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 <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;
}

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

#define fr first
#define sc second
typedef pair<int,int> Pi;
typedef pair<Pi,int> Pii;
struct edge{
  int to,cost;
};
typedef vector< vector< edge > > Graph;

int Dijkstr(Graph& info,int s,int g,int c){
  vector< vector<int> > min_cost;
  priority_queue<Pii,vector<Pii>,greater<Pii> > que;
  min_cost.resize(c+1,vector<int>(info.size(),-1)); //min_costの確保と共に、全てに-1を代入。
  
  que.push( Pii(Pi(0,s),c) ); //fr:現在額。sc:現在地。
  min_cost[c][s] = 0;
  while(!que.empty()){
    Pii p = que.top();//fr.fr:現在額。fr.sc:現在地。sc:割引券。
    que.pop();
    if(p.fr.sc == g) return p.fr.fr;
    if(p.fr.fr > min_cost[p.sc][p.fr.sc]) continue; //最も小さな値より大きい時はまわらない。
    for(int i=0;i<info[p.fr.sc].size();i++){ //p.scから伸びる道の数だけまわる。
      edge& e = info[p.fr.sc][i];//p.scから伸びる道の一つ。
      if(min_cost[p.sc][e.to] == -1 || p.fr.fr+e.cost < min_cost[p.sc][e.to]){//まだ行っていないか、いままでで一番安いか。
	min_cost[p.sc][e.to] = p.fr.fr+e.cost;//min_costを更新。
	que.push( Pii(Pi(min_cost[p.sc][e.to],e.to),p.sc));//移動後を現在額と現在値として記録。
      }
      if(p.sc > 0 && (min_cost[p.sc-1][e.to] == -1 || p.fr.fr+(e.cost/2) < min_cost[p.sc-1][e.to])){
	min_cost[p.sc-1][e.to] = p.fr.fr+e.cost/2;//min_costを更新。
	que.push( Pii(Pi(min_cost[p.sc-1][e.to],e.to),p.sc-1));//移動後を現在額と現在値として記録。
      }
    }
  }
  
  return -1;
}


int main(){
  int c,n,m,s,d;
  while(1){
    Graph info;
    cin >> c >> n >> m >> s >> d;
    if(c==0 && n==0 && m==0 && s==0 && d==0) break;
    info.resize(m + 1);
    int a,b,f;
    for(int i=0;i<m;i++){
      cin >> a >> b >> f;
      info[a].push_back((edge){b,f});
      info[b].push_back((edge){a,f});
    }
    
    //経路探索
    cout << Dijkstr(info,s,d,c) << endl;
  }
}