CS50 Credit作业Luhn校验码逻辑异常求助

我在完成CS50 2024的Credit作业时，Luhn校验逻辑出现以下两个错误：

• 卡号4222222222222的校验和为40（本应有效），却被判定无效；
• 卡号4111111111111113的校验和为28（本应无效），却误判为VISA；
  其余卡号识别正常。

以下是我的代码和问题分析：

最初的实现代码 #

#include <cs50.h>
#include <ctype.h>
#include <math.h>
#include <stdio.h>

bool digit(string str, int buffer);
int numofdigits(long long card_num);
int fst_ndigit(long long credit, int buffer, int numdigit);

int main(void)
{
    long long credit = get_long("please enter your credit card number :  ");

    //Note:
    //using a boolean variable can reduce repetition of " INVALID " message
    bool valid = true;
    if (credit < (long long) pow(10, 13) || credit > (long long) pow(10, 16))
    {
        printf("INVALID\n");
        valid = false;
    }

    int buffer = numofdigits(credit);

    long long aux = credit;
    int last_two;
    int last_one;
    //Note: variable names cannot start with numbers!
    int secondlast_one;
    int mul = 1;
    int sum1 = 0;
    int sum2 = 0;

    if(valid){
    for(int i = 0; aux > 0; i++)
    {
        //1st step :
        //Multiply every other digit by 2, starting with the number’s second-to-last digit,
        //and then add those products’ digits together.

        last_two = aux % (long long) pow(10, buffer-2);
        last_one = last_two % 10;
        secondlast_one = last_two / 10;
        mul = secondlast_one*2;

        if((mul / 10) != 0)
        {
            sum1 += (mul / 10) + (mul % 10);
        }
        else
        {
            sum1 += mul;
        }
        //2nd step:
        //Add the previous sum to the sum of the digits that weren’t multiplied by 2.
        sum2 += last_one;

        aux = aux / 100;
    }

    //3rd step:
    //If the total’s last digit is 0
    //(or, put more formally, if the total modulo 10 is congruent to 0),
    //the number is valid!
    if((sum1 + sum2) % 10 ==0)
    {
        valid = true;
    }

    int fst_two = fst_ndigit(credit, buffer, 2);
    int fst_one = fst_ndigit(credit, buffer, 1);

    char str[17];
    // Note :
    // sprintf(str, "%d", (int)credit);
    // this line is incorrect because the prog will spit out a random integer

    sprintf(str, "%lld", credit);
    // lld is format for long long int

    if (digit(str, buffer) && valid)
    {
        if (buffer == 15 && (fst_two == 34 || fst_two == 37))
        {
            printf("AMEX\n");
        }
        else if (buffer == 16 && (fst_two == 51 || fst_two == 52 || fst_two == 53 || fst_two == 54 || fst_two == 55))
        {
            printf("MASTERCARD\n");
        }
        else if ((buffer == 13 || buffer == 16) && fst_one == 4)
        {
            printf("VISA\n");
        }
        else
        {
            printf("INVALID\n");
        }
    }
    else
    {
        printf("INVALID\n");
    }
    }
}

int numofdigits(long long card_num)
{
    int count = 0;
    while (card_num > 0)
    {
        card_num /= 10;
        count++;
    }
    return count;
}

bool digit(string str, int buffer)
{
    bool all_digits = true;
    for (int i = 0; i < buffer; i++)
    {
        if (!isdigit(str[i]))
        {
            all_digits = false;
            break;
        }
    }
    return all_digits;
}

int fst_ndigit(long long credit, int buffer, int numdigit)
{
    int fstndigit = (int) (credit / (long long) pow(10, buffer - numdigit));
    return fstndigit;
}

尝试修改的代码片段 #

int buffer = numofdigits(credit);
char str[17];
// Note :
// sprintf(str, "%d", (int)credit);
// this line is incorrect because the prog will spit out a random integer

sprintf(str, "%lld", credit);
// lld is format for long long int

int sum = 0;
int len = strlen(str);
int i;

// Iterate through the digits from right to left
for (i = len - 1; i >= 0; i--) {
    int digit = str[i] - '0';

    // Double every second digit
    if ((len - i) % 2 == 0) {
        digit *= 2;

