我怎样才能加速这个python代码？

Question

So I recently coded this as a little challenge to see how quick I could do it. Now since its working an such I want to speed it up. It finds all the proper devisors of a number, the highest proper devisor and times how long it all takes. The problem is with number like 5000 it takes 0.05 secs but with numbers like 99999999999 it takes 1567.98 secs.

this the old code I have made a new and improved version below

import time

def clearfile(name):
    file = open(name + ".txt", "r")
    filedata = file.read()
    file.close()
    text_file = open(name + ".txt", "w")
    text_file.write("")
    text_file.close()

def start():
    num = input("Enter your Number: ")
    check(num)

def check(num):
    try:
        intnum = int(num)
    except ValueError:
        error(error = "NON VALID NUMBER")
    if(intnum < 0):
        error(error = "POSITIVE NUMBERS ONLY")
    else:
        finddivisor(intnum)

def finddivisor(intnum):
    starttimer = time.time()
    i = 1
    print("\nThe divisors of your number are:"),
    while i <= intnum:
        if (intnum % i) == 0:
            print(i)
            file = open("numbers.txt", "r")
            filedata = file.read()
            file.close()
            text_file = open("numbers.txt", "w")
            text_file.write(str(i) +"\n"+ filedata)
            text_file.close()
        i += 1
    properdivisor(starttimer)

def properdivisor(starttimer):
    file = open("numbers.txt", "r")
    highest = file.readlines()
    print("\nThe Highest Proper Divisor Is\n--------\n" + highest[1] + "--------" + "\nIt took"  ,round(time.time() - starttimer, 2)  ,"seconds to finish finding the divisors.\n")
    restart(errorrestart = "false")

def restart(errorrestart):
    if errorrestart == "false":
        input("Do You Want Restart?\nPress Enter To Restart Or Close The Programe To Leave")
        start()
    elif errorrestart == "true":
        input("\nThere Was An Error Detected.\nPress Enter To Restart Or Close The Programe To Leave")
        start()

def error(error):
    print("\n----------------------------------\nERROR - " + error + "\n----------------------------------")
    restart(errorrestart = "true")

clearfile(name = "numbers")
start()

Can someone speed it up for me

EDIT 1

so after looking over it I have now edited it to be moving it away from a file to an array

    import time
    from array import *
    def programme():
        num = input("Enter your Number: ")
        try:
            intnum = int(num)
        except ValueError:
           error("NOT VALID NUMBER")
        if(intnum < 0):
            error("POSITIVE NUMBERS ONLY")
        else:
                numbers = array("i",[])
                starttimer = time.time()
                i = 1
                print("\nThe divisors of your number are:"),
                while i <= intnum:
                    if (intnum % i) == 0:
                        numbers.insert(0,i)
                        print(i)
                    i += 1
                print("\nThe Highest Proper Divisor Is\n--------\n" + str(numbers[1]) + "\n--------" + "\n\nIt took"  ,round(time.time() - starttimer, 2)  ,"seconds to finish finding the divisors.\n")    
    def error(error):
        print("\n----------------------------------\nERROR - " + error + "\n----------------------------------\n")
    running = True
    while(running == True):
        programme()
        print("----------------------------------")
        restart = input("Do You Want Restart?")
        restart = restart.lower()
        if restart in ("yes", "y", "ok", "sure", ""):
            print("Restarting\n----------------------------------")
        else:
            print("closing Down")
            running = False

New Edit

import time, math
from array import *
def programme():
    num = input("Enter your Number: ")
    try:
        intnum = int(num)
        if(intnum < 0):
            error("POSITIVE NUMBERS ONLY")
        else:
            numbers = array("i",[])
            starttimer = time.time()
            i = 1
            print("\nThe divisors of your number are:"),
            while i <= math.sqrt(intnum):
                if (intnum % i) == 0:
                    numbers.insert(0,i)
                    numbers.insert(0,int(intnum/i))
                    print(i,":", int(intnum/i))
                i += 1
            numbers = sorted(numbers, reverse = True)
            print("The Highest Proper Divisor Is\n--------\n",str(numbers[1]) , "\n--------\nIt took"  ,round(time.time() - starttimer, 2)  ,"seconds to finish finding the divisors." )
    except ValueError:
       error("NOT VALID NUMBER")
    except OverflowError:
       error("NUMBER IS TO LARGE")
    except:
       error("UNKNOWN ERROR")

def error(error):
    print("\n----------------------------------\nERROR - " + error + "\n----------------------------------\n")
running = True
while(running):
    programme()
    print("----------------------------------")
    restart = input("Do You Want Restart?")
    restart = restart.lower()
    if restart in ("yes", "y", "ok", "sure", ""):
        print("Restarting\n----------------------------------")
    else:
        print("closing Down")
        running = False

Answer 1

If you have divisor a of number n then you can tell one more divisor of n b = n / a . Moreover if a <= sqrt(n) then b >= sqrt(n) and vice versa. It means in your finddivisor function you can iterate while i * i <= n and print both divisors i and n / i . By the way, you shouldn't open, read and close files in cycle. Open it once before cycle and close after if you need to read/write several times.

Answer 2

You don't need to read and rewrite the entire file every time you want to put a single entry into it. You can just do it once when you know what change you want. Also you could just append to it. Maybe something like this:

def finddivisor(intnum):
    starttimer = time.time()
    print("\nThe divisors of your number are:")
    divs = set()
    for i in range(1, int(math.sqrt(intnum)) +1):
        if intnum % i == 0:
            print(i)
            divs.add(i)
            divs.add(intnum // i)
    with open("numbers.txt", "a") as file:
        file.writelines("{}\n".format(ln) for ln in sorted(divs, reverse=True))

also your program flow is building a very deep stack. Try and flatten it with something like

def start():
    clearfile()
    while True:
        n = get_number()
        starttimer = time.time()
        finddivisor(n)
        properdivisor(starttimer)
        input("Press Enter To Restart Or Close The Programe To Leave")

in properdivisor you dont need to read the whole file either, you just need the first line. so maybe something like:

def properdivisor(starttimer):
    with open(FILENAME, "r") as file:
        highest = file.readline().strip()
    print "\nThe Highest Proper Divisor Is"
    print "--------%s--------" % highest
    print "It took %0.2f seconds to finish finding the divisors.\n" % (time.time() - starttimer)

AFTER EDIT

Something like this is how I would do it, and it runs less then a second on my box:

import math

def get_divisors(n):
    yield 1
    sqroot = int(math.sqrt(n))
    for x in xrange(2, sqroot):
        if n % x == 0:
            yield x
            yield n / x
    if sqroot**2 == n:
        yield sqroot

divisors = sorted(get_divisors(999999999999))
print divisors