Manacher Longest Palindromic Substring in Python

from bisect import bisect_left

# Manacher Longest Palindromic Substring in Python
#
# PURPOSE
# Manacher reuses mirrored palindrome radii to find a longest contiguous palindrome in
# linear time.
#
# METHOD
# Compute odd and even center radii in separate passes. Reuse the mirror radius within the
# current rightmost palindrome, then expand only beyond its known boundary.
#
# COMPLEXITY
# O(n) time and O(n) auxiliary space.
#
# CONTRACT
# Integer tokens. Returns longest palindrome LENGTH; empty input returns zero.
# Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
# counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
# Sorted order, correct tree topology, and caller-owned data-structure invariants are
# preconditions; checking them on every query would change query complexity.
# Scalar and shape checks are included. Value-range checks are included where needed to
# prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
# workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
# uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
# partly updated after arithmetic failure. These are single-threaded, in-memory
# implementations.
#
# LANGUAGE DETAILS
# Python 3.9+: automatic lengths, native lists, arbitrary-precision arithmetic, and
# bisect_left for LIS. Invalid scalar/shape inputs raise ValueError. Integer element types
# and sorted/tree invariants remain caller preconditions.
#
# EXAMPLE
# Expected return: 4.
# Run: python example.py
# Tests for this exact source artifact run before publication. The accompanying source
# archive includes unit cases, runtime results, and source hashes.

def alg_require(condition):
    if not condition:
        raise ValueError("invalid algorithm input; see contract")
def alg_size(n):
    alg_require(0 <= n <= 4000000)
    return n

def manacher(a: list[int]) -> int:
    alg_require(isinstance(a, (list, tuple)) and len(a) <= 1000000)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    radius: list[int] = [0] * alg_size(n + 1)
    parity: int = 0
    left: int = 0
    right: int = -1
    i: int = 0
    k: int = 0
    best: int = 0
    while parity < 2:
        left = 0
        right = -1
        i = 0
        while i < n:
            k = 1 - parity
            if i <= right:
                k = min(radius[left + right - i + parity], right - i + 1)
            while i - k - parity >= 0 and i + k < n and (a[i - k - parity] == a[i + k]):
                k += 1
            radius[i] = k
            best = max(best, 2 * k - 1 + parity)
            if i + k - 1 > right:
                left = i - k - parity + 1
                right = i + k - 1
            i += 1
        parity += 1
    return best

a = [1, 2, 2, 1]
result = manacher(a)
print(result)