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<utility>
#include<queue>
using namespace std;
#define rep(i,n) for(int i = 0; i < (n); i++)
typedef pair<int,int> pii;
typedef pair<int,pii> pip;

class Dijkstra{
private:
    struct edge {int to,cost;};
    vector<vector<edge> > g;
    int n;

public:
    Dijkstra(int size){
        g.resize(size);
        n = size;
    }
    vector<vector<int> > dist;
    void add(int a, int b, int c){
        edge e1 = {b,c}, e2 = {a,c};
        g[a].push_back(e1);
        g[b].push_back(e2);
    }
    int calc(int s,int t,int ma){
        priority_queue<pip,vector<pip>,greater<pip> > q;
        int n = g.size();
        dist = vector<vector<int> > (n, vector<int>(ma+1,1e9));
        dist[s][0] = 0;
        q.push(pip(0,pii(s,0)));
        while(!q.empty()){
            pip p = q.top();
            q.pop();
            int c = p.first;
            pii node = p.second;
            if(dist[node.first][node.second] < c)continue;
            rep(i,g[node.first].size()){
                edge e = g[node.first][i];
                if(dist[e.to][node.second] > dist[node.first][node.second] + e.cost){
                    dist[e.to][node.second] = dist[node.first][node.second] + e.cost;
                    q.push(pip(dist[e.to][node.second],pii(e.to,node.second)));
                }
                if(node.second < ma){
                    if(dist[e.to][node.second+1] > dist[node.first][node.second] + e.cost/2){
                        dist[e.to][node.second+1] = dist[node.first][node.second] + e.cost/2;
                        q.push(pip(dist[e.to][node.second+1],pii(e.to,node.second+1)));
                    }
                }
            }
        }
        int ret = 1e9;
        rep(i,ma+1)ret = min(ret, dist[t][i]);
        return ret;
    }
};

int main(){
    int c,n,m,s,d;
    while(cin >> c >> n >> m >> s >> d, n){
        Dijkstra dij(n);
        rep(i,m){
            int a,b,f;
            cin >> a >> b >> f;
            dij.add(a-1,b-1,f);
        }
        cout << dij.calc(s-1,d-1,c) << endl;
    }
}

C++: #include<bits/stdc++.h>
using namespace std;
using ll = long long;
int c,n,m,s,d;
const int INF = 2*1e9;
vector<pair<int,int>> G[100];
ll D[100][10];

struct P
{
	int time,v,chk;
	P(int time,int v,int chk)
	{
		this->time=time;
		this->v = v;
		this->chk = chk;
	}
};

bool operator<(P a,P b)
{
	return a.time>b.time;
}

void dijkstra(int chiket)
{
	for(int i = 0;i<100;i++)
	{
		for(int j = 0;j<10;j++)
		{
			D[i][j]=INF;
		}
	}
	D[s][chiket]=0;
	priority_queue<P> PQ;
	PQ.emplace(0,s,chiket);
	while(!PQ.empty())
	{
		//cout<<PQ.size()<<endl;
		auto now = PQ.top();
		PQ.pop();
		//cout<<now.time<<endl;
		if(D[now.v][now.chk]!=now.time)continue;
		for(auto next:G[now.v])
		{
			if(D[next.first][now.chk]>now.time+next.second)
			{
				D[next.first][now.chk]=now.time+next.second;
				PQ.emplace(D[next.first][now.chk],next.first,now.chk);
			}
			if(now.chk<1)continue;
			if(D[next.first][now.chk-1]>now.time+next.second/2)
			{
				D[next.first][now.chk-1] = now.time+next.second/2;
				PQ.emplace(D[next.first][now.chk-1],next.first,now.chk-1);
			}
		}
	}
	ll mn = INF;
	for(int i = 0;i<10;i++)
	{
		mn = min(mn,D[d][i]);
	}
	cout<<mn<<endl;
}

int main()
{
	while(1)
	{
		cin >> c >> n >> m >> s >> d;
		if(c==0)break;
		for(int i = 0;i<n;i++)
		{
			G[i].clear();
		}
		s--;
		d--;
		for(int i = 0;i<m;i++)
		{
			int a,b,f;
			cin >> a >> b >> f;
			a--;
			b--;
			G[a].emplace_back(b,f);
			G[b].emplace_back(a,f);
		}
		dijkstra(c);
	}
}

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

using namespace std;

#define INF 100000000

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;
		}
		vector< vector<int> > ff(n+1, vector<int>(n+1, INF));
		vector< vector<int> > ddd(n+1, vector<int>(n+1, INF));
		int a, b, f;
		for (int i = 0; i < m; i++) {
			cin >> a >> b >> f;
			ff[a][b] = ff[b][a] = f;
			ddd[a][b] = ddd[b][a] = f;
		}
		for (int i = 1; i <= n; i++) {
			ddd[i][i] = 0;
		}
		for (int k = 1; k <= n; k++) {
			for (int i = 1; i <= n; i++) {
				for (int j = 1; j <= n; j++) {
					ddd[i][j] = min(ddd[i][j], ddd[i][k]+ddd[k][j]);
				}
			}
		}
		vector< vector< vector<int> > > dp(n+1, vector< vector<int> >(n+1, vector<int>(c+1, INF)));
		for (int i = 1; i <= n; i++) {
			dp[s][i][0] = ddd[s][i];
		}
		for (int k = 1; k <= c; k++) {
			for (int p = 1; p <= n; p++) {
				dp[s][p][k] = dp[s][p][k-1];
				for (int i = 1; i <= n; i++) {
					if (dp[s][i][k-1] == INF) continue;
					for (int j = 1; j <= n; j++) {
						if (ddd[i][j] == INF) continue;
						for (int q = 1; q <= n; q++) {
							if (ddd[q][p] == INF) continue;
							if (ff[j][q] != INF) {
								if (dp[s][p][k] > dp[s][i][k-1]+ddd[i][j]+(ff[j][q]/2)+ddd[q][p]) {
									dp[s][p][k] = dp[s][i][k-1]+ddd[i][j]+(ff[j][q]/2)+ddd[q][p];
								}
							}
						}
					}
				}
			}
		}
		cout << dp[s][d][c] << endl;
	}
	return 0;
}