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]int)
		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}] = now.Amount
			for _, v := range pointMap[now.NowPosition] {
				next := &Node{v.NextPoint, now.DiscountTicketTCount, now.Amount + v.Fee}
				if memoAmount, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok || (ok && memoAmount > next.Amount) {
					memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}] = next.Amount
					heap.Push(&pq, next)
				}
				if now.DiscountTicketTCount > 0 {
					next = &Node{v.NextPoint, now.DiscountTicketTCount - 1, now.Amount + v.Fee/2}
					if memoAmount, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok || (ok && memoAmount > next.Amount) {
						memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}] = next.Amount
						heap.Push(&pq, next)
					}
				}
			}
		}
		runtime.GC()
	}
}

C++: #include<bits/stdc++.h>
using namespace std;

class Node{
public:
	int num;
	int c;
	int fee;

	Node(){ num = 0; c = 0; fee = 0;}
	Node(int num, int c, int fee) : num(num), c(c), fee(fee){}

};

bool operator< (const Node &n1, const Node &n2){
	return n1.fee < n2.fee;
}

bool operator>(const Node &n1, const Node &n2){
	return n1.fee > n2.fee;
}

int main(void){

	int c, n, m, s, d;
	while (cin >> c >> n >> m >> s >> d, c, n, m, s, d){
		vector<vector <int> > path(n + 1);
		vector<vector <int> > cost(n + 1);
		bool checked[101][11] = { false };

		for (int i = 0; i < m; i++){
			int a, b, f;
			cin >> a >> b >> f;
			path[a].push_back(b);
			cost[a].push_back(f);
			path[b].push_back(a);
			cost[b].push_back(f);
		}

		priority_queue<Node, vector<Node>, greater<vector<Node>::value_type> > que;

		que.push(Node(s, c, 0));

		while (!que.empty()){
			Node buff = que.top();
			que.pop();
			if (checked[buff.num][buff.c]) continue;
			checked[buff.num][buff.c] = true;
			if (buff.num == d){
				cout << buff.fee << endl;
				break;
			}

			int nnum = buff.num;
			for (int i = 0; i < path[nnum].size(); i++){
				que.push(Node(path[nnum][i], buff.c, buff.fee + cost[nnum][i]));
				if (buff.c > 0) que.push(Node(path[nnum][i], buff.c - 1, buff.fee + cost[nnum][i] / 2));
			}
		}
	}
	return 0;
}

C++: #include<iostream>
#include<queue>
#include<vector>

using namespace std;

#define REP(i, n) for(int i=0; i<n; i++)

struct edge{
    int to, cost;
};

typedef pair<int, pair<int, int> > pii; // distance, edge, ticket

int INF = 10e8;
int c, n, m, s, d;

int dis[101][11];

int main(){
    while(1){
        cin >> c >> n >> m >> s >> d;

        if(n==0) break;

        vector<edge> g[100];
        REP(i, m){
            int a, b, f;
            cin >> a >> b >> f;
            edge ae;
            ae.to = b;
            ae.cost = f;
            g[a].push_back(ae);
            edge be;
            be.to = a;
            be.cost = f;
            g[b].push_back(be);
        }

        priority_queue<pii, vector<pii>, greater<pii> > que;
        REP(i, n+1){
            REP(j, c+1){
                dis[i][j] = INF;
            }
        }
        dis[s][c] = 0;
        pii init = make_pair(0, make_pair(s, c));
        que.push(init);

        while(!que.empty()){
            pii p = que.top();
            que.pop();

            int v = p.second.first;
            int t = p.second.second;
            if(dis[v][t]<p.first) continue;
            REP(i, g[v].size()){
                edge e = g[v][i];
                if(dis[e.to][t] > dis[v][t] + e.cost){
                    dis[e.to][t] = dis[v][t] + e.cost;
                    que.push(pii(make_pair(dis[e.to][t], make_pair(e.to, t))));
                }
                if(t>0 && dis[e.to][t-1] > dis[v][t] + e.cost / 2){
                    dis[e.to][t-1] = dis[v][t] + e.cost / 2;
                    que.push(pii(make_pair(dis[e.to][t-1], make_pair(e.to, t-1))));
                }
            }
        }
        /*
        REP(i, n+1){
            REP(j, c+1){
                cout << dis[i][j] << " ";
            }
            cout << endl;
        }
        */
        cout << dis[d][0] << endl;
    }
}

C++: #include <iostream>
#include <queue>
#include <vector>
#include <functional>

using namespace std;

const int INF = 10000000;

int city[101][101];

int solve( int s, int d, int c, int n ){
	int dist[11][101];
	int history[11][101];

	for( int i = 0;i < 11;i++ ){
		for( int j = 1;j < 101;j++ ){
			dist[i][j] = INF;
			history[i][j] = 0;
		}
	}


	for( int i = 0;i < 11;i++ ) dist[i][s] = 0;

	typedef pair<int,int> data;
	typedef pair<int,data> graph;
	priority_queue<graph,vector<graph>,greater<graph> > q;

	q.push( graph( 0, data( s, c ) ) );

	while( !q.empty() ){
		graph a = q.top();
		int u = a.second.first;
		int uc = a.second.second;
		q.pop();
		history[uc][u] = 1;

		for( int i = 1;i <= n;i++ ){

			if( history[uc][i] ) continue;
			if( dist[uc][i] > dist[uc][u] + city[u][i] ){
				dist[uc][i] = dist[uc][u] + city[u][i];
				q.push( graph( dist[uc][i], data( i, uc ) ) );
			}

			if( uc && dist[uc - 1][i] > dist[uc][u] + city[u][i] / 2 ){
				dist[uc - 1][i] = dist[uc][u] + city[u][i] / 2;
				q.push( graph( dist[uc - 1][i], data( i, uc - 1 ) ) );
			}
		}
	}
	int answer = INF;
	for( int i = 0;i < 11;i++ ) answer = min( dist[i][d], answer );
	return answer;

}

int main(int argc, char const* argv[])
{
	int c,n,m,s,d;

	while( cin >> c >> n >> m >> s >> d && c != 0 ){
		int a,b,f;
		for( int i = 1;i < 101;i++ ){
			for( int j = 1;j < 101;j++ ){
				city[i][j] = INF * 2;
			}
		}
		for( int i = 0;i < m;i++ ){
			cin >> a >> b >> f;
			city[a][b] = f;
			city[b][a] = f;
		}

		cout << solve( s, d, c, n ) << endl;
	}

	return 0;
}