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)
        # Create a list of suffix indices sorted by the suffixes they point to
        sorted_suffix_indices = sorted(range(n), key=lambda suffix_index: self.text[suffix_index:])
        return sorted_suffix_indices

    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 rank_index, suffix in enumerate(suffix_array):
            rank[suffix] = rank_index

        h = 0
        for i in range(n):
            if rank[i] > 0:
                j = suffix_array[rank[i] - 1]  # Previous suffix in the sorted order
                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  # Decrease h for the next suffix comparison
        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

        """
        print("Suffix Array:")
        for suffix_index in self.suffix_array:
            print(f"{suffix_index}: {self.text[suffix_index:]}")



# Example usage:
if __name__ == "__main__":
    text = "banana"
    sa = SuffixArray(text)
    sa.display()  # Contribution for Hacktoberfest 2024