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()
	}
}

Python: from sys import stdin
readline = stdin.readline



from collections import namedtuple
Runner = namedtuple('Runner', 'd v')

def main():
    while True:
        ticket, vertex, edge, start, destination = map(int, readline().split())
        if ticket == 0:
            break

        start -= 1
        destination -= 1
        g = defaultdict(list)
        for i in range(edge):
            s, t, length = map(int, readline().split())
            s -= 1
            t -= 1
            g[s].append((length, t))
            g[t].append((length, s))
        
        d = ex_dijkstra(g, vertex, start, ticket)
        print(min(d[destination]))



from heapq import heappush, heappop
from collections import defaultdict
def ex_dijkstra(g, size, start, ticket):
    d = [[float('inf')] * (ticket + 1) for i in range(size)]
    d[start][ticket] = 0
    heap = [(d[start][ticket], start, ticket)]
    while heap:
        du, u, ticket = heappop(heap)
        for length, v in g[u]:
            if d[v][ticket] > du + length:
                d[v][ticket] = du + length
                heappush(heap,(d[v][ticket], v, ticket))
            if ticket and d[v][ticket - 1] > du + length // 2:
                d[v][ticket - 1] = du + length // 2
                heappush(heap,(d[v][ticket - 1], v, ticket - 1))

    return d

main()

Python: from sys import stdin
from heapq import heappush,heappop

while(True):
    c,n,m,s,d = map(int, stdin.readline().split())
    if not c: break
    ma = [[] for _ in range(n)]
    s -= 1
    d -= 1
    for _ in range(m):
        a,b,f = map(int, stdin.readline().split())
        a -= 1
        b -= 1
        ma[a].append([f,b])
        ma[b].append([f,a])
    cost = [[10**10]*(c+1) for _ in range(n)]
    cost[s][c] = 0
    que = [[ cost[s][c], s, c ]]
    while que:
        co, pl, ti = heappop(que)
        for fee, town in ma[pl]:
            if cost[town][ti] > co+fee:
                cost[town][ti] = co+fee
                heappush(que,[cost[town][ti],town,ti])
            if ti and cost[town][ti-1] > co+fee//2:
                cost[town][ti-1] = co+fee//2
                heappush(que,[cost[town][ti-1],town,ti-1])
    print(min(cost[d]))

Python: from heapq import *
def dijkstra(s,c):
    que=[]
    dp[0][s]=0
    heappush(que,[dp[c][s],s])

    while len(que)!=0:
        p=heappop(que)
        v=p[1] #v is the current location
        if(dp[c][v]<p[0]):
            continue
        for i in range(len(G[v])):
            e=G[v][i]
            Min=dp[c][v]+e[1] if c==0 else min(dp[c-1][v]+e[1]/2,dp[c][v]+e[1])
            if(dp[c][e[0]]>Min):
                dp[c][e[0]]=Min
                heappush(que,[dp[c][e[0]],e[0]])

while True:
    #input c,n,m,s,d & creating G
    #G[to,cost]
    c,n,m,s,d=map(int,input().split())
    
    if c==n==m==s==d==0:
        break
    
    G=[[]]
    for i in range(n):
        G.append([])
    for i in range(m):
        a,b,f=map(int,input().split())
        G[a].append([b,f])
        G[b].append([a,f])

    #creating dp[]
    INF=1e8
    dp=[]
    for i in range(c+1):
        temp=[INF for j in range(n+1)]
        dp.append(temp)

    for i in range(c+1):
        dijkstra(s,i)
    print(int(dp[c][d]))

Python: """ Created by Jieyi on 10/31/16. """
import io
import sys
import heapq

# Simulate the redirect stdin.
from collections import defaultdict

if len(sys.argv) > 1:
    filename = sys.argv[1]
    inp = ''.join(open(filename, "r").readlines())
    sys.stdin = io.StringIO(inp)


def input_data():
    while True:
        tickets, vertices, edges, start, end = map(int, input().split())
        if 0 == tickets + vertices + edges + start + end:
            break

        shortest_path = [[sys.maxsize for _ in range(vertices)] for _ in range(tickets + 1)]
        for i in range(tickets + 1):
            shortest_path[i][start - 1] = 0
        g = defaultdict(list)
        h = []
        # Generate a map.
        for _ in range(edges):
            i, j, fare = map(int, input().split())
            g[i].append((j, fare))
            g[j].append((i, fare))
        # (price, vertices, remainder ticket)
        heapq.heappush(h, (0, start, tickets))

        while True:
            if 0 == len(h):
                break
            ori_price, vertex, remain_ticket = heapq.heappop(h)
            for v, price in g[vertex]:
                if shortest_path[remain_ticket][v - 1] > ori_price + price:
                    shortest_path[remain_ticket][v - 1] = min(shortest_path[remain_ticket][v - 1], ori_price + price)
                    heapq.heappush(h, (shortest_path[remain_ticket][v - 1], v, remain_ticket))
                if remain_ticket and shortest_path[remain_ticket - 1][v - 1] > ori_price + int(price / 2):
                    shortest_path[remain_ticket - 1][v - 1] = min(shortest_path[remain_ticket - 1][v - 1], ori_price + int(price / 2))
                    heapq.heappush(h, (shortest_path[remain_ticket - 1][v - 1], v, remain_ticket - 1))

        print(shortest_path[0][end - 1])


def main():
    input_data()