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

#define loop(i, n) for (int i = 0; i < n; i++)
#define INF 1010001000

typedef pair<int, int> i_i;
typedef struct data{int pos, tick, cost;}data;

int dp(vector<vector<i_i > > &g);

int c, n, m, s, d;

int main(void)
{
    while (cin >> c >> n >> m >> s >> d, c) {
        n++;
        vector<vector<i_i > > g(n);
        loop(i, m) {
            int a, b, f;
            cin >> a >> b >> f;
            g[a].push_back(i_i(f, b));
            g[b].push_back(i_i(f, a));
        }
        cout << dp(g) << endl;
    }
    return 0;
}

int dp(vector<vector<i_i > > &g)
{
    vector<vector<int> > table(c+1, vector<int>(n, INF));
    queue<data> a;
    data dt = {s, c, 0};
    a.push(dt);
    while (!a.empty()) {
        data tmp = a.front(); a.pop();
        for (i_i i : g[tmp.pos]) {
            if (table[tmp.tick][i.second] > tmp.cost + i.first) {
                table[tmp.tick][i.second] = tmp.cost + i.first;
                dt.pos = i.second; dt.tick = tmp.tick; 
                dt.cost = tmp.cost + i.first;
                a.push(dt);
            }
            if (tmp.tick && 
                    table[tmp.tick-1][i.second] > tmp.cost + i.first) {
                table[tmp.tick-1][i.second] = tmp.cost + i.first / 2;
                dt.pos = i.second; dt.tick = tmp.tick-1; 
                dt.cost = tmp.cost + i.first / 2;
                a.push(dt);
            }
        }
    }
    int ret = INF;
    for (int i = 0; i < c+1; i++) {
        ret = min(ret, table[i][d]);
    }
    return ret;
}

C++: #include<bits/stdc++.h>
#define F first
#define S second
#define INF 1<<28
using namespace std;

int c, n, s, d;
typedef pair < int, int > P;
typedef pair < int, P > PP;
vector < P > vec[111];

int solve(){
  
  int dist[111][11]; 
  priority_queue < PP, vector<PP>, greater<PP> > que;
  
  for(int i=0;i<111;i++) for(int j=0;j<11;j++) dist[i][j] = INF;
  dist[s][c] = 0;
  que.push( PP(0, P(s, c)) ); //Now_cost, Now_node, Now_ticket
  
  while(!que.empty()){
    PP p = que.top(); que.pop();
    int cost = p.F, now = p.S.F, tic = p.S.S;
    
    for(int i=0;i<vec[now].size();i++){
      P to = vec[now][i];
      if(dist[to.S][tic] > cost + to.F){
	dist[to.S][tic] = cost + to.F;
	que.push( PP(dist[to.S][tic], P(to.S, tic)) );
      }
      if(tic && dist[to.S][tic-1] > cost + to.F/2){
	dist[to.S][tic-1] = cost + to.F/2;
	que.push( PP(dist[to.S][tic-1], P(to.S, tic-1)) );
      }
    }
  }
  
  return dist[d][0];
}

int main(){

  int m, a, b, p;
  
  while(cin >> c >> n >> m >> s >> d){
    if((c|n|m|s|d) == 0) break;
    for(int i=0;i<111;i++) vec[i].clear();
    for(;m--;){
      cin >> a >> b >> p;
      vec[a].push_back(P(p, b)); //[now] P(cost, next);
      vec[b].push_back(P(p, a));
    }
    
    cout << solve() << 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;

			if (next.to == d) {
				cout << next.cost << endl;
				break;
			}

			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) );
			}
		}
	}
}