C++ 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:

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find the maximum value
// possible by rotations of digits of N
void findLargestRotation(int num)
{
    // Store the required result
    int ans = num;

    // Store the number of digits
    int len = floor(log10(num) + 1);

    int x = pow(10, len - 1);

    // Iterate over the range[1, len-1]
    for (int i = 1; i < len; i++) {

        // Store the unit's digit
        int 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
    cout << ans;
}

// Driver Code
int main()
{
    int N = 657;
    findLargestRotation(N);

    return 0;
}

765

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