Next Lexicographic Permutation in Python

from bisect import bisect_left

# Next Lexicographic Permutation in Python
#
# PURPOSE
# Next permutation advances a sequence to its immediate lexicographic successor, including
# sequences with duplicates.
#
# METHOD
# Find the rightmost ascent, swap its left element with the rightmost larger value, then
# reverse the descending suffix. If no ascent exists, reverse the entire array.
#
# COMPLEXITY
# O(n) time and O(1) auxiliary space.
#
# CONTRACT
# Mutates input. Returns 1 when advanced, 0 when wrapped to the first permutation.
# 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: 1.
# Expected a after call: [1, 3, 2].
# 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 next_permutation(a: list[int]) -> int:
    alg_require(isinstance(a, list) and len(a) <= 1000000)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    pivot: int = n - 2
    right: int = n - 1
    left: int = 0
    temp: int = 0
    advanced: int = 0
    while pivot >= 0 and a[pivot] >= a[pivot + 1]:
        pivot -= 1
    if pivot >= 0:
        while a[right] <= a[pivot]:
            right -= 1
        temp = a[pivot]
        a[pivot] = a[right]
        a[right] = temp
        advanced = 1
    left = pivot + 1
    right = n - 1
    while left < right:
        temp = a[left]
        a[left] = a[right]
        a[right] = temp
        left += 1
        right -= 1
    return advanced

a = [1, 2, 3]
result = next_permutation(a)
print(result)
# Expected a: [1, 3, 2]
print(a)