"""Longest common prefix (LCP) array for a suffix array.

Given a text (str or bytes) and its suffix array (list of starting positions
in ascending suffix order), compute the LCP array where lcp[i] is the length
of the longest common prefix of suffix SA[i-1] and suffix SA[i], with
lcp[0] = 0 by convention.

Uses Kasai's O(n) algorithm: walk suffixes in text order, maintaining the
current match length and decrementing by one each step.
"""
from __future__ import annotations


def build_suffix_array(text):
    """Naive O(n^2 log n) suffix array; fine for modest n."""
    n = len(text)
    return sorted(range(n), key=lambda i: text[i:])


def build_lcp(text, sa):
    n = len(text)
    if len(sa) != n:
        raise ValueError("suffix array length must equal text length")
    if sorted(sa) != list(range(n)):
        raise ValueError("invalid suffix array")
    rank = [0] * n
    for i, s in enumerate(sa):
        rank[s] = i
    lcp = [0] * n
    k = 0
    for i in range(n):
        if rank[i] == 0:
            k = 0
            continue
        j = sa[rank[i] - 1]
        while i + k < n and j + k < n and text[i + k] == text[j + k]:
            k += 1
        lcp[rank[i]] = k
        if k > 0:
            k -= 1
    return lcp


def lcp_of(text, i, j):
    """Direct LCP of suffixes starting at i and j."""
    n = len(text)
    k = 0
    while i + k < n and j + k < n and text[i + k] == text[j + k]:
        k += 1
    return k


if __name__ == "__main__":
    t = "banana"
    sa = build_suffix_array(t)
    print(sa)
    print(build_lcp(t, sa))