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]struct{})
		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}] = struct{}{}
			for _, v := range pointMap[now.NowPosition] {
				next := &Node{v.NextPoint, now.DiscountTicketTCount, now.Amount + v.Fee}
				if _, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok {
					heap.Push(&pq, next)
				}
				if now.DiscountTicketTCount > 0 {
					next = &Node{v.NextPoint, now.DiscountTicketTCount - 1, now.Amount + v.Fee/2}
					if _, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok {
						heap.Push(&pq, next)
					}
				}
			}
		}
		runtime.GC()
	}
}

C++: #include <bits/stdc++.h>
using namespace std;

const double PI = acos(-1);
const double EPS = 1e-15;
using ll = long long;
using ull = unsigned long long;
const int inf = 2e9;
const ll INF = 2e18;
const ll MOD = 1e9+7;
const ll MOD1 = 998244353;
typedef pair<int,int> P;

#define REP(i,n) for (int i = 0; i < (n); i++)
#define sz(s) (s).size()
#define pb push_back
#define fi first
#define se second
#define mp make_pair

int main(){
  int c,n,m,s,d;
  while (cin >> c >> n >> m >> s >> d,c,n,m,s,d) {
    ll dp[110][11];
    REP(i,110) REP(j,11) dp[i][j] = INF;
    s--;
    d--;
    vector<pair<int,ll>> G[110];
    REP(i,m) {
      int a,b;
      ll f;
      cin >> a >> b >> f;
      a--;
      b--;
      G[a].pb({b,f});
      G[b].pb({a,f});
    }
    priority_queue<pair<ll,pair<int,int>>,vector<pair<ll,pair<int,int>>>,greater<pair<ll,pair<int,int>>>> pq;
    dp[s][0] = 0;
    pq.push({0,{s,0}});
    while (!pq.empty()) {
      pair<ll,pair<int,int>> tp = pq.top();
      //cout << tp.fi << " " << tp.se.fi << " " << tp.se.se << endl;
      pq.pop();
      int point = tp.se.fi;
      int ticket = tp.se.se;
      if (tp.fi > dp[point][ticket]) continue;
      //cout << "test" << endl;
      REP(i,sz(G[point])) {
        int next = G[point][i].fi;
        ll cost = G[point][i].se;
        if (dp[point][ticket] + cost < dp[next][ticket]) {
          dp[next][ticket] = dp[point][ticket] + cost;
          pq.push({dp[next][ticket],{next,ticket}});
        }
        if (ticket < c && dp[point][ticket] + cost/2 < dp[next][ticket+1]) {
          dp[next][ticket+1] = dp[point][ticket] + cost/2;
          pq.push({dp[next][ticket+1],{next,ticket+1}});
        }
      }
    }
    ll ans = INF;
    REP(i,c+1) {
      ans = min(ans,dp[d][i]);
    }
    cout << ans << endl;
  }
  return 0;
}

C++: #include <iostream>
#include <algorithm>
using namespace std;
#define MAX 100
#define INF 9999999

int c,n,m,s,d,a,b,f,cost[MAX+1][MAX+1],dd[MAX+1][MAX+1];
bool used[MAX+1][MAX+1];

int dijkstra(int s,int d,int c){
    fill(dd[0],dd[MAX],INF);
    fill(used[0],used[MAX],false);
    
    dd[c][s-1] = 0;
    while(true){
        int Mini = -1 , Minj;
        
        for(int i = 0 ; i < n ; i++){
            for(int j = 0 ; j <= c ; j++){
                if((dd[j][i] < dd[Minj][Mini] || Mini == -1)&&!used[j][i]){
                    Mini = i;
                    Minj = j;
                }
            }
        }
        
        if(Mini == -1) break;
        used[Minj][Mini] = true;
        
        for(int i = 0 ; i < n ; i++){
            dd[Minj][i] = min(dd[Minj][i],dd[Minj][Mini]+cost[Mini][i]);
            if(Minj > 0) dd[Minj-1][i] = min(dd[Minj-1][i],dd[Minj][Mini]+cost[Mini][i]/2);
        }
    }
    
    int res = INF;
    for(int i = 0 ; i <= c ; i++){
        res = min(res,dd[i][d-1]);
    }
    
    return res;
}

int main(){
    while(cin >> c >> n >> m >> s >> d, c+n+m+s+d){
        fill(cost[0],cost[MAX],INF);
        for(int i = 0 ; i < m ; i++){
            cin >> a >> b >> f;
            cost[a-1][b-1] = f;
            cost[b-1][a-1] = f;
        }
        
        cout << dijkstra(s,d,c) << endl;
    }

    return 0;
}

C++: #include <stdio.h>
#include <iostream>
#include <string.h>
#include <queue>
#include <algorithm>

using namespace std;


// Highway Express Bus
// input 
// c n m s d : ????????? ????????° ???????????° ????????°??? ????????°???
// a b f : a??????b?????§f???

#define INF 1e+9
typedef pair<int, int> P;
struct edge{
	int to, cost; 
};

int c, n, m, s, d;
vector<edge> G[101];
int dp[11][101];	//????????????i???????????????j??°????????§???????°??????????


void dijkstra(int s,int a){		//????????????????????????????????°???a???????????????????????????
    priority_queue<P, vector<P>, greater<P> >Q;	//greater: ????´?????°????????????§??????????????¨????????????
    for(int i=0 ;i<n; i++) dp[a][i] = INF;
    dp[a][s] = 0;
    Q.push(P(0,s));	//??????????????°???
    
    while(!Q.empty()){
        P p=Q.top();  //p<cost, vertex>
        Q.pop();
        int v = p.second;
        
        if(dp[a][v] < p.first)continue;
        for(int i=0; i<G[v].size(); i++){
            edge e = G[v][i];	//v?????????????????´????????????{??°???????????????}
            int dm;
            if(a==0) dm = dp[a][v] + e.cost;	//???????????????????????¨???
            else dm = min(dp[a][v] + e.cost, dp[a-1][v] + e.cost/2);	//v?????????????????´?????§??????????????????
            															//??????????????§???????°????

            if(dp[a][e.to] > dm){
                dp[a][e.to] = dm;	//dm????????????????????????????????´??°
                Q.push(P(dp[a][e.to],e.to));	//?????\??????(?????????,?¬???°???)??§??\??????
            }
        }
    }
}


int main(){

	while(1){
		cin >> c >> n >> m >> s >> d;
		s--;
		d--;
		if(c==0) break;

		for(int i=0 ; i<m ; i++){
			int a, b, f;
			cin >> a >> b >> f;

			a--;
			b--;

			G[a].push_back((edge){b,f});	//??£??\?????????:a??????b?????§????????????
			G[b].push_back((edge){a,f});
		}

		int ans = INF;
	    for(int i=0;i<=c;i++){
    		dijkstra(s,i);
		}
        
	    cout << dp[c][d] << endl;
	     
	    for(int i=0;i<100;i++)G[i].clear();
	}

	return 0;
}