0-1 Knapsack in Python

from bisect import bisect_left

# 0-1 Knapsack in Python
#
# PURPOSE
# Knapsack chooses items with maximum total value under a weight limit, using each item at
# most once. The one-dimensional table stores the best value for each capacity.
#
# METHOD
# Process items one at a time and capacities downward. Compare skipping the item with adding
# its value to the previous best at the remaining capacity. Descending capacities prevent
# reusing the current item.
#
# COMPLEXITY
# O(n * capacity) time and O(capacity) auxiliary space; pseudo-polynomial.
#
# CONTRACT
# Weights are positive, values nonnegative, capacity >= 0. Both arrays have n entries.
# Returns best value, not the chosen item set.
# 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: 9.
# 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 knapsack(weights: list[int], values: list[int], capacity: int) -> int:
    alg_require(isinstance(weights, (list, tuple)) and len(weights) <= 1000000)
    alg_require(isinstance(values, (list, tuple)) and len(values) <= 1000000)
    alg_require(type(capacity) is int and -2147483648 <= capacity <= 2147483647)
    n: int = len(weights)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(weights) == n)
    alg_require(len(values) == n)
    alg_require(capacity >= 0 and capacity <= 1000000)
    for value in weights:
        alg_require(value > 0)
    for value in values:
        alg_require(value >= 0)
    dp: list[int] = [0] * alg_size(capacity + 1)
    i: int = 0
    c: int = 0
    while i < n:
        c = capacity
        while c >= weights[i]:
            dp[c] = max(dp[c], dp[c - weights[i]] + values[i])
            c -= 1
        i += 1
    return dp[capacity]

weights = [2, 3, 4]
values = [4, 5, 7]
capacity = 5
result = knapsack(weights, values, capacity)
print(result)