Python3 Program to Find 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 number N 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 number N, 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:

Python3

# Python program for the above approach

# Function to find the maximum value
# possible by rotations of digits of N
def findLargestRotation(num):

    # Store the required result
    ans = num

    # Store the number of digits
    length = len(str(num))
    x = 10**(length - 1)

    # Iterate over the range[1, len-1]
    for i in range(1, length):

        # Store the unit's digit
        lastDigit = num % 10

        # Store the remaining number
        num = num // 10

        # Find the next rotation
        num += (lastDigit * x)

        # If the current rotation is
        # greater than the overall
        # answer, then update answer
        if (num > ans):
            ans = num

    # Print the result
    print(ans)

# Driver Code
N = 657
findLargestRotation(N)

# This code is contributed by rohitsingh07052.

Output:

765

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

Please refer complete article on Maximum value possible by rotating digits of a given number for more details!