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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 provided code is designed to check whether an input integer n is a palindrome by reversing its digits. Let's analyze its time complexity:

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

  2. check_palindrome Function:

    • The check_palindrome function contains a while loop for reversing the digits of the input integer n.
    • 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).
      • Update of rev_num by appending the last_digit to the right of the current rev_num using multiplication and addition (rev_num = (rev_num * 10) + last_digit).

  3. The number of iterations in the while loop depends on the number of digits in the input integer n. For an integer with d digits, the loop will run approximately d times until n becomes zero.

  4. Therefore, the time complexity of the code is proportional to the number of digits in n, which can be represented as $O(log10(n))$.

In summary, the time complexity of the given code is $O(log10(n))$, where n is the input integer. This reflects the logarithmic growth in the number of iterations as the input integer's digits increase in magnitude.

Space Complexity Analysis

  1. Initialization: The code initializes a single integer variable revNum to store the reversed number. This variable does not depend on the input size n, so its space complexity is constant (O(1)).

  2. Loop Variables:

    • The code uses a loop to iterate through the digits of n. Inside the loop, it creates a few temporary variables:
      • last_digit: To hold the value of the last digit extracted in each iteration. This variable is also an integer and takes constant space (O(1)).
      • The loop does not create any new data structures or allocate memory based on the input size. Instead, it uses these variables to perform operations.

Space Complexity:

The space complexity of this code is primarily determined by the constant amount of memory used for the variables revNum and last_digit, both of which are integers.

Therefore, the space complexity is O(1), indicating that the memory requirements of the algorithm do not grow with the size of the input n. The code uses a fixed amount of memory regardless of the value of n.

In summary, the space complexity of this code is constant, denoted as O(1).