为什么我的哈希程序无法通过测试

Question

Task:
To register in the system, each resident must come up with a password. The password consists of letters of the Latin alphabet (uppercase and lowercase), as well as numbers from 0 to 9, that is, it is possible to use 62 characters in total. The password length is from 5 to 20 characters. The password is stored in the database in encrypted form, encryption is carried out according to the following algorithm:

1. The number b of uppercase Latin letters is counted. For each uppercase letter character in the password, a cyclic shift to the right by bb characters is performed (for example, if b=3, then the D character is converted to the G character, the Y character to the B character).
2. Similarly, for each lowercase character in the password, a cyclic shift to the right is performed by m characters, where m is the number of lowercase letters in the password.

To quickly search for users in the database, a hash function is calculated for each encrypted password using the following algorithm:

1. All 62 characters are ordered, numbers come first, then lowercase letters, then uppercase letters.
2. Each character is assigned a code - the number of the character in this sequence, starting from 0. Thus, the digit codes match their values, the lowercase letter code a-10, b-11, etc.
3. All codes are summed up, and the remainder of the resulting sum s is found from dividing by the numbers p and q. The resulting pair of numbers (s mod p,s mod q) will be the value of the hash function.

A hash function is considered good if collisions rarely occur, that is, the values of the function match for different passwords.

John came up with a new password. At the same time, there are already nn passwords in the database, and I would like to avoid collisions. Will John succeed?

Input data

The first line contains a string representing John's password. The second line contains an integer n – the number of passwords in the database. The third line contains integers p and q. The following lines store passwords in unencrypted form.

Output data

An integer is the number of passwords whose hash function matches the hash function of John's password.

Sample Input:
AabB1cd
5
13 17
Nik143pasw
qeAom1
q1w2e3r4t
aBoba2012
N33iEj

Sample Output:
2

Note:
Passwords that match John's hash function are highlighted.

Processing of John's password: After cyclic shift: CefD1gh (uppercase letters are shifted by 2, lowercase by 4) The sum of the character codes is 38+14+15+39+1+16+17=140 The hash function is equal to (10,4)

My Programm:

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>

using namespace std;

int main() {
    string pas;
    cin >> pas;
    int small = 0, big = 0;
    for (int i = 0; i < pas.length(); i++)
    {
        if (pas[i] >= 'A' && pas[i] <= 'Z')big++;
        if (pas[i] >= 'a' && pas[i] <= 'z')small++;
    }
    for (int i = 0; i < pas.length(); i++)
    {
        if (pas[i] + big >= 'A' && pas[i] + big <= 'Z') pas[i] = pas[i] + big;
        else if (pas[i] >= 'A' && pas[i] <= 'Z') {
            int tempVar = big;
            while (tempVar > 0) {
                if (pas[i] == 'Z') {
                    pas[i] = 'A';
                    tempVar = tempVar - 1;
                }
                tempVar = tempVar - 1;
                pas[i] = pas[i] + 1;
            }
        }
    }
    for (int i = 0; i < pas.length(); i++)
    {
        if (pas[i] + small >= 'a' && pas[i] + small <= 'z') pas[i] = pas[i] + small;
        else if (pas[i] >= 'a' && pas[i] <= 'z') {
            int tempVar = small;
            while (tempVar > 0) {
                if (pas[i] == 'z') {
                    pas[i] = 'a';
                    tempVar = tempVar - 1;
                }
                pas[i] = pas[i] + 1;
                tempVar = tempVar - 1;
            }
        }
    }
    int hash = 0;
    for (int i = 0; i < pas.length(); i++) {
        if ('0' <= pas[i] && '9' >= pas[i]) {
            hash = hash + (pas[i] - 48);
        }
        if ('a' <= pas[i] && 'z' >= pas[i]) {
            hash = hash + (pas[i] - 87);
        }
        if ('A' <= pas[i] && 'Z' >= pas[i]) {
            hash = hash + (pas[i] - 29);
        }
    }
    int n, p, q;
    cin >> n >> p >> q;
    int hashfun1 = hash % p;
    int hashfun2 = hash % q;
    int counter = 0;

