# 1. Introduction

The "Derive Strings" problem is a string manipulation challenge that focuses on determining if one string can be derived from another through circular rotation. This problem tests understanding of string operations and is a common question in programming interviews.

## Problem

Given two strings X and Y, the task is to check if Y can be derived from X by circularly rotating X either clockwise or anti-clockwise. The rotation implies shifting all characters of X by a certain number of positions to the right or left, wrapping around the ends of the string.

# 2. Solution Steps

1. Check if the lengths of both strings are equal. If not, return false.

2. Concatenate string X with itself. This creates a string that contains all possible rotations of X.

3. Check if string Y is a substring of the concatenated string.

4. If Y is found in the concatenated string, return true; otherwise, return false.

# 3. Code Program

``````#include <iostream>
#include <string>
using namespace std;

// Function to check if Y can be derived from X by circular rotation
bool isCircularRotation(const string &X, const string &Y) {
if (X.length() != Y.length()) {
return false; // Strings of unequal length cannot be rotations of each other
}

string temp = X + X; // Concatenate X with itself
return (temp.find(Y) != string::npos); // Check if Y is a substring of temp
}

int main() {
string X = "ABCD";
string Y = "DABC";
cout << boolalpha << isCircularRotation(X, Y) << endl;
return 0;
}
``````

true

### Explanation:

The program starts by checking if strings X and Y are of equal length, as rotation is not possible between strings of different lengths. It then concatenates X with itself, forming a string that contains all possible rotations of X. By checking if Y is a substring of this concatenated string, the program efficiently determines if Y can be derived from X through rotation.

This solution is elegant and efficient, utilizing standard string operations to solve the problem.