Added Suffix Array and LCP implementation

divide_and_conquer/Suffix Array and LCP implementation.py

@@ -0,0 +1,93 @@
+from typing import List
+
+
+class SuffixArray:
+    def __init__(self, text: str) -> None:
+        """
+        Initializes the class with the input text and builds the suffix and LCP arrays.
+        """
+        self.text = text
+        self.suffix_array = self.build_suffix_array()
+        self.lcp_array = self.build_lcp_array()
+
+    def build_suffix_array(self) -> List[int]:
+        """
+        Builds the suffix array for the input string.
+        Returns the suffix array (a list of starting indices of suffixes in sorted order).
+
+        Example:
+        >>> sa = SuffixArray("banana")
+        >>> sa.suffix_array
+        [5, 3, 1, 0, 4, 2]
+        """
+        n = len(self.text)
+        suffixes = sorted(range(n), key=lambda i: self.text[i:])
+        return suffixes
+
+    def build_lcp_array(self) -> List[int]:
+        """
+        Builds the LCP (Longest Common Prefix) array for the suffix array.
+        LCP[i] gives the length of the longest common prefix of the suffixes starting at suffix_array[i] and suffix_array[i-1].
+
+        Example:
+        >>> sa = SuffixArray("banana")
+        >>> sa.lcp_array
+        [0, 1, 3, 0, 0, 2]
+        """
+        n = len(self.text)
+        suffix_array = self.suffix_array
+        rank = [0] * n
+        lcp = [0] * n
+
+        # Build the rank array where rank[i] gives the position of the suffix starting at index i
+        for i, suffix in enumerate(suffix_array):
+            rank[suffix] = i
+
+        h = 0
+        for i in range(n):
+            if rank[i] > 0:
+                j = suffix_array[rank[i] - 1]
+                while (i + h < n) and (j + h < n) and self.text[i + h] == self.text[j + h]:
+                    h += 1
+                lcp[rank[i]] = h
+                if h > 0:
+                    h -= 1
+        return lcp
+
+    def display(self) -> None:
+        """
+        Displays the suffix array and LCP array for the input string.
+
+        Example:
+        >>> sa = SuffixArray("banana")
+        >>> sa.display()
+        Suffix Array:
+        5: a
+        3: ana
+        1: anana
+        0: banana
+        4: na
+        2: nana
+
+        LCP Array:
+        LCP between a and ana: 1
+        LCP between ana and anana: 3
+        LCP between anana and banana: 0
+        LCP between banana and na: 0
+        LCP between na and nana: 2
+        """
+        print("Suffix Array:")
+        for idx in self.suffix_array:
+            print(f"{idx}: {self.text[idx:]}")
+
+        print("\nLCP Array:")
+        for i in range(1, len(self.lcp_array)):
+            print(
+                f"LCP between {self.text[self.suffix_array[i - 1]:]} and {self.text[self.suffix_array[i]:]}: {self.lcp_array[i]}")
+
+
+# Example usage:
+if __name__ == "__main__":
+    text = "banana"
+    sa = SuffixArray(text)
+    sa.display()