Go: package main

import (
	"container/heap"
	"fmt"
)

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)
		}
		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)
		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)
					}
				}
			}
		}
	}
}

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)));
        dist[s][0]=0;
        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;
            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)));
                    dist[i][ncar]=ndi+path[nat][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)));
                    dist[i][ncar+1]=ndi+path[nat][i]/2;
                }
            }
        }
        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);
    }
}

C++: #include<iostream>
#include<algorithm>
#include<queue>
#include<vector>
#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define F first
#define S second
using namespace std;
typedef pair<int,int> P;// F -> to, S -> cost
typedef pair<P,int> PP;// F->P(to,cost), S->discount
int c,n,m,s,d;
vector<PP> vec[1000];
int MD[1000][13];
const int INF = 1<<29;

void dijkstra(){
  priority_queue<PP,vector<PP>,greater<PP> > que;
  rep(i,n+1)rep(j,13)MD[i][j] = INF;
  //syokika
  MD[s][c] = 0;
  que.push(PP(P(0,s),c));//dis,start,discount

  while(!que.empty() ){
    PP p = que.top();que.pop(); //priority_queのPPと
    int v = p.F.S;
    
    for(int i=0;i<vec[v].size();i++){
      PP po = vec[v][i]; //vectorのPPは意味が違うので注意！！！
      //if(MD[v][po.S] < po.F.S)continue;
      if(MD[po.F.F][c] > MD[v][c] + po.F.S){
	MD[po.F.F][c] = MD[v][c]+po.F.S;
	que.push(PP(P(MD[po.F.F][c],po.F.F),c));
      }
      if(po.S > 0 && MD[po.F.F][p.S-1] > MD[v][p.S] + po.F.S/2 ){
	MD[po.F.F][p.S-1] = MD[v][p.S]+po.F.S/2;
	que.push(PP(P(MD[po.F.F][p.S-1],po.F.F),p.S-1));
      }
    }
  }
}


int main(){
  int x,y,co;
  while(true){
    cin >> c >> n >> m >> s >> d;
    if(c+n+m+s+d == 0)break;
    rep(i,1000)vec[i].clear();
    rep(i,m){
      cin >> x >> y >> co;
      vec[x].push_back(PP(P(y,co),c));
      vec[y].push_back(PP(P(x,co),c));
    }
    dijkstra();
    int ans = INF;
    for(int i=0;i<=c;i++){
      ans = min(ans,MD[d][i]);
    }
    cout << ans << endl;
  }
  return 0;
}