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Basic Projects:

---> Small Basics Projects and Implement Functions by C++.

The Algorithms:

---> They are algorithms for some not easy functions, And here they are:

( I ) Codes.

  1. checkBinary(string num):

    • int count = 0;: Initializes an integer variable count to zero. This variable will keep track of the number of valid binary digits encountered.
    • for (int i = 0; i < int(num.size()); i++): Iterates through each character in the input string num.
    • int(num.size()): calculates the length of the string.
    • if (num[i] == '0' || num[i] == '1'): Checks whether the current character at index i is either ‘0’ or ‘1’.
    • Inside the if block, the count variable is incremented by 1.
    • This means that for each valid binary digit encountered (‘0’ or ‘1’), the count increases.
    • After processing all characters, the function compares the final value of count with the length of the input string num.
    • If they are equal, it means that all characters in num are valid binary digits.
    • If the condition is true (i.e., all characters are valid binary digits), the function returns “Yes”.
    • Otherwise (if some characters are not valid binary digits), it returns “No”.

  2. binaryToDecimal(string num):

    • int dec = 0;: Initializes an integer variable dec to store the final decimal value.
    • deque<char> bit;: Creates a deque (double-ended queue) called bit to store the reversed binary digits.
    • for (int i = 0; i < int(num.size()); i++): Iterates through each character in the input string num.
    • bit.push_front(num[i]);: Adds each character to the front of the bit deque.
    • This effectively reverses the order of the binary digits.
    • for (int i = 0; i < int(bit.size()); i++): Iterates through each index in the bit deque.
    • static_cast<int>(bit[i]-'0'): Converts the character at index i (either ‘0’ or ‘1’) to an integer (0 or 1).
    • pow(2, i): Calculates 2 raised to the power of i.
    • dec += ...: Adds the product of the converted digit and the appropriate power of 2 to the dec value.
    • This step evaluates the value of each binary digit and accumulates the decimal value.
    • After processing all binary digits, the function returns the accumulated dec value, which represents the decimal equivalent of the binary number.

  3. decimalToBinary(int num):

    • string bin = "";: Initializes an empty string called bin to store the binary representation.
    • if (num == 0) {return "0";}: Checks if the input num is zero.
    • If it is, the function immediately returns “0” (since the binary representation of zero is just “0”).
    • while (num > 0) { ... }: Enters a loop that continues until num becomes zero.
    • Inside the loop, the following steps are performed for each iteration:
      • bin = char('0' + num % 2) + bin;: Converts the remainder to a character (‘0’ or ‘1’) and appends it to the front of the bin string.
      • The + bin part ensures that we build the binary representation from right to left.
      • num /= 2;: Divides num by 2, effectively shifting to the next binary place value.
    • After processing all binary places, the function returns the accumulated bin string, which represents the binary equivalent of the decimal number.

  4. addBinary(string A, string B):

    • if (A.length() > B.length()) {return addBinary(B, A);}:
      • If the length of string A is greater than that of string B, swap the arguments and recursively call addBinary(B, A).
      • This ensures that A is not shorter than B.
    • int diff = B.length() - A.length();: calculates the difference in lengths between B and A.
    • string padding;: initializes an empty string called padding.
    • The loop adds zeros to padding to make the lengths of A and B equal.
    • The main loop iterates through each index from right to left (from the end of the strings).
    • It performs binary addition based on the values of A[i] and B[i] and the carry (carry).
    • The result is accumulated in the res string.
    • Depending on the values of A[i] and B[i], the carry is updated accordingly.
    • If the carry is ‘1’, it propagates to the next position.
    • If there’s a carry after processing all digits, it’s appended to the result.
    • The result is reversed to obtain the correct order.
    • Leading zeros are removed by finding the first non-zero digit.
    • The function returns the final result, which is the sum of the binary numbers represented by A and B.

  5. decimalToAnyBase(int n, int k):

    • string res = "";: Initializes an empty string called res to store the result.
    • The while loop continues as long as n is greater than zero.
    • Inside the loop:
      • to_string(n % k): Converts the remainder to a string and appends it to the res string.
      • n /= k: Divides n by k, effectively shifting to the next place value.
    • After processing all place values, the res string contains the digits in reverse order.
    • reverse(res.begin(), res.end()): Reverses the order of characters in the res string.
    • The function returns the final result, which represents the number in the specified base.
( II ) Count Words & Letters.

