Longest Palindromic Subsequence in Python

from bisect import bisect_left

# Longest Palindromic Subsequence in Python
#
# PURPOSE
# A longest palindromic subsequence may skip tokens while preserving order. It differs from
# a contiguous palindromic substring.
#
# METHOD
# Scan left endpoints backward and right endpoints forward. Equal endpoints extend the inner
# solution by two; otherwise discard one endpoint. Retain one row and the old diagonal.
#
# COMPLEXITY
# O(n squared) time, O(n) auxiliary space.
#
# CONTRACT
# Integer tokens. Returns length; empty input returns 0.
# 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: 5.
# 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 palindromic_subsequence(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)
    dp: list[int] = [0] * alg_size(n + 1)
    left: int = n - 1
    right: int = 0
    diagonal: int = 0
    old: int = 0
    while left >= 0:
        dp[left] = 1
        diagonal = 0
        right = left + 1
        while right < n:
            old = dp[right]
            if a[left] == a[right]:
                dp[right] = diagonal + 2
            else:
                dp[right] = max(dp[right], dp[right - 1])
            diagonal = old
            right += 1
        left -= 1
    if n == 0:
        return 0
    return dp[n - 1]

a = [1, 2, 3, 2, 1]
result = palindromic_subsequence(a)
print(result)