        // Subtract 9 if the doubled digit is greater than 9
        if (digit > 9) {
            digit -= 9;
        }
    }

    sum += digit;
}
int checksum = sum % 10;
valid = (checksum == 0);

最终通过CS50检查的正确代码 #

#include <cs50.h>
#include <ctype.h>
#include <math.h>
#include <stdio.h>

bool digit(string str, int buffer);
int numofdigits(long int credit);
int fst_ndigit(long int credit, int buffer, int numdigit);
bool checksum(long int credit);

int main(void)
{
    long int credit = get_long("please enter your credit card number :  ");

    bool valid = true;

    if (credit < (long long) pow(10, 12) || credit > (long long) pow(10, 17))
    {
        printf("INVALID\n");
        valid = false;
    }

    if (valid)
    {
        valid = checksum(credit);
        if (valid)
        {
            int buffer = numofdigits(credit);
            int fst_two = fst_ndigit(credit, buffer, 2);
            int fst_one = fst_ndigit(credit, buffer, 1);

            if (buffer == 15 && (fst_two == 34 || fst_two == 37))
            {
                printf("AMEX\n");
            }
            else if (buffer == 16 && (fst_two == 51 || fst_two == 52 || fst_two == 53 ||
                                      fst_two == 54 || fst_two == 55))
            {
                printf("MASTERCARD\n");
            }
            else if ((buffer == 13 || buffer == 16) && fst_one == 4)
            {
                printf("VISA\n");
            }
            else
            {
                printf("INVALID\n");
            }
        }
        else
        {
            printf("INVALID\n");
        }
    }
}

bool checksum(long int credit)
{
    int digit_count = 0;
    int sum = 0;
    // checksum for the luhn algorithm
    while (credit > 0)
    {
        int digit = credit % 10;
        credit /= 10;
        digit_count++;

        if (digit_count % 2 == 0)
        {
            digit *= 2;
            if (digit > 9)
            {
                digit -= 9;
            }
        }

        sum += digit;
    }
    return (sum % 10) == 0;
}

int numofdigits(long int credit)
{
    int i = 0;
    while (credit > 0)
    {
        credit /= 10;
        i++;
    }
    return i;
}

bool digit(string str, int buffer)
{
    bool all_digits = true;
    for (int i = 0; i < buffer; i++)
    {
        if (!isdigit(str[i]))
        {
            all_digits = false;
            break;
        }
    }
    return all_digits;
}

int fst_ndigit(long int credit, int buffer, int numdigit)
{
    int fstndigit = (int) (credit / (long long) pow(10, buffer - numdigit));
    return fstndigit;
}

问题根源分析 #

1. 初始代码Luhn算法实现逻辑完全错误
   初始代码中计算last_two = aux % (long long) pow(10, buffer-2);的逻辑完全偏离了Luhn算法的要求：Luhn算法需要从卡号的最右侧（最后一位）开始向左遍历，每隔一位（从倒数第二位开始）翻倍。但这里用原始卡号的总位数buffer计算取余，导致每次获取的不是当前aux的最后两位，而是相对于原始卡号的固定偏移位，完全错误地选取了需要计算的数字，使得sum1和sum2的累加结果完全不符合校验要求。比如对于4222222222222，初始代码计算出的sum1+sum2根本不是40，因此判定无效；而4111111111111113的计算结果错误地满足了模10为0的条件，导致误判有效。

2. valid变量处理存在漏洞
   初始代码中仅在校验和符合条件时设置valid = true，但如果校验和不符合，valid会保持初始的true值（只有卡号长度超出范围时才会被设为false）。这导致即使校验和错误，只要卡号长度符合卡组织的要求，后续仍会进入卡类型判断逻辑，比如4111111111111113长度为16且首数字是4，因此被误判为VISA。

3. 最终代码的修正点

   • 将Luhn校验逻辑封装为独立的checksum函数，通过digit_count从右往左计数，正确识别需要翻倍的位（从右数第2、4、6...位），计算逻辑完全符合Luhn算法要求；
   • 修正了卡号长度的判断范围：从原来的13-16位改为12-17位，覆盖了VISA的13位卡号等合法长度；
   • valid变量的处理更严谨：校验和不通过时直接设为false，避免误判进入卡类型判断流程。

内容的提问来源于stack exchange，提问作者abeginner1