Go: package main

import (
	"container/heap"
	"fmt"
)

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)
		}
		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)
		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)
					}
				}
			}
		}
	}
}

C++: #include <iostream>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#define REP(i, n) for(int i = 0;i < n;i++)
#define REPR(i, n) for(int i = n;i >= 0;i--)
#define FOR(i, m, n) for(int i = m;i < n;i++)
#define FORR(i, m, n) for(int i = m;i >= n;i--)
#define SORT(v, n) sort(v, v+n);
#define VSORT(v) sort(v.begin(), v.end());
#define llong long long
#define pb(a) push_back(a)
#define INF 999999999
using namespace std;
typedef pair<int, int> P;
typedef pair<llong, llong> LP;
typedef pair<int, P> PP;
typedef pair<llong, LP> LPP;

//int dy[]={0, 0, 1, -1, 0};
//int dx[]={1, -1, 0, 0, 0};

struct edge{
  int to, cost;
};

int c, n, m, start, goal;
vector<edge> v[105];	       
vector<int> d(105, INF);
priority_queue<int> q, q2;

int dijkstra(int s){
  vector<int> d2(105, INF);

  d[s]=0;
  q.push(s);
  while(!q.empty()){
    int u=q.top();
    q.pop();
    
    REP(i, v[u].size()){
      int to=v[u][i].to;
      int cost=v[u][i].cost;
      if(d[to]>d[u]+cost){
	d[to]=d[u]+cost;
	q.push(to);
      }
      if(d2[to]>d[u]+cost/2){
	d2[to]=d[u]+cost/2;
	q2.push(to);
      }
    }
  }
  
  d=d2;
  q=q2;
  while(!q2.empty()) q2.pop();
}

int main(){
  while(1){
    scanf("%d%d%d%d%d", &c, &n, &m, &start, &goal);
    start--; goal--;
    if(c==0) return 0;
    
    REP(i, m){
      int from, to, f;
      scanf("%d%d%d", &from, &to, &f);
      from--; to--;
      v[to].push_back((edge){from, f});
      v[from].push_back((edge){to, f});
    }

    REP(i, c+1){
      dijkstra(start);
    }

    printf("%d\n", d[goal]);

    REP(i, 105){
      v[i].erase(v[i].begin(), v[i].end());
      d[i]=INF;
    }
  }
}

C++: //Solution for aoj:0212 Highway Express Bus
#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<functional>
using namespace std;
typedef pair<int, int>P;


struct S {
	int cost, to, num;
	S(int c, int t, int n) : cost(c), to(t), num(n){}
	bool operator>(const S &s) const {
		return cost > s.cost;
	}
};

const int INF = 1 << 30;
int c, n, m, s, d, ans;
int tocost[101][11];
vector<P> town[101];
priority_queue<S, vector<S>, greater<S> > pq;


void dijkstra(){
	while (!pq.empty()){
		S a = pq.top();
		pq.pop();
		for (int i = 0; i < town[a.to].size(); i++){
			int tt = town[a.to][i].first, cc = town[a.to][i].second;
			if (tocost[tt][a.num] > cc + a.cost){
				tocost[tt][a.num] = cc + a.cost;
				pq.push({ cc + a.cost, tt, a.num });
			}
			if (a.num>0&&tocost[tt][a.num-1] > cc/2 + a.cost){
				tocost[tt][a.num-1] = cc/2 + a.cost;
				pq.push({ cc/2 + a.cost, tt, a.num-1 });
			}
		}
	}
}
	int main(){
		while (cin >> c >> n >> m >> s >> d&&c&&n&&m&&s){
			for (int i = 0; i < 101; i++)
				fill(tocost[i], tocost[i] + 11, INF);
			tocost[s][c] = 0;
			ans = INF;
			while (pq.size())
				pq.pop();
			for (int i = 0; i < 101; i++)
				town[i].clear();
			for (int i = 0; i < m; i++){
				int a, b, c;
				cin >> a >> b >> c;
				town[a].push_back({ b, c });
				town[b].push_back({ a, c });
			}
			pq.push({ 0, s, c });
			dijkstra();
			for (int i = 0; i <= c; i++)
				ans = min(ans, tocost[d][i]);
			cout << ans << endl;
		}
		return 0;
	}

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

#define INF 1010000000
#define rep(i,n) for(int i=0;i<n;i++)
#define reps(i,n) for(int i=1;i<=n;i++)
#define sint(i) scanf("%d",&i);
#define sintt(i,j) scanf("%d%d",&i,&j);
#define sinttt(i,j,k) scanf("%d%d%d",&i,&j,&k);

using namespace std;

class S{
	public:
	int p;
	int v;
	int n;
	
	S(int p,int v,int n):p(p),v(v),n(n){}
	
	bool operator<(const S&a)const{
		return v>a.v;
		return v==a.v ? v>a.v : n <a.n;
	}
};

int main(){
	while(1){
		int c,n,m,s,g;
		scanf("%d%d%d%d%d",&c,&n,&m,&s,&g);
		if(c==0&&n==0&&m==0&&s==0&&g==0)break;
		
		int root[101][101];
		rep(i,101)rep(j,101)root[i][j]=INF;
		
		rep(i,101)root[i][i]=0;
		
		rep(i,m){
			int a,b,d;
			sinttt(a,b,d);
			root[a][b]=d;
			root[b][a]=d;
		}
		
		priority_queue<S> qui;
		qui.push(S(s,0,0));
		int ans=0;
		
		int visit[101][11];
		rep(i,101)rep(j,11)visit[i][j]=0;
		
		while(1){
			if(qui.empty()==1){
				ans=-1;
				break;
			}
			
			S u=qui.top();qui.pop();
			
			printf("%d %d %d\n",u.p,u.v,u.n);
			if(u.p==g){
				ans=u.v;
				break;
			}
			
			visit[u.p][u.n]=1;
			
			reps(i,n){
				if(root[u.p][i]!=INF){
					if(visit[i][u.n]==0){
						qui.push(S(i,u.v+root[u.p][i],u.n));
					}
					if(visit[i][u.n+1]==0 && visit[u.p][u.n+1]==0 && u.n+1 <= c){
						qui.push(S(i,u.v+root[u.p][i]/2,u.n+1));
					}
				}
			}
		}
		printf("%d\n",ans);
	}
}