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
}

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)
		for len(pq) != 0 {
			now := heap.Pop(&pq).(*Node)
			if now.NowPosition == d {
				fmt.Println(now.Amount)
				break
			}
			for _, v := range pointMap[now.NowPosition] {
				next := &Node{v.NextPoint, now.DiscountTicketTCount, now.Amount + v.Fee}
				heap.Push(&pq, next)
				if now.DiscountTicketTCount > 0 {
					next = &Node{v.NextPoint, now.DiscountTicketTCount - 1, now.Amount + v.Fee/2}
					heap.Push(&pq, next)
				}
			}
		}
	}
}

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

using namespace std;

struct node {
	int to, cost, ticket;

	node(int to, int cost) : to(to), cost(cost) { this -> ticket = 0; }
	node(int to, int cost, int ticket) : to(to), cost(cost), ticket(ticket) { }
	node() { this -> to = this -> cost = this -> ticket = 0; }
};

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

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

int main() {
	int c, n, m, s, d;
	while (cin >> c >> n >> m >> s >> d, c || n || m || s || d) {
		--s, --d;

		vector< vector<node> > v(n);
		for (int i = 0; i < m; ++i) {
			int a, b, f; cin >> a >> b >> f;
			--a, --b;
			v[a].push_back( node(b, f) );
			v[b].push_back( node(a, f) );
		}

		int rest = c;
		vector< vector<int> > cost(n, vector<int>(c+1, -1));
		vector<bool> used(n, -1);
		priority_queue< node, vector<node>, greater<node> > que; que.push( node(s, 0, c) );
		while ( !que.empty() ) {
			node next = que.top(); que.pop();

			if (cost[next.to][next.ticket] >= 0) continue;
			cost[next.to][next.ticket] = next.cost;

			if (next.to == d) {
				cout << next.cost << endl;
				break;
			}

			for (int i = 0; i < v[next.to].size(); ++i) {
				que.push( node(v[next.to][i].to, next.cost + v[next.to][i].cost, next.ticket) );
				if (next.ticket) que.push( node(v[next.to][i].to, next.cost + v[next.to][i].cost/2, next.ticket-1) );
			}
		}
	}
}

C++: #include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <cstring>
#include <cstdio>
#include <queue>
#include <stack>
#include <map>
#include <set>

#define rep(i, n) for(int i = 0; i < (n); i++)
#define FOR(i, a, b) for(int i = (a); i < (b); i++)
#define all(v) (v).begin(), (v).end()
#define rev(s) string((s).rbegin(), (s).rend())
#define MP make_pair
#define X first
#define Y second

using namespace std;

typedef long long ll;
typedef pair<int, int> P;

const int INF = 10000;


class V{
public:
	int total;
	int ticket;
	int to;
};
bool operator>(const V &lh, const V &rh){
	return (lh.total > rh.total);
}


int main(){
	while(1){

		int c, n, m, s, d;
		cin >> c >> n >> m >> s >> d;
		if(!(c+n+m+s+d))break;
		n++;
		vector<vector<int> > fare(n, vector<int>(n, INF));
		rep(i, m){
			int a, b, f;
			cin >> a >> b >> f;
			fare[a][b] = fare[b][a] = f;
		}

		vector<vector<int> > done(c+1, vector<int>(n, 0));	// 確定済みか
		vector<vector<int> > best(c+1, vector<int>(n, INF));	// 最短

		V start;
		start.total = 0;
		start.ticket = 0;
		start.to = s;

		priority_queue<V, vector<V>, greater<V> > q;
		q.push(start);

		while(!q.empty()){
			V p = q.top();
			q.pop();

			if(done[p.ticket][p.to] != 0) continue;
			done[p.ticket][p.to] = 1;
			best[p.ticket][p.to] = p.total;

			rep(i, n){
				if(fare[p.to][i] == INF ) continue;
				V next;
				if(done[p.ticket][i]) continue;
				next.total = p.total + fare[p.to][i];
				next.ticket = p.ticket;
				next.to = i;
				q.push(next);
				if(p.ticket < c){
					if(done[p.ticket+1][i]) continue;
					next.total = p.total + fare[p.to][i]/2;
					next.ticket = p.ticket+1;
					next.to = i;
					q.push(next);
				}
			}
		}
		//rep(i, c+1){
		//	rep(j, n){
		//		printf("%5d", best[i][j]);
		//	}
		//	cout << endl;
		//}

		cout << best[c][d] << endl;
	}

	return 0;
}

C++: #include <iostream>
#include <vector>
#include <stack>
#include <queue>
#include <algorithm>
#include <string>
#include <bitset>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <string.h>

#define X first
#define Y second
#define MP make_pair
typedef long long ll;
using namespace std;

int mindis[101], pre[101];
bool used[101];
int eCost[101][101];

int getPathSum(int c, int p, int g){
	vector<int> edge;
	edge.push_back(eCost[p][g]);
		
	int to = p;
	for(int from = pre[to]; from != 0; from = pre[from]){
		edge.push_back(eCost[from][to]);
		to = from;
	}

	sort(edge.begin(), edge.end());

	int idx = edge.size()-1;
	for(int i = 0; i < c; i++){
		edge[idx--] /= 2;
		if(idx < 0) break;
	}
	
	int ans = 0;
	for(int i = 0; i < edge.size(); i++){
		ans += edge[i];
	}

	return ans;
}

int main(){
	int c, n, m, s, d;
	while(cin >> c >> n >> m >> s >> d){
		if(c == 0 && n == 0 && m == 0 && s == 0 && d == 0) break;

		fill(mindis, mindis+101, 1<<30);
		fill(pre, pre+101, 0);
		fill(used, used+101, false);
		for(int i = 0; i < 101; i++) fill(eCost[i], eCost[i]+101, 1<<30);

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

		mindis[s] = 0;
		vector<int> goals;

		//最短経路(ダイクストラ)
		while(true){
			int v = -1;
			for(int i = 1; i <= n; i++){
				if(!used[i] && (v == -1 || mindis[v] > mindis[i])) v = i;
			}

			if(v == d) break;
			used[v] = true;

			for(int i = 1; i <= n; i++){
				if(mindis[i] > mindis[v]+eCost[v][i]){
					if(i == d){
						//次がゴールならここでチケットを適用した総和を出して最終的な結果にする
						//それをgoalsに格納していく
						goals.push_back(getPathSum(c, v, i));
					}else{
						mindis[i] = mindis[v]+eCost[v][i];
						pre[i] = v;
					}
				}
			}
		}

		int minc = 10000000;
		for(int i = 0; i < goals.size(); i++){
			if(minc > goals[i]) minc = goals[i];
		}

		cout << minc << endl;
	}
	return 0;
}