From db6a052a62db2cf367e96741fbc6d83bd6b03f0c Mon Sep 17 00:00:00 2001
From: rudrajiii <rudrasaha305@gmail.com>
Date: Mon, 28 Oct 2024 22:14:48 +0530
Subject: [PATCH] feat/implementation of Booth's Algorithm

---
 strings/booths_algorithm.py | 66 +++++++++++++++++++++++++++++++++++++
 1 file changed, 66 insertions(+)
 create mode 100644 strings/booths_algorithm.py

diff --git a/strings/booths_algorithm.py b/strings/booths_algorithm.py
new file mode 100644
index 000000000..a087d6dc8
--- /dev/null
+++ b/strings/booths_algorithm.py
@@ -0,0 +1,66 @@
+class BoothsAlgorithm:
+    """
+    Booth's Algorithm finds the lexicographically minimal rotation of a string.
+
+    Time Complexity: O(n) - Linear time where n is the length of input string
+    Space Complexity: O(n) - Linear space for failure function array
+
+    For More Visit - https://en.wikipedia.org/wiki/Booth%27s_multiplication_algorithm
+    """
+
+    def find_minimal_rotation(self, string: str) -> str:
+        """
+        Find the lexicographically minimal rotation of the input string.
+
+        Args:
+            string (str): Input string to find minimal rotation.
+
+        Returns:
+            str: Lexicographically minimal rotation of the input string.
+
+        Raises:
+            ValueError: If the input is not a string or is empty.
+
+        Examples:
+            >>> ba = BoothsAlgorithm()
+            >>> ba.find_minimal_rotation("baca")
+            'abac'
+            >>> ba.find_minimal_rotation("aaab")
+            'aaab'
+            >>> ba.find_minimal_rotation("abcd")
+            'abcd'
+            >>> ba.find_minimal_rotation("dcba")
+            'adcb'
+            >>> ba.find_minimal_rotation("aabaa")
+            'aaaab'
+        """
+        if not isinstance(string, str) or not string:
+            raise ValueError("Input must be a non-empty string")
+
+        n = len(string)
+        s = string + string  # Double the string to handle all rotations
+        f = [-1] * (2 * n)  # Initialize failure function array with twice the length
+        k = 0  # Starting position of minimal rotation
+
+        for j in range(1, 2 * n):
+            sj = s[j]
+            i = f[j - k - 1]
+
+            while i != -1 and sj != s[k + i + 1]:
+                if sj < s[k + i + 1]:
+                    k = j - i - 1
+                i = f[i]
+
+            if i == -1 and sj != s[k]:
+                if sj < s[k]:
+                    k = j
+                f[j - k] = -1
+            else:
+                f[j - k] = i + 1
+
+        return s[k : k + n]
+
+
+if __name__ == "__main__":
+    ba = BoothsAlgorithm()
+    print(ba.find_minimal_rotation("bca"))  # output is 'abc'