.time = cost[nowp][nowdep] + edge.second;
				in.dep = nd.dep;
				cost[in.now][in.dep] = in.time;
				q.push(in);
			}

			if(nowdep < c){
				if(cost[edge.first][nowdep + 1] > cost[nowp][nowdep] + edge.second / 2){
					data in;
					in.now = edge.first;
					in.time = nowtime + (edge.second / 2);
					in.dep = nowdep + 1;
					cost[in.now][in.dep] = in.time;
					q.push(in);
				}			
			}

		}
	}

	return;
}

int main(){
	while(cin >> c >> n >> m >> s >> d, n){
		fill_n(*cost, 101 * 11, 99999999);
		for(int i = 0; i <= c; i++){
			cost[s][i] = 0;
		}
		for(int i = 0; i < m; i++){
			int n, to, cos;
			cin >> n >> to >> cos;
			edges[n].push_back(P(to, cos));
			edges[to].push_back(P(n, cos));
		}

		solve();

		cout << cost[d][c] << endl;


		for(int i = 0; i < 101; i++){
			edges[i].clear();
		}
	}

	return 0;
}

C++: #include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <utility>
#include <tuple>
#include <queue>

#define REP(i, a, b) for (int i = int(a); i < int(b); i++)
#ifdef _DEBUG_
#define dump(val) cerr << __LINE__ << ":\t" << #val << " = " << (val) << endl
#else
#define dump(val)
#endif

using namespace std;

typedef long long int ll;
typedef tuple<int, int> P;
typedef tuple<ll, int, int> T;

template<typename T>
vector<T> make_v(size_t a, T b) {
    return vector<T>(a, b);
}

template<typename... Ts>
auto make_v(size_t a, Ts... ts) {
    return vector<decltype(make_v(ts...))>(a, make_v(ts...));
}

template<typename T>
void chmin(T &a, T b) {
    a = min(a, b);
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int c, n, m, s, t;
    while (cin >> c >> n >> m >> s >> t, c + n + m + s + t) {
        s--;
        t--;
        vector<vector<P>> G(n);
        REP(i, 0, m) {
            int a, b, f;
            cin >> a >> b >> f;
            a--;
            b--;
            G[a].push_back({b, f});
            G[b].push_back({a, f});
        }
        const ll inf = 1LL << 60;
        auto dist = make_v(n, c + 1, inf);
        priority_queue<T, vector<T>, greater<T>> pq;
        // cost, ticket, vertex
        pq.emplace(0LL, c, s);
        REP(i, 0, c + 1) {
            dist[s][i] = 0;
        }
        while (pq.size()) {
            ll cost;
            int ticket, vertex;
            tie(cost, ticket, vertex) = pq.top();
            pq.pop();
            if (dist[vertex][ticket] < cost) continue;
            dist[vertex][ticket] = cost;
            for (auto p : G[vertex]) {
                int to, f;
                tie(to, f) = p;
                // use ticket
                if (ticket > 0 && dist[to][ticket - 1] > cost + f / 2) {
                    dist[to][ticket - 1] = cost + f / 2;
                    pq.emplace(dist[to][ticket - 1], ticket - 1, to);
                }
                // do not use ticket
                if (dist[to][ticket] > cost + f) {
                    dist[to][ticket] = cost + f;
                    pq.emplace(dist[to][ticket], ticket, to);
                }
            }
        }
        ll ans = inf;
        REP (i, 0, c + 1) {
            chmin(ans, dist[t][i]);
        }
        cout << ans << endl;
    }

    return 0;
}