Interpolation Search in Python

from bisect import bisect_left

# Interpolation Search in Python
#
# PURPOSE
# Interpolation search estimates the target position from endpoint values, which can help on
# roughly uniform numeric data.
#
# METHOD
# Estimate a position proportional to the target value between endpoint values. Compare
# there and discard the impossible side. Handle equal endpoints separately.
#
# COMPLEXITY
# Expected O(log log n) comparisons for suitable uniform distributions; O(n) worst case,
# O(1) space.
#
# CONTRACT
# Ascending nonnegative integers <= 10000; n <= 10000 so the interpolation product fits
# signed 32-bit. Returns any matching index or -1.
# 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: 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 interpolation_search(a: list[int], target: int) -> int:
    alg_require(isinstance(a, (list, tuple)) and len(a) <= 1000000)
    alg_require(type(target) is int and -2147483648 <= target <= 2147483647)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    alg_require(n <= 10000)
    for value in a:
        alg_require(value >= 0 and value <= 10000)
    low: int = 0
    high: int = n - 1
    pos: int = 0
    while low <= high and target >= a[low] and (target <= a[high]):
        if a[low] == a[high]:
            return low
        pos = low + (target - a[low]) * (high - low) // (a[high] - a[low])
        if a[pos] == target:
            return pos
        if a[pos] < target:
            low = pos + 1
        else:
            high = pos - 1
    return -1

a = [0, 10, 20, 30]
target = 20
result = interpolation_search(a, target)
print(result)