pe29.py

'''
Problem 29

Consider all integer combinations of a**b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

If they are then placed in numerical order, with any repeats removed, 
we get the following sequence of 15 distinct terms:

    4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by a**b for 2 ≤ a ≤ 100 
and 2 ≤ b ≤ 100?

Ans: 9183
'''
import numpy as np
from typing import Tuple


Range = Tuple[int, int] # List[int, int] is unsupported however for Python 3.9+ we can do list[int, int]


def find_combos(bases: np.array, powers: np.array) -> set:
    '''
    QA investigation found that an input of findCombos(np.arange(2,10+1), np.arange(2,10+1))
    returns a set containing -808182895 which is an error.
    '''
    combos = set([])
    for i in bases:
        combos.update(np.power(i, powers))
    return combos


def generate_combinations(a_range: Range, b_range: Range) -> set:
    '''
    Parameters
    ----------
    a_range : Range
         The min and max (inclusive) values of bases to consider.
    b_range : Range
        The min and max (inclusive) values of powers to consider.

    Raises
    ------
    TypeError
        If input is not a valid Tuple[int, int].
    ValueError
        If input contains value outside of allowed bounds of [2, 100].

    Returns
    -------
    set
        Set of distinct terms with bases a and powers b corresponding
        to the equation a**b.
    '''
    if sum(type(element)!=int for element in a_range + b_range):
        raise TypeError("Function only accepts lists of two integers as inputs.")
    elif sum((element > 100 or element < 2) for element in a_range + b_range):
        raise ValueError("Input contains value outside of allowed bounds of [2, 100].")
    combos = set()
    a1, a2 = a_range
    b1, b2 = b_range
    for a in range(a1, a2+1):
        for b in range(b1, b2+1):
            combos.update([a**b])
    return combos

    
def number_of_distinct_terms(combos: set) -> int:
    return len(list(combos))


if __name__ == "__main__":
    result = generate_combinations([2, 100], [2, 100])
    print(number_of_distinct_terms(result))