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 <cstdio>
#include <cmath>
#include <vector>
#include <map>
#include <stack>
#include <queue>
#include <algorithm>
#include <set>

#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,j) FOR(i,0,j)

const int INF = 1 << 24;
const int dx[4] = {0, 0, 1, -1}, dy[4] = {1, -1, 0, 0};

typedef unsigned long long ull;

struct Edge{
    int to, cost;
};

int C, N, M, S, D;
int cost[110][110];
int d[110][20], used[110][20];

void dijkstra(){
    REP(i, 110){
        REP(j, 20){
            d[i][j] = INF;
            used[i][j] = 0;
        }
    }

    d[S][0] = 0;

    while(1){
        int u = -1, v = -1;
        REP(i, N){
            REP(j, C){
                if(!used[i][j] && (u == -1 || d[u][v] > d[i][j])){u = i; v = j;}
            }
        }

        if(u == -1){break;}
        used[u][v] = 1;

        REP(i, N){
            d[i][v+1] = std::min(d[i][v+1], d[u][v] + cost[u][i] / 2);
            d[i][v] = std::min(d[i][v], d[u][v] + cost[u][i]);
        }
    }
}

int main(){
    while(std::cin >> C >> N >> M >> S >> D, C){
        S--; D--;

        REP(i, 110){
            REP(j, 110){
                cost[i][j] = INF;
            }
        }

        REP(i, M){
            int from, to, co;
            std::cin >> from >> to >> co;
            from--; to--;
        
            cost[from][to] = co;
            cost[to][from] = co;
        }

        dijkstra();

        int res = INF;
        REP(i, C+1){
            res = std::min(res, d[D][i]);
        }

        std::cout << res << std::endl;
    }
}

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

struct Node{
    int townNum, fare, ticketNum;
    bool operator<(const Node &obj)const{
        if(fare != obj.fare)return fare > obj.fare;
        return false;
    }
};

int mini[100][11];

int main(){
    while(1){
        int c,n,m,s,d;
        scanf("%d %d %d %d %d",&c,&n,&m,&s,&d);
        if(c == 0 && n == 0 && m == 0 && s == 0 && d == 0)break;
        vector< vector<Node> > graph;
        graph.resize(n+1);

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

        for(int i=0;i<n;++i){
            for(int j=0;j<=c;++j){
                mini[i][j] = INT_MAX;
            }
        }
        mini[s-1][c] = 0;

        priority_queue<Node> Q;
        Q.push((Node){s,0,c});
        while(!Q.empty()){
            Node now = Q.top();
            Q.pop();
            if(now.townNum == d){
                cout << now.fare << endl;
                break;
            }
            for(int i=0;i<graph[now.townNum].size();++i){
                Node nextTown = graph[now.townNum][i];
                int newfare=now.fare+nextTown.fare;
                if(newfare < mini[nextTown.townNum-1][now.ticketNum]){
                    Q.push((Node){nextTown.townNum,newfare,now.ticketNum});
                    mini[nextTown.townNum-1][now.ticketNum] = newfare;
                }
                if(now.ticketNum > 0){
                    newfare = now.fare + nextTown.fare / 2;
                    if(newfare < mini[nextTown.townNum-1][now.ticketNum-1]){
                        Q.push((Node){nextTown.townNum,newfare,now.ticketNum-1});
                        mini[nextTown.townNum-1][now.ticketNum-1] = newfare;
                    }
                }
            }
        }
    }

    return 0;
}

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

const int INF = 1 << 31;
int c, n, m, s, d, w;
int tocost[101][11];
vector<P> town[101];
priority_queue<S, vector<S>, greater<S> > pq;

void pq_set(int p, int sum, int j){
	for (int i = 0; i < town[p].size(); i++){
			pq.push(S(town[p][i].second + sum, town[p][i].first, j, 0));
			if (j)
				pq.push(S(town[p][i].second / 2 + sum, town[p][i].first, j - 1, 1));
	}
}

void dijkstra(){
	while (!pq.empty()){
		S a = pq.top();
		pq.pop();
		if (a.jud){
			if (tocost[a.to][a.num] < a.cost&&a.to!=s){
				tocost[a.to][a.num] = a.cost;
					pq_set(a.to, tocost[a.to][a.num], a.num);

			}
		}
			else{
				if (tocost[a.to][a.num] < a.cost&&a.to!=s){
					tocost[a.to][a.num] = a.cost;
					pq_set(a.to, tocost[a.to][a.num], a.num);
					
				}
			}
	}
}
	int main(){
		while (cin >> c >> n >> m >> s >> d&&c){
			for (int i = 0; i < 101; i++)
				fill(tocost[i], tocost[i] + 11, INF);
			fill(tocost[s], tocost[s] + 11, 0);
			while (pq.size())
				pq.pop();
			for (int i = 0; i < n; i++)
					town[i].erase(town[i].begin(),town[i].end());
			for (int i = 0; i < m; i++){
				int a, b, c;
				cin >> a >> b >> c;
				town[a].push_back({ b, c*-1 });
				town[b].push_back({ a, c*-1 });
			}
			pq_set(s, 0, c);
			dijkstra();
			cout << -tocost[d][0] << endl;
		}
	}