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<cstdio>
#include<algorithm>
#include<queue>
#include<cstring>
#include<vector>
#include<string>
#define reep(a,s,d) for(int a=d;a<s;a++)
#define rep(a,s) reep(a,s,0)
using namespace std;
struct edge{
    int to,cost,tick;
    edge(int to,int cost,int tick):to(to),cost(cost),tick(tick){}
    edge(){}
};
bool operator<(const edge &a,const edge &b){
    return a.cost>b.cost;
}
int main(){
    int c,n,m,s,d;
    while(cin>>c>>n>>m>>s>>d,c){
        vector<edge> G[128];
        rep(i,m){
            int a,b,c;
            cin>>a>>b>>c;
            G[--a].push_back(edge(--b,c,0));
            G[b].push_back(edge(a,c,0));
        }
        bool vis[16][128];
        memset(vis,false,sizeof(vis));
        priority_queue<edge> Q;
        Q.push(edge(s-1,0,0));
        int ret=-1;
        while(!Q.empty()){
            edge n=Q.top();Q.pop();
            if(vis[n.tick][n.to])continue;
            vis[n.tick][n.to]=true;
            if(n.to==d-1){
                ret=n.cost;
                break;
            }
            rep(i,G[n.to].size()){
                Q.push(edge(G[n.to][i].to,n.cost+G[n.to][i].cost,n.tick));
                if(n.tick<c){
                    Q.push(edge(G[n.to][i].to,n.cost+G[n.to][i].cost/2,n.tick+1));
                }
            }
        }
        cout<<ret<<endl;
    }
}

C++: #include<iostream>
#include<queue>
#include<string.h>
using namespace std;

const int INF = 1<<30;

struct Node{
  int use,to,weight;
  Node() {;}
  Node(int use,int to,int weight) : use(use), to(to), weight(weight) {;}
};
bool operator<(const Node &e,const Node &f) {
  return e.weight > f.weight;
}

int dist[110][110];
bool visit[110];
int dist2[110][110];

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

      for(int i=0; i<110; ++i) {
	for(int j=0; j<110; ++j) {
	  dist[i][j] = INF;
	}
	visit[i] = false;
      }

      for(int i=0; i<110; ++i)
	for(int j=0; j<110; ++j)
	  dist2[i][j] = INF;

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

      priority_queue<Node> Q;
      Q.push(Node(0,s,0));
      visit[s] = true;
      while(!Q.empty()) {
	Node now = Q.top(); Q.pop();

	if(now.to == d) {
	  cout<<now.weight<<endl;
	  break;
	}

	visit[now.to] = true;
	for(int i=0; i<n; ++i) {
	  if(!visit[i] && dist[now.to][i] != INF) {
	    if(dist2[now.use+1][i]
	       > now.weight + dist[now.to][i]/2 && now.use < c) {
	      dist2[now.use+1][i] = now.weight + dist[now.to][i]/2;
	      Q.push(Node(now.use+1, i, dist2[now.use+1][i]));
	    }
	    if(dist2[now.use][i]
	       > now.weight + dist[now.to][i]) {
	      dist2[now.use][i] = now.weight + dist[now.to][i];
	      Q.push(Node(now.use, i, dist2[now.use][i]));
	    }
	  }
	}
      }

/*
      for(int i=0; i<=c; ++i) {
	cout<<dist2[i][d]<<" : "<<i<<endl;
      }
*/
    }
}

C++: #include <algorithm>
#include <bitset>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <ctime>
#include <climits>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#define ALL(A)		(A).begin(),(A).end()
#define DUMP(A)    cout<<#A<<"="<<(A)<< endl
#define SIZE(A)    (int)((A).size())
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
typedef pair<int,P> PP;

int main(){
    int c,n,m,s,d;
    for(;;){
        scanf("%d%d%d%d%d",&c,&n,&m,&s,&d);
        if(c==0&&n==0&&m==0&&s==0&&d==0) break;
        s--;d--;
        int path[100][100];
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                path[i][j]=-1;
            }
        }
        int fr,to,co;
        for(int i=0;i<m;i++){
            scanf("%d%d%d",&fr,&to,&co);
            fr--;to--;
            path[fr][to]=path[to][fr]=co;
        }
        int dist[100][11];
        for(int i=0;i<n;i++){
            for(int j=0;j<=c;j++){
                dist[i][j]=-1;
            }
        }
        priority_queue<PP> pque;
        pque.push(PP(0,P(0,s)));
        while(!pque.empty()){
            PP now=pque.top();
            pque.pop();
            int ndi=now.first,ncar=now.second.first,nat=now.second.second;
            if(dist[nat][ncar]!=-1 && dist[nat][ncar]<=ndi) continue;
            dist[nat][ncar]=ndi;
            for(int i=0;i<n;i++){
                if(path[nat][i]!=-1 && (dist[i][ncar]==-1 || ndi+path[nat][i]<dist[i][ncar])){
                    pque.push(PP(ndi+path[nat][i],P(ncar,i)));
                }
                if(path[nat][i]!=-1 && ncar+1<=c && (dist[i][ncar+1]==-1 || ndi+path[nat][i]/2 < dist[i][ncar+1])){
                    pque.push(PP(ndi+path[nat][i]/2,P(ncar+1,i)));
                }
            }
        }
        int mi=INT_MAX;
        for(int i=0;i<=c;i++){
            if(dist[d][i]!=-1 && dist[d][i]<mi) mi=dist[d][i];
        }
        printf("%d\n",mi);
    }
}