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]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 <cstdio>
#include <vector>
#include <algorithm>
#include <string>
#include <map>
#include <set>
#include <queue>
#include <climits>

using namespace std;

#define reep(i,f,t) for(int i=f ; i<int(t) ; ++i)
#define rep(i,n) reep(i, 0, n) 

typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int,int> pii;

struct Edge
{
	int src, dst;
	int weight;
	Edge(int src, int dst, int weight) : src(src), dst(dst), weight(weight) {}

	bool operator< (const Edge& e)const
	{
		return weight != e.weight ? weight > e.weight :
			src != e.src ? src < e.src : dst < e.dst;
	}
};

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

void Dijkstra(const Graph& g, int s, vi& dist, vi& prev)
{
	int n = g.size();
	dist.assign(n, INT_MAX);
	dist[s] = 0;
	prev.assign(n, -1);
	
	priority_queue<Edge> Q;
	Q.push(Edge(-2, s, 0));

	while(!Q.empty()){
		Edge e = Q.top();
		Q.pop();
		if(prev[e.dst] != -1)
			continue;
		prev[e.dst] = e.src;

		rep(i, g[e.dst].size()){
			int pw = e.weight + g[e.dst][i].weight;
			if(dist[g[e.dst][i].dst] > pw){
				dist[g[e.dst][i].dst] = pw;
				Q.push(Edge(g[e.dst][i].src, g[e.dst][i].dst, pw));
			}
		}
	}
}


vi buildPath(const vi& prev, int t)
{
	vi path;
	for(int u = t; u >= 0; u = prev[u])
		path.push_back(u);
	reverse(path.begin(), path.end());
	return path;
}

int main()
{
	int c, n, m, s, d;
	while(scanf("%d%d%d%d%d", &c, &n, &m, &s, &d), c){
		--s; --d;
		Graph g(n*(c+1));
		rep(i, m){
			int a, b, f;
			scanf("%d%d%d", &a, &b, &f);
			--a; --b;

			rep(j, c+1){
				g[j*n+a].push_back(Edge(j*n+a, j*n+b, f));
				g[j*n+b].push_back(Edge(j*n+b, j*n+a, f));
				if(j){
					g[(j-1)*n+a].push_back(Edge((j-1)*n+a, j*n+b, f/2));
					g[(j-1)*n+b].push_back(Edge((j-1)*n+b, j*n+a, f/2));
				}
			}
		}

		vi dist, prev;
		Dijkstra(g, s, dist, prev);

		int ans = INT_MAX;
		rep(j, c+1){
			ans = min(ans, dist[j*n+d]);
		}
		printf("%d\n", ans);
	}

	return 0;
}

C++: #include<iostream>
#include<utility>
#include<vector>
#include<cstdio>
#include<queue>
#include <map>
using namespace std;
typedef pair<int, int> P;
typedef pair<int, P> PP;
//int in(){int x;cin>>x;return x;}

int main ()
{
	int c,n,m,s,d;
	while(cin>>c>>n>>m>>s>>d&&c&&n&&m&&s&&d)
	{
		int flg[110]={};
		int ans =0;
		priority_queue < PP, vector<PP>, greater<PP> > q;
		vector< pair< int,int > > way[110];
		for(int i=0;i<m;i++)
		{
			int a,b,f;
			cin>>a>>b>>f;
			way[a].push_back(pair<int,int>(b,f));
			way[b].push_back(pair<int,int>(a,f));
		}
		pair< int , pair<int,int> > next;
		next.first=0;next.second.first=s;next.second.second=c;
		q.push(next);
		while(!q.empty())
		{
			pair< int , pair<int,int> > now=q.top();q.pop();
			flg[now.second.first]=1;
			if(now.second.first==d)
			{
				ans=now.first;
				break;
			}
			
			for(int i=0;i<way[now.second.first].size();i++)
			{
				if(flg[way[now.second.first][i].first]==1)continue;
				next.first=now.first+way[now.second.first][i].second;
				next.second.first=way[now.second.first][i].first;
				q.push(next);
				next.first=now.first+way[now.second.first][i].second/2;
				next.second.first=way[now.second.first][i].first;
				next.second.second=now.second.second-1;
				q.push(next);
			}
			
		}
		cout<<ans<<endl;
	}
	
	
	return 0;
}