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 <bits/stdc++.h>
using namespace std;
#define FOR(i, s, n) for(int i = s; i < (int)n; i++)
#define per(i, n) for(int i = n; i >= 0; i--)
#define ROF(i, s, n) for(int i = s; i >= (int)n; i--)
#define FORIT(i, A) for (auto i : A)
#define PRINT(x) cout << (x) << "\n"
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define MP make_pair
#define EACH(i, n) for (__typeof((n).begin()) i = (n).begin(); i != (n).end(); ++i)
#define SZ(a) int((a).size())
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort((c).begin(),(c).end())
#define CLR(a) memset((a), 0 ,sizeof(a))
#define NCLR(a) memset((a), -1 ,sizeof(a))
#define dump(x) cout << #x << " = " << (x) << "\n";
#define debug(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << "\n";
#define sq(n) (n) * (n)
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef long long LL;
typedef vector<LL> VLL;
typedef vector<VLL> VVLL;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef priority_queue<int> maxpq;
typedef priority_queue< int, vector<int>, greater<int> > minpq;
static const double EPS = 1e-10;
static const double PI = acos( -1.0 );
static const int mod = 1000000007;
static const int INF = 1 << 30;
static const LL LL_INF = 1152921504606846976;
static const int dx[] = { -1, 0, 1, 0, 1, -1, 1, -1 };
static const int dy[] = { 0, -1, 0, 1, 1, 1, -1, -1 };



int c, n, m, s, d;
LL dp[ 11 ][ 101 ];
static LL _root[ 100 ][ 100 ];

LL solve( int now, int can_use, set<int> p ) {
	if ( now == d ) {
		if ( can_use ) {
			return LL_INF;
		}
		return 0;
	}
	p.insert( now );
	
	LL res = LL_INF;
	if ( dp[ can_use ][ now ] >= 0 ) {
		res = dp[ can_use ][ now ];
	}
	for ( int i = 0; i < n; ++i ) {
		if ( p.count( i ) || _root[ now ][ i ] >= res ) {
			continue;
		}
		res = min( res, solve( i, can_use, p ) + _root[ now ][ i ] );
		if ( can_use ) {
			res = min( res, solve( i, can_use - 1, p ) + _root[ now ][ i ] / 2 );
		}

	}
	return dp[ can_use ][ now ] = res;
}

int main() {
	while ( ~scanf( "%d %d %d %d %d", &c, &n, &m, &s, &d ) && n && m ) {
		--s;
		--d;
		for ( int i = 0; i < n; ++i ) {
			for ( int j = 0; j < n; ++j ) {
				_root[ i ][ j ] = LL_INF;
			}
			_root[ i ][ i ] = 0;
		}
		for ( int i = 0; i < m; ++i ) {
			int a, b, f;
			scanf( "%d %d %d", &a, &b, &f );
			--a;
			--b;
			_root[ a ][ b ] = _root[ b ][ a ] = f;
		}
		NCLR( dp );
		LL ans = solve( s, c, set<int>() );
		printf( "%lld\n", ans );
	}
	return 0;
}

C++: #include <iostream>
#include <stdio.h>
#include <sstream>
#include <string>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>
#include <set>
#include <math.h>
#include <utility>
#include <stack>
#include <string.h>
#include <complex>
using namespace std;
const int INF = 1<<29;
const double EPS = 1e-8;

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

struct node{
    int d,c,n;
    bool operator<( const node& right ) const {
        return d == right.d ? c < right.c : d > right.d;
    }
};

int main(){
    while(1){
        int c, n, m, s, goal;
        scanf("%d%d%d%d%d",&c,&n,&m,&s,&goal);
        if(!c)break;
        s--;goal--;

        vector<vector<edge> > g(n);
        for(int i=0;i<m;i++){
            int a, b, f;
            scanf("%d%d%d",&a,&b,&f);
            a--;b--;
            g[a].push_back((edge){b,f});
            g[b].push_back((edge){a,f});
        }

        vector<vec> d(c+1,vec(n,INF));
        d[c][s] = 0;
        priority_queue<node> que;
        que.push((node){0,c,s});

        int ans = INF;
        while(que.size()){
            node p = que.top(); que.pop();
            //printf("n=%d d=%d c=%d\n",p.n,p.d,p.c);
            if(d[p.c][p.n] < p.d) continue;
            if(p.n == goal){
                ans = p.d;
                break;
            }
            for(int i=0;i<g[p.n].size();i++){
                int to = g[p.n][i].to;
                if(p.c > 0){
                    int dist_to_use_c = p.d + g[p.n][i].cost/2;
                    if(d[p.c-1][to] > dist_to_use_c){
                        d[p.c-1][to] = dist_to_use_c;
                        //printf("pushed d=%d c=%d n=%d\n",dist_to_use_c,p.c-1,to);
                        que.push((node){dist_to_use_c,p.c-1,to});
                    }
                }
                int dist_to = p.d + g[p.n][i].cost;
                if(d[p.c][to] > dist_to){
                    d[p.c][to] = dist_to;
                    //printf("pushed d=%d c=%d n=%d\n",dist_to,p.c,to);
                    que.push((node){dist_to,p.c,to});
                }
            }
        }
        cout << ans << endl;
    }

    return 0;
}