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NOTES.md

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Approach

Input

  • The code takes an integer input n from the user.

Initialization

  • It initializes a variable given_num with the value of n. This variable is used to store the original value of n because n will be modified during the process.

check_palindrome Function

  • The check_palindrome function is defined to determine whether a number is a palindrome.
  • It initializes a variable rev_num to 0. This variable will be used to store the reverse of n.

Reversing n

  • The code enters a while loop that continues as long as n is greater than 0.
  • In each iteration of the loop:
    • It calculates the last digit of n using the modulo operation (n % 10) and stores it in the last_digit variable.
    • It updates n by removing the last digit using integer division (n //= 10).
    • It updates rev_num by appending the last_digit to the right of the current rev_num. This is done by multiplying rev_num by 10 and adding last_digit to it (rev_num = (rev_num * 10) + last_digit).
    • This process effectively reverses the digits of n and stores the result in rev_num.

Checking for Palindrome

  • After the loop completes, rev_num contains the reversed value of the original number n.
  • It then checks whether rev_num is equal to the given_num (the original number) using the equality operator (rev_num == given_num).
  • The result of this comparison is a Boolean value (True if n is a palindrome, False otherwise).
  • To match the expected output format mentioned in the problem statement, the Boolean value is first converted to a string using str(), and then it is converted to lowercase using .lower().

Printing the Result

  • Finally, the code prints the result of the check_palindrome function, which will be either "true" (if n is a palindrome) or "false" (if n is not a palindrome).

Time Complexity Analysis

The time complexity of this code can be analyzed as follows:

  1. Input: The code starts by taking an integer input n from the user. This input operation is a constant-time operation and does not affect the overall time complexity.

  2. check_armstrong Function:

    • The check_armstrong function is defined to check whether a number is an Armstrong number.
    • It calculates the number of digits in n using the len function, which converts the integer to a string and counts the characters. This operation takes O(log n) time, where n is the input integer.

  3. Looping through Digits:

    • The code then enters a while loop that continues as long as n is greater than 0. In each iteration of the loop, the following operations are performed:
      • Calculation of the last digit of n using the modulo operation (n % 10).
      • Integer division to remove the last digit from n (n //= 10).
      • Calculation of the last_digit raised to the power of num_of_digits using the math.pow function.
      • Accumulation of the result in the sum variable.

  4. Loop Iterations: Since each iteration of the loop reduces the value of n by a factor of 10 (due to integer division), the number of iterations required is proportional to the number of digits in n. For an integer with d digits, the loop will run approximately d times until n becomes zero.

  5. Therefore, the dominant factor in the time complexity is the number of digits in n, which can be represented as $O(log n)$.

In summary, the time complexity of the given code is $O(log n)$, where n is the input integer. The frequency count method confirms that the code's time complexity matches the stated O(log n) complexity.

Space Complexity Analysis

The space complexity of the provided code is determined by the additional memory space required as the code executes. In this case, the code uses a constant amount of memory space regardless of the input size.

  1. Input: The code takes an integer input n from the user, which requires a constant amount of memory space. This input operation does not contribute to space complexity.

  2. check_armstrong Function:

    • The check_armstrong function defines a few variables (num_of_digits, last_digit, sum), but the memory space required for these variables is constant. These variables do not depend on the input size and remain the same regardless of the magnitude of n.

  3. Loop Variables:

    • Within the loop, variables such as last_digit and sum are used to perform calculations. These variables require a constant amount of space and do not grow with the input size.

  4. Overall:

    • The code does not use any data structures that would grow with the input size, and it does not create additional arrays, lists, or other dynamic data structures.

Therefore, the space complexity of the code is O(1), indicating constant space usage. The amount of memory used by the code remains the same, regardless of the input size.