Egg Dropping by Number of Moves in Python

from bisect import bisect_left

# Egg Dropping by Number of Moves in Python
#
# PURPOSE
# Instead of trying every floor, this DP counts how many floors can be distinguished with a
# given number of moves and eggs.
#
# METHOD
# For each move, update egg counts downward using
# reachable[e]=reachable[e]+reachable[e-1]+1. Stop when the available egg count covers all
# floors.
#
# COMPLEXITY
# O(eggs * moves) time and O(eggs) space, where moves is the answer.
#
# CONTRACT
# 1<=eggs<=30, 0<=floors<=1000000. Returns the minimum worst-case number of drops.
# Reachability is capped at floors to avoid unnecessary growth.
# 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: 14.
# 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 egg_drop(eggs: int, floors: int) -> int:
    alg_require(type(eggs) is int and -2147483648 <= eggs <= 2147483647)
    alg_require(type(floors) is int and -2147483648 <= floors <= 2147483647)
    alg_require(eggs >= 1 and eggs <= 30 and (floors >= 0) and (floors <= 1000000))
    reachable: list[int] = [0] * alg_size(eggs + 1)
    moves: int = 0
    e: int = 0
    while reachable[eggs] < floors:
        moves += 1
        e = eggs
        while e > 0:
            reachable[e] = min(floors, reachable[e] + reachable[e - 1] + 1)
            e -= 1
    return moves

eggs = 2
floors = 100
result = egg_drop(eggs, floors)
print(result)