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, 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)
					}
				}
			}
		}
	}
}

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

using namespace std;

struct P {
	int from, cost, coupon;

	bool operator >(const P& p) const {
		return cost > p.cost;
	}
};

int ecost[101][101];
int ccost[101][11];
int c, n, m, s, d;
int i;

int main() {
	while(cin >> c >> n >> m >> s >> d, c|n|m|s|d) {
		fill_n((int *)ecost, 101*101, -1);
		fill_n((int *)ccost, 101*11, 1e8);
		for(i=0; i<11; i++) ccost[s][i] = 0;
		for(i=0; i<m; i++){
			int a, b, f;
			cin >> a >> b >> f;
			ecost[a][b] = f;
			ecost[b][a] = f;
		}
		priority_queue<P, vector<P>, greater<P>> q;
		q.push((P){s, 0, 0});
		int dcost;
		while(!q.empty()){
			P p = q.top(); q.pop();
			// cout << "pos=" << p.from << endl;
			// goal
			if(p.from == d) {
				dcost = p.cost;
				break;
			}
			//
			for(i=0; i<n+1; i++){ // i:to
				if(ecost[p.from][i] != -1){
					bool ifpush = true;
					for(int j=0; j <= p.coupon; j++) ifpush = ifpush && p.cost + ecost[p.from][i] < ccost[i][j];
					if(ifpush) {
					//if(p.cost + ecost[p.from][i] < ccost[i][p.coupon]){
						ccost[i][p.coupon] = p.cost + ecost[p.from][i];
						q.push((P){i, p.cost + ecost[p.from][i], p.coupon});
					}
					if(p.coupon+1 <= c) {
						bool ifpush = true;
						for(int j=0; j <= p.coupon+1; j++) ifpush = ifpush && p.cost + ecost[p.from][i]/2 < ccost[i][j];
						if(ifpush) {
						// if(p.cost + ecost[p.from][i]/2 < ccost[i][p.coupon+1]){
							ccost[i][p.coupon+1] = p.cost + ecost[p.from][i]/2;
							q.push((P){i, p.cost + ecost[p.from][i]/2, p.coupon+1});
						}
					}
				}
			}
		}
		cout << dcost << endl;
	}
	return 0;
}

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

using namespace std;

struct P {
	int from, cost, coupon;

	bool operator >(const P& p) const {
		return cost > p.cost;
	}
};

int ecost[101][101];
int ccost[101][11]; // 0:not use coupon 1:use coupon
int c, n, m, s, d;
int i;

int main() {
	while(cin >> c >> n >> m >> s >> d, c|n|m|s|d) {
		fill_n((int *)ecost, 101*101, -1);
		fill_n((int *)ccost, 101*11, 1e8);
		for(i=0; i<m; i++){
			int a, b, f;
			cin >> a >> b >> f;
			ecost[a][b] = f;
			ecost[b][a] = f;
		}
		priority_queue<P, vector<P>, greater<P>> q;
		q.push((P){s, 0, 0});
		int dcost;
		while(!q.empty()){
			P p = q.top(); q.pop();
			// goal
			if(p.from == d) {
				dcost = p.cost;
				break;
				P p2 = q.top();
				while(p.cost <= p2.cost && p.coupon <= p2.coupon){
					q.pop();
				}
				if(q.empty()) break;
				else continue;
			}
			//
			for(i=0; i<n+1; i++){ // i:to
				if(ecost[p.from][i] != -1){
					q.push((P){i, p.cost + ecost[p.from][i], p.coupon});
					if(p.coupon+1 <= c) {
						if(p.cost + ecost[p.from][i]/2 < ccost[i][p.coupon+1]){
							q.push((P){i, p.cost + ecost[p.from][i]/2, p.coupon+1});
						}
					}
					ecost[p.from][i] = -1;
					ecost[i][p.from] = -1;
				}
			}
		}
		cout << dcost << endl;
	}
	return 0;
}

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

#define MAX 100
#define INF 100000000
int G[MAX][MAX];
int c, n, m, s, d, a, b, f;

int dijkstra(){
    int D[MAX][11];
    bool visited[MAX][11];
    for (int i = 0; i < n; i++) {
        for (int j = 0; j <= c; j++) {
            D[i][j] = INF;
            visited[i][j] = false;
        }
    }
    D[s][c] = 0;
    while (true) {
        int u, w, minv = INF;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j <= c; j++) {
                if (!visited[i][j] && minv > D[i][j]) {
                    minv = D[i][j];
                    u = i;
                    w = j;
                }
            }
        }
        if (minv == INF) {
            break;
        }
        visited[u][w] = true;
        for (int v = 0; v < n; v++) {
            if (G[u][v] == INF) {
                continue;
            }
            D[v][w] = min(D[v][w], D[u][w] + G[u][v]);
            if (w) {
                D[v][w-1] = min(D[v][w-1], D[u][w] + G[u][v] / 2);
            }
        }
    }
    int minv = INF;
    for (int i = 0; i <= c; i++) {
        minv = min(minv, D[d][i]);
    }
    return minv;
}

int main()
{
    while (true) {
        cin >> c >> n >> m >> s >> d;
        if (s == 0 && d == 0) {
            break;
        }
        s--;
        d--;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                G[i][j] = INF;
            }
        }
        for (int i = 0; i < n; i++) {
            cin >> a >> b >> f;
            a--;
            b--;
            G[a][b] = G[b][a] = f;
        }
        cout << dijkstra() << endl;
    }

    return 0;
}