Go: package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
	"strings"
)

var scanner = bufio.NewScanner(os.Stdin)

const INF = 0x7FFFFFFF

var pass [][]int

func main() {
	for scanner.Scan() {
		pass = make([][]int, 200)
		for i := range pass {
			pass[i] = make([]int, 200)
		}
		buf := strings.Split(scanner.Text(), " ")
		c, _ := strconv.Atoi(buf[0])
		n, _ := strconv.Atoi(buf[1])
		m, _ := strconv.Atoi(buf[2])
		s, _ := strconv.Atoi(buf[3])
		d, _ := strconv.Atoi(buf[4])
		if c == 0 && n == 0 && m == 0 && s == 0 && d == 0 {
			break
		}
		s--
		d--
		for i := 0; i < 200; i++ {
			for j := 0; j < 200; j++ {
				pass[i][j] = INF
			}
		}
		for i := 0; i < 200; i++ {
			pass[i][i] = 0
		}
		for i := 0; i < m; i++ {
			scanner.Scan()
			buf_ := strings.Split(scanner.Text(), " ")
			a, _ := strconv.Atoi(buf_[0])
			b, _ := strconv.Atoi(buf_[1])
			f, _ := strconv.Atoi(buf_[2])
			a--
			b--
			pass[a][b] = f
			pass[b][a] = f
		}
		fmt.Println(dijkstra(s, d, c, n))
	}
}

func dijkstra(s, g, c, n int) float64 {
	d := make([][]float64, 200)
	used := make([][]bool, 200)
	for i := 0; i < 200; i++ {
		d[i] = make([]float64, 20)
		used[i] = make([]bool, 20)
	}
	for i := range d {
		for j := range d[i] {
			d[i][j] = INF
		}
	}
	d[s][c] = 0
	for {
		v := -1
		w := -1
		for u := 0; u < n; u++ {
			for i := 0; i < c+1; i++ {
				if !used[u][i] && (v == -1 || d[u][i] < d[v][w]) {
					v = u
					w = i
				}
			}
		}
		if v == -1 {
			break
		}
		used[v][w] = true
		for u := 0; u < n; u++ {
			d[u][w] = math.Min(d[u][w], d[v][w]+float64(pass[v][u]))
			if w-1 >= 0 && pass[v][u] != INF {
				d[u][w-1] = math.Min(d[u][w-1], d[v][w]+(float64(pass[v][u]/2.0)))
			}
		}
	}
	ret := float64(INF)
	for i := 0; i < c+1; i++ {
		ret = math.Min(ret, d[g][i])
	}
	return ret
}

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()