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 <algorithm>
#include <vector>
#include <queue>

using namespace std;

struct edge {
    int to, cost;
    edge() {}
    edge(int to_, int cost_): to(to_), cost(cost_) {}
};

struct state {
    int pos, cost;
    state (){}
    state (int pos_, int cost_): pos(pos_), cost(cost_) {}

    bool operator < (const state& o) const {
        return cost > o.cost;
    }
};

constexpr int INF = 1 << 29;

int C, M, N, S, D;

const int W = 100;
vector<edge> graph[1100];

int min_cost[1100];

bool solve() {
    cin >> C >> N >> M >> S >> D;
    if (C+N+M+S+D == 0) { return false; }
    --S; --D;

    for (int j = 0; j < 1100; ++j) {
        graph[j] = vector<edge>();
    }
    fill(min_cost, min_cost+1100, INF);
    min_cost[S] = 0;


    for (int j = 0; j < M; ++j) {
        int a, b, f; cin >> a >> b >> f;
        --a; --b;
        for (int j = 0; j < C; ++j) {
            graph[a+j*W].emplace_back(b+j*W, f);
            graph[b+j*W].emplace_back(a+j*W, f);

            graph[a+j*W].emplace_back(b+(j+1)*W, f/2);
            graph[b+j*W].emplace_back(a+(j+1)*W, f/2);
        }
        graph[a+C*W].emplace_back(b+C*W, f);
        graph[b+C*W].emplace_back(a+C*W, f);
    }

    priority_queue<state, vector<state>> que;
    que.emplace(S, 0);

    while (!que.empty()) {
        state st = que.top(); que.pop();
        int pos = st.pos;
        int cost = st.cost;
        if (cost > min_cost[st.pos]) { continue; }

        for (edge& e : graph[pos]) {
            int next_cost = cost + e.cost;
            if (next_cost < min_cost[e.to]) {
                min_cost[e.to] = next_cost;
                que.emplace(e.to, next_cost);
            }
        }
    }

    int ans = INF;
    for (int j = 0; j <= C; ++j) {
        ans = min(ans, min_cost[D+j*W]);
    }
    cout << ans << endl;

    return true;
}

int main() {
    for (; solve(); ) ;
    return 0;
}

C++: #include <iostream>
#include <queue>
#include <algorithm>
#define INF 9999999
using namespace std;

class State {
public:
  int id;
  int cost;
  int tiket;
  bool operator <(const State &s) const {
    if(tiket != s.tiket) return tiket < s.tiket;
    return cost > s.cost;
  }
  State(int id, int cost, int tiket) : id(id), cost(cost), tiket(tiket) {}
};

int main() {
  while(1) {
    int c, n, m, s, d;
    cin >> c >> n >> m >> s >> d;
    if(c == 0 && n == 0 && m == 0 && s == 0 && d == 0) break;
    int data[n+1][n+1];
    fill(&data[0][0], &data[n][n]+1, INF);
    for(int i = 0; i < m; i++) {
      int a, b, f;
      cin >> a >> b >> f;
      data[a][b] = data[b][a] = f;
    }

    priority_queue<State> PQ;
    PQ.push(State(s, 0, c));
    bool visited[n+1][c+1];
    int cost[n+1][c+1];
    fill(&visited[0][0], &visited[n][c] + 1, false);
    fill(&cost[0][0], &cost[n][c] + 1, INF);
    cost[s][c] = 0;
    while(!PQ.empty()) {
      State s = PQ.top();
      PQ.pop();
      visited[s.id][s.tiket] = true;
      for(int i = 1; i <= n; i++) {
	if(!visited[i][s.tiket] && data[s.id][i] != INF) {
	  int newValue = cost[s.id][s.tiket] + data[s.id][i];
	  if(newValue < cost[i][s.tiket]) {
	    cost[i][s.tiket] = newValue;
	    PQ.push(State(i, newValue, s.tiket));
	  }
	}
	if(s.tiket >= 1 && !visited[i][s.tiket-1] && data[s.id][i] != INF) {
	  int newValue = cost[s.id][s.tiket] + data[s.id][i]/2;
	  if(newValue < cost[i][s.tiket-1]) {
	    cost[i][s.tiket-1] = newValue;
	    PQ.push(State(i, newValue, s.tiket-1));
	  }
	}
      }
    }
    int min = INF;
    for(int i = 0; i <= c; i++) {
      if(cost[d][i] < min) min = cost[d][i];
    }
    cout << min << endl;
  }
  return 0;
}

C++: #include <iostream>
#include <vector>
#include <algorithm>
#include <functional>
#include <queue>
#include <numeric>

using namespace std;

struct edge{ int to, cost; };
typedef pair<int, int> P;
const int INF = 1 << 29;

int V;
vector<edge> G[100];
int D[100];
int pre[100];

int c, n, m, s, d;

void dijkstra(int s)
{
	priority_queue<P, vector<P>, greater<P> > que;
	fill(D, D + 100, INF);
	fill(pre, pre + 100, -1);
	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] > D[v] + e.cost)
			{
				D[e.to] = D[v] + e.cost;
				pre[e.to] = v;
				que.push(P(D[e.to], e.to));
			}
		}
	}
}

int solve()
{
	dijkstra(s - 1);
	vector<int> vec;
	for (int t = d - 1; pre[t] != -1 ; t = pre[t])
	{
		for (int i = 0; i < G[t].size(); i++)
		{
			if(pre[t] == G[t][i].to)
			{
				vec.push_back(G[t][i].cost);
				break;
			}
		}
	}
	sort(vec.begin(), vec.end(), greater<int>());
	for (int i = 0; i < c && i < vec.size(); i++)
	{
		vec[i] = vec[i] / 2;
	}
	return accumulate(vec.begin(), vec.end(), 0);
}

int main()
{
	while (cin >> c >> n >> m >> s >> d && c && n && m && s && d)
	{
		for (int i = 0; i < 100; i++)
		{
			G[i] = vector<edge>();
		}
		for (int i = 0; i < m; i++)
		{
			int a, b, f;
			cin >> a >> b >> f;
			edge e;
			e.to = b - 1;
			e.cost = f;
			G[a - 1].push_back(e);
			e.to = a - 1;
			e.cost = f;
			G[b - 1].push_back(e);
		}
		cout << solve() << endl;
	}
	return 0;
}