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 <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <ctime>
#include <cassert>
#include <iostream>
#include <cctype>
#include <sstream>
#include <string>
#include <list>
#include <vector>
#include <queue>
#include <set>
#include <stack>
#include <map>
#include <utility>
#include <numeric>
#include <algorithm>
#include <iterator>
#include <bitset>
#include <complex>
#include <fstream>
using namespace std;
typedef long long ll;
const double EPS = 1e-9;
typedef vector<int> vint;
typedef pair<int, int> pint;
#define rep(i, n) REP(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define MSG(a) cout << #a << " " << a << endl;
#define REP(i, x, n) for(int i = x; i < n; i++)
template<class T> T RoundOff(T a){ return int(a+.5-(a<0)); }
template<class T, class C> void chmax(T& a, C b){ if(a < b) a = b; }
template<class T, class C> void chmin(T& a, C b){ if(b < a) a = b; }
template<class T, class C> pair<T, C> mp(T a, C b){ return make_pair(a, b); }


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

struct P
{
  int pnt, ticket, cost;
  P(int pnt = 0, int ticket = 0, int cost = 0) : pnt(pnt), ticket(ticket), cost(cost) {}
};

bool operator>(const P& left, const P& right)
{
  return left.cost > right.cost;
}

int D[16][128];

int main()
{
  int c, n, m, s, d;
  while(cin >> c >> n >> m >> s >> d && c){
    memset(D, -1, sizeof D);
    vector<vector<edge> > edges(n);

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

      edges[a - 1].push_back(edge(b - 1, f));
      edges[b - 1].push_back(edge(a - 1, f));
    }

    priority_queue<P, vector<P>, greater<P> > que;
    for(que.push(P(s - 1, c, 0)); !que.empty(); que.pop()){
      P v = que.top();

      if(D[v.ticket][v.pnt] != -1 && D[v.ticket][v.pnt] <= v.cost) continue;
      D[v.ticket][v.pnt] = v.cost;
      
      rep(i, edges[v.pnt].size()){
	int to = edges[v.pnt][i].to, cost = edges[v.pnt][i].cost;

	que.push(P(to, v.ticket, v.cost + cost));
	if(0 < v.ticket) que.push(P(to, v.ticket - 1, v.cost + cost / 2));
      }
    }

    int ans = 1 << 30;
    rep(i, c+1) if(D[i][d - 1] != -1) chmin(ans, D[i][d - 1]);

    cout << ans << endl;
  }
}

C++: #include <iostream>
#include <queue>
#include <algorithm>
#include <vector>
#define INF 10e8 
using namespace std;

int c,n,m,s,d;

int cost[101][101];
int state[101][11];
struct node{
	int c;  //cost
	int n;	//number
	int t;	//times
	bool operator >(node b)const{
    return c > b.c;
	}
};

int dijkstra(int s,int g){
	node start;
	start.c=0,start.n=s,start.t=c;
	priority_queue<node,vector<node>,greater<node> > q;
	q.push(start);
	while(!q.empty()){
		node cur=q.top();
		q.pop();
		if(cur.n == g){
			int ans=cur.c;
			return ans;
		}
		if(state[cur.n][cur.t]<=cur.c)
			continue;
		else
			state[cur.n][cur.t]=cur.c;
		for(int i=1;i<=n;i++){
			if(cur.n== i)
				continue;
			node next;
			if(cur.t > 0){
				next.c=cur.c+(cost[cur.n][i]/2);
				next.n=i;
				next.t=cur.t-1;
				q.push(next);
			}
			next.c=cur.c+cost[cur.n][i];
			next.n=i;
			next.t=cur.t;
			q.push(next);
		}
	} 
}
int main(void){
	while(cin >> c >> n >> m >> s >> d,c|n|m|s|d){
		for(int i=1;i<=n;i++)
			for(int j=1;j<=c;j++)
				state[i][j]=INF;
		for(int i=1;i<=n;i++)
			for(int j=1;j<=n;j++)
				cost[i][j]=INF;
		int a,b,f;
		for(int i=0;i<m;i++){
			cin >> a >> b >> f;
			cost[a][b]=cost[b][a]=f;
		}
		int ans=dijkstra(s,d);
		cout << ans << endl;
	}
	return 0;
}

C++: // 2010/12/29 Tazoe

#include <iostream>
using namespace std;

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

		int wgt[102][102];
		int hlf[102][102];
		for(int i=1; i<=n; i++)
			for(int j=1; j<=n; j++)
				if(i==j){
					wgt[i][j] = 0;
					hlf[i][j] = 20000;
				}
				else{
					wgt[i][j] = 20000;
					hlf[i][j] = 20000;
				}

		for(int i=0; i<m; i++){
			int a, b, f;
			cin >> a >> b >> f;
			wgt[a][b] = f;
			wgt[b][a] = f;
			hlf[a][b] = f/2;
			hlf[b][a] = f/2;
		}

		int djk[12][102];
		bool flg[12][102];
		for(int i=1; i<=n; i++){
			djk[c][i] = wgt[s][i];
			flg[c][i] = false;
			djk[c-1][i] = hlf[s][i];
			flg[c-1][i] = false;
		}
		for(int j=c-2; j>=0; j--)
			for(int i=1; i<=n; i++){
				djk[j][i] = 20000;
				flg[j][i] = false;
			}

		while(true){
			int j_min = 11;
			int i_min = 0;
			int w_min = 2000000;
			for(int j=0; j<=c; j++)
				for(int i=1; i<=n; i++)
					if((!flg[j][i])&&(djk[j][i]<w_min)){
						j_min = j;
						i_min = i;
						w_min = djk[j][i];
					}

			flg[j_min][i_min] = true;
			if(i_min==d){
				cout << djk[j_min][i_min] << endl;
				break;
			}

			for(int j=0; j<=c; j++)
				for(int i=1; i<=n; i++)
					if(!flg[j][i])
						if(wgt[i_min][i]!=20000)
							if(djk[j][i]>djk[j][i_min]+wgt[i_min][i])
								djk[j][i] = djk[j][i_min]+wgt[i_min][i];

			for(int j=1; j<=c; j++)
				for(int i=1; i<=n; i++)
					if(!flg[j-1][i])
						if(hlf[i_min][i]!=20000)
							if(djk[j-1][i]>djk[j][i_min]+hlf[i_min][i])
								djk[j-1][i] = djk[j][i_min]+hlf[i_min][i];
		}
	}

	return 0;
}