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]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)
					}
				}
			}
		}
		runtime.GC()
	}
}

C++: //Solution for aoj:0212 Highway Express Bus
#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<functional>
using namespace std;
typedef pair<int, int>P;
typedef pair < P, int > PP;
#define f first
#define s second

//struct S {
//	int cost, to, num;
//	S(int c, int t, int n) : cost(c), to(t), num(n){}
//	bool operator>(const S &s) const {
//		return cost > s.cost;
//	}
//};

const int INF = 1 << 29;
int c, n, m, s, d, ans;
int tocost[101][11];
vector<P> town[501];
priority_queue<PP, vector<PP>, greater<PP> > pq;


void dijkstra(){
	while (!pq.empty()){
		PP a = pq.top();
		pq.pop();
		for (int i = 0; i < town[a.f.s].size(); i++){
			int tt = town[a.f.s][i].f, cc = town[a.f.s][i].s;
			if (tocost[tt][a.s] > cc + a.f.f){
				tocost[tt][a.s] = cc + a.f.f;
				pq.push({ { cc + a.f.f, tt }, a.s });
			}
			if (a.s&&tocost[tt][a.s-1] > cc/2 + a.f.f){
				tocost[tt][a.s-1] = cc/2 + a.f.f;
				pq.push({ { cc / 2 + a.f.f, tt }, a.s - 1 });
			}
		}
	}
}
	int main(){
		while (cin >> c >> n >> m >> s >> d&&c&&n&&m&&s){
			for (int i = 0; i < 101; i++)
				fill(tocost[i], tocost[i] + 11, INF);
			tocost[s][c] = 0;
			ans = INF;
			while (pq.size())
				pq.pop();
			for (int i = 0; i < n; i++)
				town[i].clear();
			for (int i = 0; i < m; i++){
				int a, b, c;
				cin >> a >> b >> c;
				town[a].push_back({ b, c });
				town[b].push_back({ a, c });
			}
			pq.push({ { 0, s }, c });
			dijkstra();
			for (int i = 0; i <= c; i++)
				ans = min(ans, tocost[d][i]);
			cout << ans << endl;
		}
		return 0;
	}

C++: #include <iostream>
#include <cstdio>
#include <algorithm>
#include <vector>
#include <sstream>
#include <cmath>
#include <queue>

using namespace std;

#define INF (1 << 26)
#define MAX_V 10000

struct edge{
	int to;
	int cost;
};

typedef pair<int, int> P; // first??????????????¢???second??????????????????

vector<edge> G[MAX_V];
int d[MAX_V];

// ?????????O(|E|log|V|)

void shortest_path(int s, int V){ // V???????????°
	
	priority_queue<P, vector<P>, greater<P> > que;
	
	for(int i = 0; i < V; i++){
		d[i] = INF;
	}
	d[s] = 0;
	
	que.push(P(0, s));
	
	while(!que.empty()){
		
		P p = que.top();
		que.pop();
		
		int v = p.second;
		
		if(d[v] < p.first){
			continue;
		}
		
		for(int i = 0; i < G[v].size(); i++){
			edge e = G[v][i];
			if(d[e.to] > e.cost + d[v]){
				d[e.to] = d[v] + e.cost;
				que.push(P(d[e.to], e.to));
			}
		} // ????????????????°???????????????´??°
	}
}

int main(){
	
	int c, n, m, s, g;
	
	while(true){
		cin >> c >> n >> m >> s >> g;
		if(c == 0 && n == 0 && m == 0 && s == 0 && g == 0){
			break;
		}
		int V = n * (c + 1);
		for(int i = 0; i <= V; i++){
			G[i].erase(G[i].begin(), G[i].end());
		}
		for(int i = 0; i < m; i++){
			int a, b, f;
			cin >> a >> b >> f;
			
			int cost = f;
			
			for(int j = 0; j <= c; j++){
				
				int index1 = (a - 1) * (c + 1) + j;
				int index2 = (b - 1) * (c + 1) + j;
				
				edge e1, e2;
				e1.to = index2;
				e2.to = index1;
				e1.cost = cost;
				e2.cost = cost;
				G[index1].push_back(e1);
				G[index2].push_back(e2);
			}
			
			for(int j = 0; j < c; j++){
				
				int index1 = (a - 1) * (c + 1) + j;
				int index2 = (b - 1) * (c + 1) + j + 1;
				
				edge e1;
				e1.to = index2;
				e1.cost = cost / 2;
				G[index1].push_back(e1);
			}
			
			for(int j = 0; j < c; j++){
				
				int index1 = (a - 1) * (c + 1) + j + 1;
				int index2 = (b - 1) * (c + 1) + j;
				
				edge e1;
				e1.to = index1;
				e1.cost = cost / 2;
				G[index2].push_back(e1);
			}
			
		}
		s = (s - 1) * (c + 1);
		g--;
		
		shortest_path(s, V);
		
		int min = INF;
		
		for(int i = 0; i <= c; i++){
			if(d[g * (c + 1) + i] < min){
				min = d[g * (c + 1) + i];
			}
		}
		
		cout << min << endl;
		
	}
	
	return 0;
}

C++: #include <stdio.h>
#include <cctype>
#include <limits.h>
#include <math.h>
#include <complex>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <cstring>
#include <string>
#include <sstream>
#include <algorithm>
#include <iomanip>
#include <iostream>

#define VARIABLE(x) cerr << #x << "=" << x << endl
#define BINARY(x) static_cast<bitset<16> >(x);
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define REP(i,m,n) for (int i=m;i<(int)(n);i++)
#define if_range(x, y, w, h) if (0<=(int)(x) && (int)(x)<(int)(w) && 0<=(int)(y) && (int)(y)<(int)(h))

const int INF = 1e9;
const double EPS = 1e-8;
const double PI = 3.14159;
int dx[4]={0, 1, 0, -1}, dy[4]={-1, 0, 1, 0};
using namespace std;
typedef long long ll;
//typedef pair<int, int> P;
struct P {
	int x, y, n;
	P(int n, int x, int y):n(n), x(x), y(y){}
	P(){}
};

/** Problem0212 : Highway Express Bus **/
struct edge{
	int from, to, cost;
	edge(int f, int t, int c):from(f), to(t), cost(c){}
	edge(){}
};
vector<edge> G;

int main()
{
	int C, N, M, S, D;
	while (cin>>C>>N>>M>>S>>D, C) {
		S--, D--;
		G.clear();
		
		rep(i, M) {
			int a, b, f;
			cin>>a>>b>>f;
			a--, b--;
			G.push_back(edge(a, b, f));
			G.push_back(edge(b, a, f));
		}
		
		int d[100][11];
		fill(d[0], d[0]+1000, INF);
		for (int i=0; i<C+1; i++) d[S][i]=0;
		
		while (true) {
			bool update=false;
			
			for (int i=0; i<G.size(); i++) {
				edge e = G[i];
				for (int j=0; j<C+1; j++) {
					if (d[e.to][j] > d[e.from][j] + e.cost) {
						d[e.to][j] = d[e.from][j] + e.cost;
						update = true;
					}
					
					
					if (j+1<=C) {
						if (d[e.to][j+1] > d[e.from][j]+e.cost/2) {
							d[e.to][j+1] = d[e.from][j]+e.cost/2;
							update = true;
						}
					}
				}
			}
			
			if (!update) break;
		}
		
		int ans = INF;
		for (int i=0; i<C+1; i++) {
			ans = min(ans, d[D][i]);
		}
		cout << ans << endl;
	}
}