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;
typedef complex<double> P;
static const double EPS = 1e-10;
static const double PI = acos( -1.0 );
static const int mod = 1000000007;
static const int INF = 1 << 29;
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, ans;
vector<vector<PII> > v;
int dp[ 11 ][ 100 ];

int solve( int canUseT, int now ) {
	if ( now == d ) {
		return 0;
	}
	if ( dp[ canUseT ][ now ] >= 0 ) {
		return dp[ canUseT ][ now ];
	}
	dp[ canUseT ][ now ] = INF;
	int res = INF;
	for ( int i = 0; i < v[now].size(); i++ ) {
		if ( canUseT ) {
			res = min( res, solve( canUseT - 1, v[ now ][ i ].first ) + v[ now ][ i ].second / 2 );
		}
		res = min( res, solve( canUseT, v[ now ][ i ].first ) + v[ now ][ i ].second );
	}
	return dp[ canUseT ][ now ] = res;
}

int main() {
	while ( ~scanf( "%d %d %d %d %d", &c, &n, &m, &s, &d ) && c && n && m && s && d ) {
		s--;
		d--;
		v.resize( n );
		NCLR( dp );
		for ( int i = 0; i < m; i++ ) {
			int a, b, f;
			scanf( "%d %d %d", &a, &b, &f );
			v[ a - 1 ].push_back( MP( b - 1, f ) );
			v[ b - 1 ].push_back( MP( a - 1, f ) );
		}
		ans = solve( c, s );
		printf( "%d\n", ans );
		v.clear();
	}
	return 0;
}

C++: #include <iostream>
#include <list>
#include <queue>
using namespace std;

#define INF 100000000

struct Edge {
    int dst, fare;
    Edge(int d, int f) {
        dst = d;
        fare = f;
    }
};

struct Town {
    list<Edge*> edge;
};

struct Vertex {
    int c, tid, cost;
    Vertex (int ticket_count, int town_id, int icost) {
        c = ticket_count;
        tid = town_id;
        cost = icost;
    }
    void dump() {
        cout << "[" << c << "]" << " " << tid << "(" << cost << ")" << endl;
    }
};

bool operator<(const Vertex &a, const Vertex &b) {
    return a.cost > b.cost;
}

int main() {
    int c, n, m, s, d, a, b, f, i, j;
    while (cin >> c >> n >> m >> s >> d, c) {
        Town town[n+1];
        int cost[c+1][n+1];
        for (i = 0; i < m; i++) {
            cin >> a >> b >> f;
            town[a].edge.push_back(new Edge(b, f));
            town[b].edge.push_back(new Edge(a, f));
        }
        for (i = 0; i <= c; i++) {
            for (j = 1; j <= n; j++) {
                cost[i][j] = INF;
            }
        }
        priority_queue<Vertex*> q;
        cost[0][s] = 0;
        Vertex *v = new Vertex(0, s, 0);
        q.push(v);
        while (!q.empty()) {
            v = q.top(); q.pop();
            if (v->tid == d) {
                if (v->c == c) {
                    delete v;
                    break;
                }
                delete v;
                continue;
            }
            list<Edge*> e = town[v->tid].edge;
            for (list<Edge*>::iterator itr = e.begin();
                 itr != e.end(); itr++) {
                int ncost = v->cost + (*itr)->fare;
                int dst = (*itr)->dst;
                if (ncost < cost[v->c][dst]) {
                    cost[v->c][dst] = ncost;
                    q.push(new Vertex(v->c, dst, ncost));
                }
                if (v->c < c) {
                    ncost = v->cost + (*itr)->fare / 2;
                    if (ncost < cost[v->c+1][dst]) {
                        cost[v->c+1][dst] = ncost;
                        q.push(new Vertex(v->c+1, dst, ncost));
                    }
                }
            }
            delete v;
        }
        int min_cost = INF;
        for (i = 0; i <= c; i++) {
            if (cost[i][d] < min_cost) min_cost = cost[i][d];
        }
        cout << min_cost << endl;
    }
    return 0;
}