Linear Search in Python

from bisect import bisect_left

# Linear Search in Python
#
# PURPOSE
# Scan the input from left to right until the target is found. No ordering is required, so
# linear search is useful for small or unsorted collections.
#
# METHOD
# Compare each element with target. Return immediately on a match; return -1 after the scan.
# Before each iteration, every earlier position is known not to match.
#
# COMPLEXITY
# O(n) time in the worst case, O(1) auxiliary space.
#
# CONTRACT
# n is the array length. Returns the first matching index, or -1. Empty input is valid.
# 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.
# 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 linear_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)
    i: int = 0
    while i < n:
        if a[i] == target:
            return i
        i += 1
    return -1

a = [4, 2, 4]
target = 4
result = linear_search(a, target)
print(result)