    while (n--) {
        cin >> pas;
        int small = 0, big = 0;
        for (int i = 0; i < pas.length(); i++)
        {
            if (pas[i] >= 'A' && pas[i] <= 'Z')big++;
            if (pas[i] >= 'a' && pas[i] <= 'z')small++;
        }
        for (int i = 0; i < pas.length(); i++)
        {
            if (pas[i] + big >= 'A' && pas[i] + big <= 'Z') pas[i] = pas[i] + big;
            else if (pas[i] >= 'A' && pas[i] <= 'Z') {
                int tempVar = big;
                while (tempVar > 0) {
                    if (pas[i] == 'Z') {
                        pas[i] = 'A';
                        tempVar = tempVar - 1;
                    }
                    tempVar = tempVar - 1;
                    pas[i] = pas[i] + 1;
                }
            }
        }
        for (int i = 0; i < pas.length(); i++)
        {
            if (pas[i] + small >= 'a' && pas[i] + small <= 'z') pas[i] = pas[i] + small;
            else if (pas[i] >= 'a' && pas[i] <= 'z') {
                int tempVar = small;
                while (tempVar > 0) {
                    if (pas[i] == 'z') {
                        pas[i] = 'a';
                        tempVar = tempVar - 1;
                    }
                    pas[i] = pas[i] + 1;
                    tempVar = tempVar - 1;
                }
            }
        }
        int hash = 0;
        for (int i = 0; i < pas.length(); i++) {
            if ('0' <= pas[i] && '9' >= pas[i]) {
                hash = hash + (pas[i] - 48);
            }
            if ('a' <= pas[i] && 'z' >= pas[i]) {
                hash = hash + (pas[i] - 87);
            }
            if ('A' <= pas[i] && 'Z' >= pas[i]) {
                hash = hash + (pas[i] - 29);
            }
        }
        int hashfun3 = hash % p;
        int hashfun4 = hash % q;
        if (hashfun1 == hashfun3 && hashfun2 == hashfun4) {
            counter++;
        }
    }
    std::cout << counter;
    return 0;
}

Tests:
Test 1. OK
Test 2. Wrong answer
Test 3. OK
Test 4. OK
Test 5. Wrong answer

3 of 5 tests passed.

Answer 1

You have a few logic problems in your code. When you are rotating your upper and lower-case characters to their "encrypted" forms, you iterate through the password twice, and sometimes incorrectly rotate the characters. Take for example just the line

if (pas[i] + big >= 'A' && pas[i] + big <= 'Z') pas[i] = pas[i] + big;

Consider the case where pas[i] == '9' and big == 8 . You will end up transforming all of your 9 's into A s.

Now consider the line in the next loop

if (pas[i] + small >= 'a' && pas[i] + small <= 'z') pas[i] = pas[i] + small;

Which will similarly transform some upper-case letters into lower-case if small is large enough.

You can also combine these two problems. Consider the case where pas[i] is originally Y , big is 1, little is 7. You'll transform Y --> Z , and then in the next step transform Z --> a .

1. Compartmentalize and abstract your single large main function into smaller functional blocks. This will allow you to reason about each piece individually instead of trying to keep the entirely of main() in your head. Humans have limited short-term memory.

Some suggested functions would include

• bool is_upper(char c)
• bool is_lower(char c)
• bool is_numeric(char c)
• char rotate_upper(char c, int steps)
• char rotate_lower(char c, int steps)

2. Instead of looping through the password twice on your transformation step, consider looping through the password once. If the character is upper-case, transform accordingly. If it's lower-case, transform accordingly. This will prevent you from double-rotating some numbers.

Combining all of the above, the two encryption loops of your main function could turn from:

for (int i = 0; i < pas.length(); i++)
    {
        if (pas[i] + big >= 'A' && pas[i] + big <= 'Z') pas[i] = pas[i] + big;
        else if (pas[i] >= 'A' && pas[i] <= 'Z') {
            int tempVar = big;
            while (tempVar > 0) {
                if (pas[i] == 'Z') {
                    pas[i] = 'A';
                    tempVar = tempVar - 1;
                }
                tempVar = tempVar - 1;
                pas[i] = pas[i] + 1;
            }
        }
    }
    for (int i = 0; i < pas.length(); i++)
    {
        if (pas[i] + small >= 'a' && pas[i] + small <= 'z') pas[i] = pas[i] + small;
        else if (pas[i] >= 'a' && pas[i] <= 'z') {
            int tempVar = small;
            while (tempVar > 0) {
                if (pas[i] == 'z') {
                    pas[i] = 'a';
                    tempVar = tempVar - 1;
                }
                pas[i] = pas[i] + 1;
                tempVar = tempVar - 1;
            }
        }
    }

to

for (int i = 0; i < pas.length(); i++) {
    char c = pas[i];
    if (is_upper(c)) {
        pas[i] = rotate_upper(c, big);
    }
    else if (is_lower(c)) {
        pas[i] = rotate_lower(c, small);
    }
}

You can transform 30 lines of code into just under 10. That's much easier to read for both you, the developer, and for any potential reviewers.