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<queue>
#include<algorithm>
#include<map>
using namespace std;

struct edge { int to,cost; };
typedef pair<int,int> P;
typedef pair<int,P> PP;

#define INF (1<<30)
int main(){
  int c,n,m,s,d;
  int a,b,f;
  edge e;
  int ans = INF;
  while(1){
    cin >> c >> n >> m >> s >> d;
    if(c == 0 && n == 0 && m == 0 && s == 0 && d == 0)break;
    vector<edge> G[101];
    int min_cost[101][20];
    for(int i=0;i<=n;i++){
      for(int j=0;j<=c+1;j++){
	min_cost[i][j] = INF;
      }
    }
    for(int i=0;i<m;i++){
      cin >> a >> b >> f;
      e.to = b;
      e.cost = f;
      G[a].push_back(e);
      e.to = a;
      e.cost = f;
      G[b].push_back(e);
    }
    
    priority_queue<PP,vector<PP>,greater<PP> > que;
    min_cost[s][c] = 0;
    que.push(PP(0,P(s,c)));
    while(!que.empty()){
      PP p;
      p = que.top();
      que.pop();
      int now = p.second.first;
      int tick = p.second.second;
      if(min_cost[now][tick] < p.first) continue;
      for(int i=0;i<G[now].size();i++){
	edge e = G[now][i];
	if(min_cost[e.to][tick] > min_cost[now][tick] + e.cost){
	  min_cost[e.to][tick] = min_cost[now][tick] + e.cost;
	  que.push(PP(min_cost[e.to][tick],P(e.to,tick)));
	}
	if( tick ){
	  if(min_cost[e.to][tick-1] > min_cost[now][tick] + e.cost / 2){
	    min_cost[e.to][tick-1] = min_cost[now][tick] + e.cost / 2;
	    que.push(PP(min_cost[e.to][tick-1],P(e.to,tick-1)));
	  }
	}
      }
    }
    ans = INF;
    for(int i=0;i<c+1;i++){
      if(ans > min_cost[d][i]){
	ans = min_cost[d][i];
      }
    }
    cout << ans << endl;
  }
}

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

using namespace std;

struct node {
	int to, cost, ticket;

	node(int to, int cost) : to(to), cost(cost) { this -> ticket = 0; }
	node(int to, int cost, int ticket) : to(to), cost(cost), ticket(ticket) { }
	node() { this -> to = this -> cost = this -> ticket = 0; }
};

bool operator < (const node &a, const node &b) {
	return a.cost < b.cost;
}

bool operator > (const node &a, const node &b) {
	return a.cost > b.cost;
}

int main() {
	int c, n, m, s, d;
	while (cin >> c >> n >> m >> s >> d, c || n || m || s || d) {
		--s, --d;

		vector< vector<node> > v(n);
		for (int i = 0; i < m; ++i) {
			int a, b, f; cin >> a >> b >> f;
			--a, --b;
			v[a].push_back( node(b, f) );
			v[b].push_back( node(a, f) );
		}

		int rest = c;
		vector< vector<int> > cost(n, vector<int>(c+1, -1));
		vector<bool> used(n, -1);
		priority_queue< node, vector<node>, greater<node> > que; que.push( node(s, 0, c) );
		while ( !que.empty() ) {
			node next = que.top(); que.pop();

			if (cost[next.to][next.ticket] >= 0) continue;
			cost[next.to][next.ticket] = next.cost;

			rest = min(rest, next.ticket);

			for (int i = 0; i < v[next.to].size(); ++i) {
				que.push( node(v[next.to][i].to, next.cost + v[next.to][i].cost, next.ticket) );
				if (next.ticket) que.push( node(v[next.to][i].to, next.cost + v[next.to][i].cost/2, next.ticket-1) );
			}
		}

		cout << cost[d][rest] << 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=0;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;
}