  1. Function Definitions:

    1. void letter_count(string s):

      • This function counts the occurrences of each letter in a given string and prints them out. Here’s how it works step by step:
        • sort(all(s));: The string s is sorted alphabetically, so all identical letters are next to each other.
        • for (int i = 0; s[i] != '\0'; i++): A for loop starts, iterating over each character in the string until the null character \0 is reached (end of the string).
        • if (isalpha(s[i])): Inside the loop, it checks if the current character is an alphabetic character.
        • ll count = 1;: A variable count is initialized to 1 to start counting the occurrences of the current letter.
        • while (s[i] == s[i + 1]) {i++, count++;}: A while loop continues as long as the current character is the same as the next one. For each match, i is incremented to move to the next character, and count is incremented to keep track of the number of occurrences.
        • cout << s[i] << " => "<< count << endl;: Once the while loop ends, the character and its count are printed.

    2. int word_count(string st, char sep = ' '):

      • This function counts the number of words in a string, where words are separated by a specified separator (default is a space character ’ ') .Here’s how it works step by step:
        • int count = 0;: Initializes a word count to 0.
        • bool inWord = false;: A boolean flag to track whether the current position is inside a word.
        • for (int i = 0; i < st.length(); i++): A for loop iterates over each character in the string.
        • if (st[i] == sep): If the current character is the separator, it checks if it’s at the end of a word.
        • else {inWord = true;}: If the current character is not a separator, it’s part of a word, so set the flag to true.
        • if (inWord) {count++;}: After the loop, if it ends inside a word, increment the word count.

  2. Example.:

    Suppose we have the following input string:

    "Hello World! Welcome to C++ programming."

    Here's what the output would look like after running the main function with this input:

    The number of letters in the sentence in details:
C => 1
H => 1
W => 2
a => 1
c => 1
d => 1
e => 3
g => 2
i => 1
l => 4
m => 3
n => 1
o => 5
p => 1
r => 3
t => 1

The number of words in the sentence = 6 words.
( III ) Distinct Values & Get Index.

  1. Function Definitions:

    1. int cntDistinct(string str):

      • This function takes a string str as input.
      • It calculates the number of distinct characters (unique characters) in the given string.
      • Here's how it works:
        • It uses an unordered_set<char> (a set that automatically removes duplicates) to store unique characters.
        • The loop traverses the string, and for each character:
          • If the character is not already in the set, it inserts it.
          • If the character is already in the set, it is ignored (since it's not unique).
        • Finally, it returns the size of the set, which represents the count of distinct characters in the string.

    2. int countDistinct(int arr[], int n):

      • This function takes an array of integers arr and its size n as input.
      • It calculates the number of distinct elements in the array.
      • Here's how it works:
        • It uses a set<int> (a set that automatically removes duplicates) to store unique elements.
        • The loop traverses the array, and for each element:
          • If the element is not already in the set, it inserts it.
          • If the element is already in the set, it is ignored (since it's not unique).
        • Finally, it returns the size of the set, which represents the count of distinct elements in the array.

    3. long long getIndex(vector<ll> v, ll K):

      • This function takes a vector of ll (long long) integers v and a target value K.
      • It searches for K in the vector and returns its index if found; otherwise, it returns -1.
      • Here's how it works:
        • It uses the find function from the <algorithm> library to search for K in the vector.
        • If K is found, it calculates the index by subtracting the iterator position from the beginning of the vector.
        • If K is not present in the vector, it returns -1.

  2. Main Function:

    • Reads a string e and calculates the number of distinct characters using cntDistinct(e).
    • Reads an integer n and an array of integers arr. Calculates the number of distinct elements using countDistinct(arr, n).
    • Reads a long long integer k and finds its index in the array using getIndex(arr, k).
    • Prints the results accordingly.
    • Finally, the program returns 0, indicating successful execution.

  3. End of Program.

( IV ) Five in One.

  1. Function Definitions:

    • Max() : This function sorts the array in descending order (largest to smallest) and then prints the first element, which is the largest number in the array.
    • Min() : Similar to the Max function, but it sorts the array in ascending order (smallest to largest) and prints the first element, which is the smallest number.
    • Prime() : This function counts the number of prime numbers in the array. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
    • Palindrome() : This function checks how many numbers in the array are palindromes. A palindrome is a number that reads the same backward as forward.
    • divisors() : This function returns the number of divisors of a given number. A divisor is a number that can divide another number without leaving a remainder.

