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 <vector>
#include <map>
#include <algorithm>
#define INF 1000010;

using namespace std;


int main(void){
  long c,n,m,s,d;
  while(true){
    cin>>c>>n>>m>>s>>d;
    if(c==0 and n==0 and m==0 and s==0 and d==0)break;
    d--;
    s--;

    long a,b,f;
    map<long,long> costs[n];
    for(int i=0;i<m;i++){
      cin>>a>>b>>f;
      a--;
      b--;
      costs[a][b]=f;
      costs[b][a]=f;
    }
    map<long,long> dist[n];
    for(long i=0;i<n;i++){
      for(long j=0;j<=c;j++){
        dist[i][j]=INF;
      }
    }
    dist[s][0]=0;

    vector<long> next,_next;
    next.push_back(s);
    while(next.empty()==false){
      _next.clear();
      for(auto iter=next.begin();iter!=next.end();iter++){
        long city=*iter;
        for(auto iter2=costs[city].begin();iter2!=costs[city].end();iter2++){
          long next_city=iter2->first;
          long fee=iter2->second;
          for(long ticket=0;ticket<=c;ticket++){
            if(dist[next_city][ticket]>dist[city][ticket]+fee){
              dist[next_city][ticket]=dist[city][ticket]+fee;
              _next.push_back(next_city);
            }
          }
          for(long ticket=1;ticket<=c;ticket++){
            if(dist[next_city][ticket]>dist[city][ticket-1]+fee/2){
              dist[next_city][ticket]=dist[city][ticket-1]+fee/2;
              _next.push_back(next_city);
            }
          }
        }
      }

      sort(_next.begin(),_next.end());
      _next.erase(unique(_next.begin(),_next.end()),_next.end());
      next.clear();
      copy(_next.begin(),_next.end(),back_inserter(next));

    }
    long retval=INF;
    for(long ticket=0;ticket<=c;ticket++){
        retval=min(dist[d][ticket],retval);
    }
    cout<<retval<<endl;
  }
}

C++: #include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<queue>
#include<vector>
#include<map>
using namespace std;

const int INF=10000000;
typedef struct edge{
  int t,c;
  edge(){}
  edge(int t,int c):t(t),c(c){}
};
typedef pair<int ,pair<int,int> > P;


vector<edge> g[105];
int id[11][105];
int c,n,m,s,d;

int main(void){
  while(1){
    scanf("%d %d %d %d %d",&c,&n,&m,&s,&d);
    if(!c && !n && !m && !s && !d) break;
    for(int i=0;i<=n;i++)g[i].clear();

    for(int i=0;i<m;i++){
      int a,b,f;
      scanf("%d %d %d",&a,&b,&f);
      g[a].push_back(edge(b,f));
      g[b].push_back(edge(a,f));
    }


    priority_queue<P,vector<P>,greater<P> > que;
    for(int i=0;i<=c;i++) fill(id[i],id[i]+n+1,INF);
    for(int i=0;i<10;i++)id[i][s]=0;
    que.push(P(0,pair<int,int>(s,c)));
    while(!que.empty()){
      P p=que.top();
      que.pop();
      int v=p.second.first;
      int nc=p.second.second;
      if(id[c-nc][v]<p.first) continue;
      for(int i=0;i<g[v].size();i++){
	edge e = g[v][i];
	if(id[c-nc][e.t]>id[c-nc][v]+e.c){
	  id[c-nc][e.t]=id[c-nc][v]+e.c;
	  que.push(P(id[c-nc][e.t],pair<int,int>(e.t,nc)));
	}
	if(nc>0 && id[c-nc+1][e.t]>id[c-nc][v]+e.c/2){
	  id[c-nc+1][e.t]=id[c-nc][v]+e.c/2;
	  que.push(P(id[c-nc+1][e.t],pair<int,int>(e.t,nc-1)));
	}
      }
    }
    printf("%d\n",id[c][d]);
  }
}

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

#define REP(i,k,n) for(int i=k;i<n;i++)
#define rep(i,n) for(int i=0;i<n;i++)
#define INF 1<<28

using namespace std;
typedef pair<int,int> P;


struct edge
{
	int to;
	int cost;

	edge(int to,int cost) : to(to),cost(cost) {}
};

int d[101][11];
vector<edge> G[101];

void dijkstra(int s,int n,int ticket)
{
	priority_queue<P,vector<P>,greater<P> > que;
	rep(i,n) d[i][ticket] = INF;
	d[s][ticket] = 0;
	que.push(P(0,s));

	while(!que.empty())
	{
		P p = que.top();
		que.pop();

		int v = p.second;
		if(d[v][ticket] < p.first) continue;

		rep(i,G[v].size())
		{
			edge e = G[v][i];
			int temp;

			if(ticket == 0)
			{
				temp = d[v][ticket] + e.cost;
			}
			else
			{
				temp =  min(d[v][ticket]+e.cost,d[v][ticket-1]+e.cost/2);
			}

			if(d[e.to][ticket] > temp)
			{
				d[e.to][ticket] = temp;
				que.push(P(d[e.to][ticket],e.to));
			}
		}
	}
}

int main()
{
	int c,n,m,s,t;
	while(cin >> c >> n >> m >> s >> t)
	{
		if(c == 0 && n == 0 && m == 0 && s == 0 && t == 0) break;
		
		s--;
		t--;
		rep(i,100) G[i].clear();

		rep(i,m)
		{
			int a,b,cost;
			cin >> a >> b >> cost;
			a--;
			b--;

			edge e(b,cost);
			G[a].push_back(e);

			edge e2(a,cost);
			G[b].push_back(e2);
		}
		
		rep(i,n) dijkstra(s,n,i);

		cout <<  d[t][c] << endl;
	}

	return 0;
}