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 <queue>
using namespace std;

struct state {
  int node;
  int ticket;
  int cost;
  state(int n, int t, int c) : node(n), ticket(t), cost(c) {}
  bool operator<(const state& s) const
  {
    return cost > s.cost;
  }
};

int main()
{
  int c, n, m, s, d;
  while (cin >> c >> n >> m >> s >> d && c != 0) {
    --s;  --d;
    vector<vector<pair<int,int> > > g(n);
    for (int i = 0; i < m; i++) {
      int a, b, f;
      cin >> a >> b >> f;
      --a;  --b;
      g[a].push_back(make_pair(b, f));
      g[b].push_back(make_pair(a, f));
    }

    priority_queue<state> q;
    q.push(state(s, c, 0));
    vector<vector<int> > city(n, vector<int>(c+1, 1000000));
    city[s][c] = 0;
    while (!q.empty()) {
      const state s = q.top();
      q.pop();
      if (s.node == d) {
        cout << s.cost << endl;
        break;
      }

      city[s.node][s.ticket] = s.cost;
      for (vector<pair<int,int> >::const_iterator it(g[s.node].begin()); it != g[s.node].end(); ++it) {
        const int next = it->first;
        const int cost = s.cost + it->second;
        if (cost < city[next][s.ticket]) {
          city[next][s.ticket] = cost;
          q.push(state(next, s.ticket, cost));
        }
        if (s.ticket > 0) {
          const int cost2 = s.cost + it->second/2;
          if (cost2 < city[next][s.ticket-1]) {
            city[next][s.ticket-1] = cost2;
            q.push(state(next, s.ticket-1, cost2));
          }
        }
      }
    }
  }
  return 0;
}

C++: // AOJ 0212
#define _CRT_SECURE_NO_WARNINGS
#include<cstdio>
#include<algorithm>
#include<functional>
#include<vector>
#include<queue>
#define rep(i,a) for( int i = 0; i != (a); ++i )

typedef std::pair<int, int> P;
typedef std::pair<P, int> PP;

const int INF = 10000000;

int c, n, m, s, d;	
std::vector<P> G[101];
int dist[101][11];

int dijkstra()
{
	std::fill( (int*)dist, (int*)dist+101, INF );
	dist[s][0] = 0;
	std::priority_queue<PP, std::vector<PP>, std::greater<PP> > pque;
	pque.push( PP( P( s, 0 ), 0 ) );
	while( !pque.empty() )
	{
		PP p = pque.top(); pque.pop();
		int v = p.first.first, cost = p.first.second, tic = p.second;

		if( dist[v][tic] < cost )
			continue;

		rep( i, G[v].size() )
		{
			P &e = G[v][i];

			if( tic < c && dist[e.first][tic+1] > dist[v][tic]+e.second/2 )
			{
				dist[e.first][tic+1] = dist[v][tic]+e.second/2;
				pque.push( PP( P( e.first, dist[e.first][tic+1] ), tic+1 ) );
			}

			if( dist[e.first][tic] > dist[v][tic]+e.second )
			{
				dist[e.first][tic] = dist[v][tic]+e.second;
				pque.push( PP( P( e.first, dist[e.first][tic] ), tic ) );
			}
		}
	}

	return *std::min_element( dist[d], dist[d]+11 );
}

int main()
{
	while( scanf( "%d%d%d%d%d", &c, &n, &m, &s, &d ), c|n|m|s|d )
	{
		rep( i, 101 )
			G[i].clear();

		rep( i, m )
		{
			int a, b, f;
			scanf( "%d%d%d", &a, &b, &f );
			G[a].push_back( P( b, f ) );
			G[b].push_back( P( a, f ) );
		}

		printf( "%d\n", dijkstra() );
	}

	return 0;
}

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

typedef long long ll;
#define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i))
#define each(itr,c) for(__typeof(c.begin()) itr=c.begin(); itr!=c.end(); ++itr)
#define all(x) (x).begin(),(x).end()
#define pb push_back
#define fi first
#define se second

typedef pair<int,int> pi;

struct edge{int to,cost;};
vector<edge> G[100];

const int INF=123456789;
int dist[11][100];

int main()
{
    int c,n,m,s,d;
    while(cin >>c >>n >>m >>s >>d,c)
    {
        rep(i,100) G[i].clear();

        --s;
        --d;
        rep(i,m)
        {
            int a,b,f;
            scanf(" %d %d %d", &a, &b, &f);
            --a;
            --b;
            G[a].pb(edge{b,f});
            G[b].pb(edge{a,f});
        }

        fill(dist[0],dist[11],INF);
        dist[0][s]=0;
        queue<pi> que;
        que.push(pi(0,s));
        while(!que.empty())
        {
            pi p=que.front(); que.pop();
            int ticket=p.fi;
            int now=p.se;
            rep(i,G[now].size())
            {
                edge e=G[now][i];
                if(dist[ticket][e.to]>dist[ticket][now]+e.cost)
                {
                    dist[ticket][e.to]=dist[ticket][now]+e.cost;
                    que.push(pi(ticket,e.to));
                }
                if(ticket<c)
                {
                    if(dist[ticket+1][e.to]>dist[ticket][now]+e.cost/2)
                    {
                        dist[ticket+1][e.to]=dist[ticket][now]+e.cost/2;
                        que.push(pi(ticket+1,e.to));
                    }
                }
            }
        }

        int ans=INF;
        rep(i,c+1) ans=min(ans,dist[i][d]);
        printf("%d\n", ans);
    }
    return 0;
}