Added Python Implementation of Suffix Arrays and LCP Arrays

divide_and_conquer/suffix_array_lcp.py

@@ -0,0 +1,82 @@
+#!/usr/bin/env python3
+
+import doctest
+
+
+def build_suffix_array(input_string: str) -> list[int]:
+    """
+    Build the suffix array for the given string.
+
+    Parameters:
+        input_string (str): The input string.
+
+    Returns:
+        list[int]: The suffix array (a list of starting indices of
+                    suffixes in sorted order).
+
+    Example:
+        >>> build_suffix_array("banana")
+        [5, 3, 1, 0, 4, 2]
+    """
+    suffixes = [(input_string[i:], i) for i in range(len(input_string))]
+    suffixes.sort()  # Sort the suffixes lexicographically
+    suffix_array = [suffix[1] for suffix in suffixes]
+    return suffix_array
+
+
+def build_lcp_array(input_string: str, suffix_array: list[int]) -> list[int]:
+    """
+    Build the LCP array for the given string and suffix array.
+
+    Parameters:
+        input_string (str): The input string.
+        suffix_array (list[int]): The suffix array.
+
+    Returns:
+        list[int]: The LCP array.
+
+    Example:
+        >>> suffix_arr = build_suffix_array("banana")
+        >>> build_lcp_array("banana", suffix_arr)
+        [0, 1, 3, 0, 0, 2]
+    """
+    n = len(input_string)
+    rank = [0] * n
+    lcp = [0] * n
+
+    # Compute the rank of each suffix
+    for i, suffix_index in enumerate(suffix_array):
+        rank[suffix_index] = i
+
+    # Compute the LCP array
+    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 (input_string[i + h] == input_string[j + h])
+            ):
+                h += 1
+            lcp[rank[i]] = h
+            if h > 0:
+                h -= 1  # Decrease h for the next suffix
+    return lcp
+
+
+# Example usage
+if __name__ == "__main__":
+    test_string = "banana"
+    suffix_array = build_suffix_array(test_string)
+    lcp_array = build_lcp_array(test_string, suffix_array)
+
+    print("Suffix Array:")
+    for i in range(len(suffix_array)):
+        print(f"{suffix_array[i]}: {test_string[suffix_array[i]:]}")
+
+    print("\nLCP Array:")
+    for i in range(1, len(lcp_array)):
+        print(
+            f"LCP between {test_string[suffix_array[i - 1]:]} and {test_string[suffix_array[i]]}: {lcp_array[i]}"
+        )