diff --git a/solutions/0041.PandigitalPrime/euler_41.py b/solutions/0041.PandigitalPrime/euler_41.py new file mode 100644 index 0000000..c009e60 --- /dev/null +++ b/solutions/0041.PandigitalPrime/euler_41.py @@ -0,0 +1,76 @@ +""" +We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. +For example, 2143 is a 4-digit pandigital and is also prime. + +What is the largest n-digit pandigital prime that exists? +""" + +import random +import time +from functools import lru_cache +from itertools import permutations + + +def timer(func): + def wrapper(*args, **kwargs): + start_time = time.perf_counter() + result = func(*args, **kwargs) + end_time = time.perf_counter() + print(f"Execution time: {end_time - start_time} seconds") + return result + + return wrapper + + +def miller_rabin_test(n: int, k: int = 10) -> bool: + if n < 2: + return False + if n == 2 or n == 3: + return True + if n % 2 == 0 or n % 3 == 0: + return False + r, s = 0, n - 1 + while s % 2 == 0: + r += 1 + s //= 2 + for _ in range(k): + a = random.randrange(2, n - 1) + x = pow(a, s, n) + if x == 1 or x == n - 1: + continue + for _ in range(r - 1): + x = pow(x, 2, n) + if x == n - 1: + break + else: + return False + return True + + +@lru_cache(maxsize=128) +def is_even_or_five_ending(num: int) -> bool: + """快速检查是否为偶数或以5结尾""" + return num % 2 == 0 or num % 5 == 0 + + +@timer +def main() -> None: + str_nums = "987654321" + stop = False + for i in range(9, 0, -1): + if sum(int(digit) for digit in str_nums[-i:]) % 3 == 0: + continue + for perm in permutations(str_nums[-i:], i): + num = int("".join(perm)) + if is_even_or_five_ending(num): + continue + if miller_rabin_test(num): + print(num) + stop = True + break + if stop: + break + + +if __name__ == "__main__": + main() diff --git a/solutions/0042.CodedTriangleNum/0042_words.txt b/solutions/0042.CodedTriangleNum/0042_words.txt new file mode 100644 index 0000000..7177624 --- /dev/null +++ b/solutions/0042.CodedTriangleNum/0042_words.txt @@ -0,0 +1 @@ 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\ No newline at end of file diff --git a/solutions/0042.CodedTriangleNum/euler_42.py b/solutions/0042.CodedTriangleNum/euler_42.py new file mode 100644 index 0000000..e9dbc37 --- /dev/null +++ b/solutions/0042.CodedTriangleNum/euler_42.py @@ -0,0 +1,78 @@ +""" +The nth term of the sequence of triangle numbers is given by, $t_n = \frac{n(n+1)}{2}$ ; +so the first ten triangle numbers are: + 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... +By converting each letter in a word to a number corresponding to its alphabetical position +and adding these values we form a word value. For example, the word value for SKY is 19+11+25 = 55 = t_10 . +If the word value is a triangle number then we shall call the word a triangle word. + +Using words.txt (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand +common English words, how many are triangle words? +""" + +import time +from pathlib import Path + + +def timer(func): + def wrapper(*args, **kwargs): + start_time = time.perf_counter() + result = func(*args, **kwargs) + end_time = time.perf_counter() + print(f"Time taken by {func.__name__}: {end_time - start_time:.8f} seconds") + return result + + return wrapper + + +def word_to_num(txt: str) -> int: + """ + 将单词转换为数字，每个字母对应其在字母表中的位置（A=1, B=2, ..., Z=26） + + 参数: + txt: 要转换的单词 + + 返回: + 单词的数字表示 + + 示例: + >>> word_to_num("SKY") + 55 + """ + return sum(ord(c) - ord("A") + 1 for c in txt) + + +def is_triangle_number(n: int) -> bool: + """ + 判断一个数是否为三角形数 + + 参数: + n: 要判断的数 + + 返回: + True 如果 n 是三角形数，否则 False + + 示例: + >>> is_triangle_number(10) + True + >>> is_triangle_number(11) + False + """ + # 使用二次方程求解，如果结果是整数则为三角形数 + # 三角形数公式：n = k(k+1)/2 + # 解得 k = (-1 + sqrt(1 + 8n)) / 2 + k = (-1 + (1 + 8 * n) ** 0.5) / 2 + return k.is_integer() + + +@timer +def main() -> None: + with open(Path(__file__).parent / "0042_words.txt", "r") as file: + words = file.read().replace('"', "").split(",") + + triangle_words = [word for word in words if is_triangle_number(word_to_num(word))] + print(f"Number of triangle words: {len(triangle_words)}") + + +if __name__ == "__main__": + main()