Greedy Interval Scheduling in Python

from bisect import bisect_left

# Greedy Interval Scheduling in Python
#
# PURPOSE
# Earliest-finish-time scheduling selects a maximum-size collection of non-overlapping
# intervals.
#
# METHOD
# Process intervals sorted by finish time. Accept the next interval whenever its start is at
# least the finish of the last accepted interval.
#
# COMPLEXITY
# O(n) scan time and O(1) auxiliary space once sorted; sorting unsorted intervals first
# costs O(n log n).
#
# CONTRACT
# start and finish arrays have n entries; finish is nondecreasing and start[i]<finish[i].
# Half-open intervals allow touching endpoints. Returns selected count.
# 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: 4.
# 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 interval_schedule(start: list[int], finish: list[int]) -> int:
    alg_require(isinstance(start, (list, tuple)) and len(start) <= 1000000)
    alg_require(isinstance(finish, (list, tuple)) and len(finish) <= 1000000)
    n: int = len(start)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(start) == n)
    alg_require(len(finish) == n)
    count: int = 0
    end: int = 0
    i: int = 0
    while i < n:
        if count == 0 or start[i] >= end:
            count += 1
            end = finish[i]
        i += 1
    return count

start = [1, 3, 0, 5, 8, 5]
finish = [2, 4, 6, 7, 9, 9]
result = interval_schedule(start, finish)
print(result)