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from functools import lru_cache, cmp_to_key |
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from itertools import product, starmap |
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from math import log |
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4
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from operator import mul |
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5
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6
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PRIME_FACTORS = (2, 3, 5) |
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8
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9
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class Factors: |
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def __init__(self, factor): |
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self.factor = factor |
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self.current = 1 |
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14
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def pop(self, value: int) -> int | None: |
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if value == self.current: |
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ret = self.current |
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self.current *= self.factor |
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return ret |
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@lru_cache |
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def is_ugly(n: int) -> bool: |
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if n == 1: |
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return True |
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for prime in PRIME_FACTORS: |
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while n % prime == 0: |
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n //= prime |
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return n == 1 |
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30
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def find_ugly_number(n: int, ugly_numbers=[1], queue=[1], confirmed_to=1) -> int: |
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32
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if len(ugly_numbers[:ugly_numbers.index(confirmed_to) + 1]) >= n: |
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return ugly_numbers[n - 1] |
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new_numbers = list(starmap(mul, product(PRIME_FACTORS, queue))) |
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return find_ugly_number(n, sorted(set(ugly_numbers + new_numbers)), new_numbers, min(new_numbers)) |
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37
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38
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def find_ugly_number2(n: int, current_number=1) -> int: |
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counter = 0 |
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while counter < n: |
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if is_ugly(current_number): |
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counter += 1 |
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current_number += 1 |
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else: |
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current_number += 1 |
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return current_number - 1 |
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48
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49
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def find_ugly_number3(n: int) -> int: |
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permutations = product(range(n), set([0] + list(range(n * 2 // 3))), set([0] + list(range(n * 2 // 5)))) |
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numbers = sorted([2 ** i[0] * 3 ** i[1] * 5 ** i[2] for i in permutations]) |
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return numbers |
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54
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55
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def find_ugly_number4(n: int) -> int: |
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factor_list = [Factors(i) for i in [2, 3, 5, 6, 10, 15, 30]] |
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for i in range(n): |
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value_to_pick = min([i.current for i in factor_list]) |
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[i.pop(value_to_pick) for i in factor_list] |
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print(value_to_pick) |
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62
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63
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def compare_tuples(a, b): |
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return (a[0] - b[0]) * log(2) + (a[1] - b[1]) * log(3) + (a[2] - b[2]) * log(5) |
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def find_ugly_number5(n: int) -> int: |
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known_ugly_numbers = [] |
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candidates = [(0, 0, 0)] |
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for _ in range(n): |
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next_to_add = candidates[0] |
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del candidates[0] |
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known_ugly_numbers.append(next_to_add) |
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new_candidate2 = (next_to_add[0] + 1, next_to_add[1], next_to_add[2]) |
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new_candidate3 = (next_to_add[0], next_to_add[1] + 1, next_to_add[2]) |
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new_candidate5 = (next_to_add[0], next_to_add[1], next_to_add[2] + 1) |
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for i in [new_candidate2, new_candidate3, new_candidate5]: |
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if i not in candidates and i not in known_ugly_numbers: |
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candidates.append(i) |
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80
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candidates = sorted(candidates, key=cmp_to_key(compare_tuples)) |
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81
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return 2 ** known_ugly_numbers[-1][0] * 3 ** known_ugly_numbers[-1][1] * 5 ** known_ugly_numbers[-1][2] |
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82
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83
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84
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def ugly_number(n: int) -> int: |
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return find_ugly_number5(n) |
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86
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87
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88
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if __name__ == "__main__": |
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print("Example:") |
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print(ugly_number(4)) |
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92
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# These "asserts" are used for self-checking and not for an auto-testing |
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assert ugly_number(4) == 4 |
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assert ugly_number(6) == 6 |
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95
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assert ugly_number(11) == 15 |
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96
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print("Ugly Numbers coding complete? Click 'Check' to earn cool rewards!") |
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KenMercusLai /
checkio
