在Python中找到两个3位数字的乘积的最大回文 [英] Finding the largest palindrome of the product of two 3-digit numbers in Python

问题描述

所以我要解决的难题是找到由两个3位数字的乘积组成的最大回文.我是Python的新手，所以我的代码尚不完善或精简，但是似乎找不到逻辑错误.

So the challenge I'm trying to solve is to find the largest palindrome made from the product of two 3-digit numbers. I'm new to Python and so my code is not elegant or refracted yet, but there is a logical error that I can't seem to find.

def ispalindrome(n):
    rev_n = str(n)[::-1]
    if n == rev_n:
        return True
    else:
        return False


first_num = 100
second_num = 100
mylist=[]
while first_num < 1000:
    while second_num < 1000:
        item = first_num * second_num
        mylist.append(item)
        second_num += 1
    second_num = 100
    first_num +=1
# print (mylist)
num_as_string = []
for i in mylist:
    i = str(i)
    num_as_string.append(i)
print("Total products of two 3-digit numbers: {}").format(len(num_as_string))
print("-----------------------------------------------------")

def convert_to_num_list(string_list):
    new_num_list = []
    item = int(string_list)
    new_num_list.append(item)
    return new_num_list



palindrome_list = []

for j in num_as_string:
    if ispalindrome(j) == True:
        palindrome_list.append(j)
        palindrome_list.sort()
        # print(palindrome_list)
        x = convert_to_num_list(j)
        largest_palindrome = max(x)

print("Total palindroms of product of two 3-digit numers: {}").format(len(palindrome_list))

print("Largest palindrome = {}").format(largest_palindrome)

问题是我得到的最大回文为580085，它是995 * 583，但不是最大的回文.我相信最大的回文是906609，即993 * 913，但是我的代码找不到此回文.谁能帮助我解决我的逻辑缺陷?

The problem is that I'm getting the largest palindrome as 580085, which is 995*583 but is NOT the largest palindrome. I believe the largest palindrome is 906609, which is 993*913, but my code is not finding this. Can anyone help me with the flaw in my logic?

推荐答案

您的代码在数字和字符串之间进行了很多不必要的转换，从而使错误很难发现.代码中唯一需要字符串表示形式的地方是确定数字是否为回文式时.因此，这应该是代码进行转换的唯一位置.

Your code does a lot of unnecessary conversion between numbers and strings, which made the error hard to find. The only place in the code that needs a string representation is when determining if the number is a palindrome or not. So that should be the only place that the code does the conversion.

函数convert_to_num_list()中存在逻辑错误.它采用 one 数字的字符串表示形式，并返回一个包含该数字的1-list.因此，"123321"返回为[123321].然后，您采用该1-list的max()，该值始终是传递给convert_to_num_list()的值.因此，代码永远不会保留最大值，因为如果以后输入较小的值，它将被覆盖.该代码将995*583报告为最大，因为它出现在993*913之后，这又是因为995> 993.

The logic error is in your function convert_to_num_list(). It takes a string representation of one number and returns a 1-list containing that number. So, "123321" gets returned as [123321]. You then take the max() of that 1-list, which is always the value that was passed to convert_to_num_list(). So the code never keeps the largest value because if a smaller value comes in later it will be overwritten. The code reports 995*583 as the largest because it comes in later than 993*913, which in turn is because 995 > 993.

您可以使用if语句修复该错误，但是该程序过于复杂并且可能包含其他错误.我建议将代码简化为产生最大回文的基本任务，而不必打印出中间结果，因为代码越简单，就越容易发现逻辑错误.

You can fix that error with an if statement, but the program is overcomplicated and may well contain other bugs. I recommend reducing the code to the essential task of producing the largest palindrome, without printing out the intermediate results, because the simpler the code the easier it is to see a logic error.

def ispalindrome(n):
    return str(n) == str(n)[::-1]

mylist=[]
for first_num in range(100,1000):
    for second_num in range(100,1000):
        item = first_num*second_num
        if ispalindrome(item):
            mylist.append(item)
print(max(mylist))

这给出了您所期望的答案:

This gives your expected answer:

906609

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