  2. Main Function:

    1. Read Number of Elements:

      • The program prompts the user to enter the number of elements (num) that will be in the array.

    2. Create and Fill the Array:

      • An array arr is created with the size specified by the user. The program then reads the elements of the array from the user input.

    3. Find and Display Maximum and Minimum:

      • The Max and Min functions are called to find and display the largest and smallest numbers in the array.

    4. Count and Display Prime Numbers:

      • The Prime function is called to count and display the number of prime numbers in the array.

    5. Count and Display Palindrome Numbers:

      • The Palindrome function is called to count and display the number of palindrome numbers in the array.

    6. Find the Number with Maximum Divisors:

      • A loop runs through each element in the array, calling the divisors function to find the number of divisors for each element. It keeps track of the number with the most divisors and, in case of a tie, the larger number.

    7. Display the Number with Maximum Divisors:

      • After the loop, the program prints the number that has the maximum number of divisors.

    8. End of Program:

      • The program returns 0, which is a signal that the program has ended successfully.
( V ) Multiply the matrix by the scalar.

  1. Function Definitions:

    • void read_matrix(ll row, ll column, int** matrix): This function reads the elements of a matrix from the user. It takes the number of rows and columns as well as a pointer to a pointer of integers (which represents the matrix) as arguments.
    • void write_matrix(ll row, ll column, int** matrix): This function prints the matrix to the console. It also takes the number of rows and columns and the matrix as arguments.
    • void multiply_by_scalar(ll row, ll column, int** matrix, ll scalar): This function multiplies each element of the matrix by a scalar value provided by the user.

  2. Main Function:

    • The main function begins with a greeting message to the user.
    • It then prompts the user to enter the number of rows and columns for the matrix.
    • Memory is dynamically allocated for the matrix using new based on the number of rows and columns entered by the user.
    • The read_matrix function is called to read the matrix elements from the user.
    • The write_matrix function is called to print the original matrix.
    • The user is prompted to enter a scalar value.
    • The multiply_by_scalar function is called to multiply the matrix by the scalar.
    • The write_matrix function is called again to print the modified matrix.

  3. Program Flow:

    • The user is interactively involved throughout the program, entering the size of the matrix, its elements, and the scalar value for multiplication.
    • The program outputs the matrix before and after the scalar multiplication.

  4. Memory Management:

    • We allocate memory for the matrix dynamically using new.
    • After using the matrix, we free the allocated memory using delete[].

  5. End of Program:

    • We display a thank-you message and terminate the program.
( VI ) Sequence Arrangement Solver.

  1. Input and Initialization:

    • int n;: We declare an integer variable n to store the number of elements (people in line).
    • cin >> n;: We read the value of n from the standard input (keyboard).
    • vector<int> arr(n), position(n, 0);: We create two vectors:
      • arr to store the input sequence of people.
      • position to keep track of the positions directly behind each person (initialized with zeros).
    • int x = 0;: We initialize an integer variable x to zero. This variable will later store the starting position.

  2. Reading the Input Sequence:

    • We use a for loop to read the input sequence into the arr vector.
    • If the current element is not -1, we update the position vector to reflect the position of that element in the sequence.
    • If the current element is -1, we set x to the current index plus one, indicating the starting position.

  3. Output the Sequence:

    • We print the starting position (stored in x).
    • Then, we follow the chain of positions using a while loop:
      • If the next position is not zero (i.e., there's a valid successor), we print the next position and update x to that position.
      • We continue this process until we reach the end of the chain (when the next position is zero).

  4. End of Program.

( VII ) The Most Repeated Character.

  1. Function mostFrequent:

    • This function takes a string text as input.
    • It initializes variables: max (to track the maximum count), count (to count occurrences of each character), and maxCharcter (to store the most frequent character).
    • The outer loop iterates over characters from space ' ' to tilde '~'.
    • The inner loop counts how many times the current character appears in the input string text.
    • If the count is greater than the current maximum, it updates the maximum count and the most frequent character.
    • The function returns the most frequent character.

  2. Main Function:

    • The main function starts by declaring an integer variable test.
    • It reads a string txt from standard input (keyboard).
    • It calls the mostFrequent function with txt as the argument and prints the result (the most frequent character).

  3. End of Program.:

    • The program returns 0 to indicate successful execution.
( VIII ) .
( IX ) .