CS50 Caesar程序处理非数字密钥超时问题修复求助

我是CS50新手，正在完成Caesar密码作业。当前程序测试反馈如下：

• ✅ caesar.c exists.
• ✅ caesar.c compiles.
• ✅ encrypts "a" as "b" using 1 as key
• ✅ encrypts "barfoo" as "yxocll" using 23 as key
• ✅ encrypts "BARFOO" as "EDUIRR" using 3 as key
• ✅ encrypts "BaRFoo" as "FeVJss" using 4 as key
• ✅ encrypts "barfoo" as "onesbb" using 65 as key
• ✅ encrypts "world, say hello!" as "iadxp, emk tqxxa!" using 12 as key
• ✅ handles lack of argv[1]
• ❌ handles non-numeric key（timed out while waiting for program to exit）
• ✅ handles too many arguments

仅「处理非数字密钥」测试失败，提示等待程序退出时超时。我的代码如下：

#include <cs50.h>
#include <stdio.h>
#include <ctype.h>
#include <string.h>
#include <stdlib.h>

int main(int argc, string argv[])
{
    if (argc != 2)
    {
        printf("Usage: ./ceasar key\n");
        return 1;
    }

    if (atoi(argv[1]) == 0)
    {
        printf("Usage: ./ceasar key\n");
        return 1;
    }

    int k = atoi(argv[1]);
    k = k % 26;
    string plaintext = get_string("plaintext:  ");
    string ciphertext = plaintext;
    int n = strlen(plaintext);

    for (int i = 0; i < n; i++)
    {
        if ('a' <= plaintext[i] && plaintext[i] <= 'z')
        {
            if ((plaintext[i] + k) > 'z')
            {
                ciphertext[i] = ((plaintext[i] + k) - 26);
            }
            else
            {
                ciphertext[i] = (plaintext[i] + k);
            }
        }
        else if ('A' <= plaintext[i] && plaintext[i] <= 'Z')
        {
            if ((plaintext[i] + k) > 'Z')
            {
                ciphertext[i] = ((plaintext[i] + k) - 26);
            }
            else
            {
                ciphertext[i] = (plaintext[i] + k);
            }
        }
    }
    printf("ciphertext: %s\n", ciphertext);
    return 0;
}

问题根源 #

超时的核心原因是密钥合法性判断逻辑错误：

• 用atoi(argv[1]) == 0判断非数字密钥不可靠：
  1. 合法密钥"0"会被错误判定为非法，直接退出；
  2. 输入混合数字与非数字的字符串（比如"12a"）时，atoi会返回前半部分有效数字，程序不会触发错误提示，反而继续执行到get_string等待用户输入明文，导致测试用例超时。

正确的做法是遍历密钥的每个字符，确保所有字符都是数字，而非依赖atoi的返回值。

修复后的代码 #

#include <cs50.h>
#include <stdio.h>
#include <ctype.h>
#include <string.h>
#include <stdlib.h>

int main(int argc, string argv[])
{
    if (argc != 2)
    {
        printf("Usage: ./ceasar key\n");
        return 1;
    }

    // 遍历密钥字符，检查是否全为数字
    for (int i = 0; argv[1][i] != '\0'; i++)
    {
        if (!isdigit(argv[1][i]))
        {
            printf("Usage: ./ceasar key\n");
            return 1;
        }
    }

    int k = atoi(argv[1]);
    k = k % 26;
    // 处理负密钥，转换为等效正偏移
    if (k < 0)
    {
        k += 26;
    }
    
    string plaintext = get_string("plaintext:  ");
    string ciphertext = plaintext;
    int n = strlen(plaintext);

    for (int i = 0; i < n; i++)
    {
        if ('a' <= plaintext[i] && plaintext[i] <= 'z')
        {
            ciphertext[i] = (plaintext[i] - 'a' + k) % 26 + 'a';
        }
        else if ('A' <= plaintext[i] && plaintext[i] <= 'Z')
        {
            ciphertext[i] = (plaintext[i] - 'A' + k) % 26 + 'A';
        }
        // 非字母字符保持不变，无需额外处理
    }
    printf("ciphertext: %s\n", ciphertext);
    return 0;
}

额外优化说明 #

• 替换了原有的字母偏移边界判断，用(字符 - 基准字母 + 偏移) %26 + 基准字母的方式，逻辑更简洁且避免边界错误；
• 增加了负密钥处理，确保输入负数时也能得到正确的加密结果；
• 移除冗余的分支判断，代码可读性更强。

内容的提问来源于stack exchange，提问作者zisegneD