Maximum value possible by rotating digits of a given number

Given a positive integer N, the task is to find the maximum value among all the rotations of the digits of the integer N.

Examples:

Input: N = 657
Output: 765
Explanation: All rotations of 657 are {657, 576, 765}. The maximum value among all these rotations is 765.

Input: N = 7092
Output: 9270
Explanation:
All rotations of 7092 are {7092, 2709, 9270, 0927}. The maximum value among all these rotations is 9270.

Approach: The idea is to find all rotations of the numberN and print the maximum among all the numbers generated. Follow the steps below to solve the problem:

• Count the number of digits present in the numberN, i.e. upper bound of log₁₀N.
• Initialize a variable, say ans with the value of N, to store the resultant maximum number generated.
• Iterate over the range [1, log₁₀(N) - 1] and perform the following steps:
  • Update the value of N with its next rotation.
  • Now, if the next rotation generated exceeds ans, then update ans with the rotated value of N
• After completing the above steps, print the value of ans as the required answer.

Below is the implementation of the above approach:

765

Time Complexity: O(log₁₀N)
Auxiliary Space: O(1)

 Convert number to string, rotate the string and convert back to integer in python:

Approach:

Initialize a variable max_num with the input number n.
Convert the input number n to a string str_num.
Loop through the indices of the string str_num, starting from index 1 to the end of the string.
Inside the loop, slice the string str_num from index 1 to the end and concatenate it with the first character of the string str_num using the string concatenation operator +.
Convert the resulting rotated string to an integer rotated_num.
Check if rotated_num is greater than max_num, if yes, update max_num to rotated_num.
Return max_num.
Test the function with some inputs and measure the execution time using the time module.

Max Rotation for 657: 765
Max Rotation for 7092: 9270

Time complexity: O(n^2), where n is the number of digits in the input number.
Auxiliary Space: O(n), where n is the number of digits in the input number.