Monotonic Stack Next Greater Element in Python

from bisect import bisect_left

# Monotonic Stack Next Greater Element in Python
#
# PURPOSE
# A monotonic stack finds each position's next strictly greater value without rescanning the
# suffix.
#
# METHOD
# Store indices with decreasing values. On a larger value, pop and resolve every smaller
# pending index. Each index is pushed and popped at most once.
#
# COMPLEXITY
# O(n) time and O(n) auxiliary space.
#
# CONTRACT
# output has n entries. Writes next greater INDEX or -1 for each position, 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: 0.
# Expected output after call: [2, 2, -1].
# 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_greater(a: list[int], output: list[int]) -> int:
    alg_require(isinstance(a, (list, tuple)) and len(a) <= 1000000)
    alg_require(isinstance(output, list) and len(output) <= 1000000)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    alg_require(len(output) == n)
    stack: list[int] = [0] * alg_size(n + 1)
    top: int = 0
    i: int = 0
    index: int = 0
    while i < n:
        output[i] = -1
        while top > 0 and a[stack[top - 1]] < a[i]:
            top -= 1
            index = stack[top]
            output[index] = i
        stack[top] = i
        top += 1
        i += 1
    return 0

a = [2, 1, 3]
output = [0, 0, 0]
result = next_greater(a, output)
print(result)
# Expected output: [2, 2, -1]
print(output)