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 <iostream>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#define REP(i, n) for(int i = 0;i < n;i++)
#define REPR(i, n) for(int i = n;i >= 0;i--)
#define FOR(i, m, n) for(int i = m;i < n;i++)
#define FORR(i, m, n) for(int i = m;i >= n;i--)
#define SORT(v, n) sort(v, v+n);
#define VSORT(v) sort(v.begin(), v.end());
#define llong long long
#define pb(a) push_back(a)
#define INF 999999999
using namespace std;
typedef pair<int, int> P;
typedef pair<llong, llong> LP;
typedef pair<int, P> PP;
typedef pair<llong, LP> LPP;

//int dy[]={0, 0, 1, -1, 0};
//int dx[]={1, -1, 0, 0, 0};

struct edge{
  int to, cost;
};

int c, n, m, start, goal;
vector<edge> v[105];	       
vector<int> d(105, INF);
priority_queue<P> q, q2;

int dijkstra(int s){
  vector<int> d2(105, INF);

  d[s]=0;
  q.push(P(0, s));
  while(!q.empty()){
    int u=q.top().second;
    q.pop();
    
    REP(i, v[u].size()){
      int to=v[u][i].to;
      int cost=v[u][i].cost;
      if(d[to]>d[u]+cost){
	d[to]=d[u]+cost;
	q.push(P(-d[to], to));
      }
      if(d2[to]>d[u]+cost/2){
	d2[to]=d[u]+cost/2;
	q2.push(P(-d2[to], to));
      }
    }
  }
  
  d=d2;
  q=q2;
  while(!q2.empty()) q2.pop();
}

int main(){
  while(1){
    scanf("%d%d%d%d%d", &c, &n, &m, &start, &goal);
    start--; goal--;
    if(c==0) return 0;
    
    REP(i, m){
      int from, to, f;
      scanf("%d%d%d", &from, &to, &f);
      from--; to--;
      v[to].push_back((edge){from, f});
      v[from].push_back((edge){to, f});
    }

    REP(i, c+1){
      dijkstra(start);
    }

    printf("%d\n", d[goal]);

    REP(i, 105){
      v[i].erase(v[i].begin(), v[i].end());
      d[i]=INF;
    }
  }
}

C++: #include <bits/stdc++.h>
#define INF (1<<29)
#define all(c) (c).begin(),(c).end()
#define pb(c) push_back(c)
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
typedef pair<int, P> PP;

int dis[111][111];
int c, n, m, s, d;
int next[111][11];

void dfs(int cur, int sum, int cost){
  if(next[cur][sum] < cost) return;
  next[cur][sum] = cost;
  for(int i = 0; i < n; i++){
    if(dis[cur][i] == (1<<29)) continue;
    if(sum > 0) dfs(i, sum-1, cost+(dis[cur][i]/2));
    dfs(i, sum, cost+dis[cur][i]);
  }
}

int main(){
  ios::sync_with_stdio(false);

  while(cin >> c >> n >> m >> s >> d && (c||n||m||s||d)){

    for(int i = 0; i < n; i++){
      for(int j = 0; j < n; j++){
        dis[i][j] = next[i][j] = (1<<29);
      }
    }

    for(int i = 0; i < m; i++){
      int a, b, f;
      cin >> a >> b >> f;
      a--; b--;
      dis[a][b] = f;
      dis[b][a] = f;
    }

    dfs(s-1,c,0);
    int ans = (1<<29);
    for(int i =0; i < c; i++){
      ans = min(ans, next[d-1][i]);
    }
    cout << ans << endl;
  }


}

C++: #include <iostream>
#include <vector>
#include <queue>
#include <map>
#include <cassert>
#include <algorithm>
using namespace std;
typedef pair<int, int> edge;
struct state{
  int cost, coupon, station;
  state(int cost_, int coupon_, int station_):cost(cost_), coupon(coupon_), station(station_){}
  bool operator< (const state &s) const{
    /*
    if(cost == s.cost){
      return coupon > s.coupon;
    }
    */
    return cost > s.cost;
  }
};
int djikstra(vector<vector<edge> > graph, int start, int goal, int coupon){
  priority_queue<state> pq;
  pq.push(state(0, coupon, start));
  bool visited[coupon][graph.size()];
  //fill_n((bool*)visited, (coupon+1) * graph.size(), false);
  for(int i = 0; i < coupon+1; ++i){
    for(int j = 0; j < graph.size(); ++j){
      visited[i][j] = false;
    }
  }
  while(!pq.empty()){
    state cur = pq.top(); pq.pop();
    //cout << cur.station << ": " << cur.cost << ": " << cur.coupon << endl;
    if(visited[cur.coupon][cur.station]){
      continue;
    }
    if(cur.station == goal){
      return cur.cost;
    }
    visited[cur.coupon][cur.station] = true;
    for(int i = 0; i < graph[cur.station].size(); ++i){
      int to = graph[cur.station][i].first;
      int c = graph[cur.station][i].second;
      if(cur.coupon > 0){
        pq.push(state(cur.cost+c/2, cur.coupon-1, to));
      }
      pq.push(state(cur.cost+c, cur.coupon, to));
    }
  }
  //assert(false);
  return -1;
}
int main(){
  int c, n, m, s, d;
  while(true){
    cin >> c >> n >> m >> s >> d;
    if((c|n|m|s|d) == 0){
      break;
    }
    vector<vector<edge> > graph(n+1, vector<edge>());
    for(int i = 0; i < m; ++i){
      int a, b, f;
      cin >> a >> b >> f;
      graph[a].push_back(make_pair(b, f));
      graph[b].push_back(make_pair(a, f));
    }
    cout << djikstra(graph, s, d, c) << endl;
  }
  return 0;
}