#903628 (PyPy3) No.2379 Burnside's Theorem

提出ソース

結果

問題	No.2379 Burnside's Theorem
ユーザー	McGregorsh
提出日時	2023-08-13 12:18:12
言語	PyPy3 (7.3.15)
結果	WA
実行時間	-
コード長	12,096 bytes
コンパイル時間	159 ms
コンパイル使用メモリ	82,508 KB
実行使用メモリ	91,872 KB
最終ジャッジ日時	2024-11-21 07:00:12
合計ジャッジ時間	4,966 ms
ジャッジサーバーID （参考情報）	judge4 / judge2

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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	159 ms 91,064 KB
testcase_01	AC	159 ms 91,256 KB
testcase_02	AC	163 ms 91,264 KB
testcase_03	AC	157 ms 91,392 KB
testcase_04	AC	158 ms 91,136 KB
testcase_05	AC	158 ms 91,136 KB
testcase_06	AC	157 ms 91,136 KB
testcase_07	AC	159 ms 91,008 KB
testcase_08	AC	158 ms 91,648 KB
testcase_09	AC	160 ms 91,484 KB
testcase_10	AC	159 ms 91,392 KB
testcase_11	AC	160 ms 91,076 KB
testcase_12	AC	157 ms 91,136 KB
testcase_13	AC	168 ms 91,472 KB
testcase_14	AC	165 ms 91,392 KB
testcase_15	AC	167 ms 91,872 KB
testcase_16	AC	161 ms 91,264 KB
testcase_17	AC	161 ms 91,264 KB
testcase_18	AC	158 ms 91,264 KB
testcase_19	AC	158 ms 91,136 KB
testcase_20	AC	159 ms 91,364 KB
testcase_21	AC	159 ms 91,068 KB
testcase_22	WA	-
testcase_23	AC	155 ms 91,168 KB

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ソースコード

raw source code

import math
from bisect import bisect_left, bisect_right, insort
from typing import Generic, Iterable, Iterator, TypeVar, Union, List
T = TypeVar('T')

class SortedMultiset(Generic[T]):
    BUCKET_RATIO = 50
    REBUILD_RATIO = 170

    def _build(self, a=None) -> None:
        "Evenly divide `a` into buckets."
        if a is None: a = list(self)
        size = self.size = len(a)
        bucket_size = int(math.ceil(math.sqrt(size / self.BUCKET_RATIO)))
        self.a = [a[size * i // bucket_size : size * (i + 1) // bucket_size] for i in range(bucket_size)]
    
    def __init__(self, a: Iterable[T] = []) -> None:
        "Make a new SortedMultiset from iterable. / O(N) if sorted / O(N log N)"
        a = list(a)
        if not all(a[i] <= a[i + 1] for i in range(len(a) - 1)):
            a = sorted(a)
        self._build(a)

    def __iter__(self) -> Iterator[T]:
        for i in self.a:
            for j in i: yield j

    def __reversed__(self) -> Iterator[T]:
        for i in reversed(self.a):
            for j in reversed(i): yield j
    
    def __len__(self) -> int:
        return self.size
    
    def __repr__(self) -> str:
        return "SortedMultiset" + str(self.a)
    
    def __str__(self) -> str:
        s = str(list(self))
        return "{" + s[1 : len(s) - 1] + "}"

    def _find_bucket(self, x: T) -> List[T]:
        "Find the bucket which should contain x. self must not be empty."
        for a in self.a:
            if x <= a[-1]: return a
        return a

    def __contains__(self, x: T) -> bool:
        if self.size == 0: return False
        a = self._find_bucket(x)
        i = bisect_left(a, x)
        return i != len(a) and a[i] == x

    def count(self, x: T) -> int:
        "Count the number of x."
        return self.index_right(x) - self.index(x)

    def add(self, x: T) -> None:
        "Add an element. / O(√N)"
        if self.size == 0:
            self.a = [[x]]
            self.size = 1
            return
        a = self._find_bucket(x)
        insort(a, x)
        self.size += 1
        if len(a) > len(self.a) * self.REBUILD_RATIO:
            self._build()

    def discard(self, x: T) -> bool:
        "Remove an element and return True if removed. / O(√N)"
        if self.size == 0: return False
        a = self._find_bucket(x)
        i = bisect_left(a, x)
        if i == len(a) or a[i] != x: return False
        a.pop(i)
        self.size -= 1
        if len(a) == 0: self._build()
        return True

    def lt(self, x: T) -> Union[T, None]:
        "Find the largest element < x, or None if it doesn't exist."
        for a in reversed(self.a):
            if a[0] < x:
                return a[bisect_left(a, x) - 1]

    def le(self, x: T) -> Union[T, None]:
        "Find the largest element <= x, or None if it doesn't exist."
        for a in reversed(self.a):
            if a[0] <= x:
                return a[bisect_right(a, x) - 1]

    def gt(self, x: T) -> Union[T, None]:
        "Find the smallest element > x, or None if it doesn't exist."
        for a in self.a:
            if a[-1] > x:
                return a[bisect_right(a, x)]

    def ge(self, x: T) -> Union[T, None]:
        "Find the smallest element >= x, or None if it doesn't exist."
        for a in self.a:
            if a[-1] >= x:
                return a[bisect_left(a, x)]
    
    def __getitem__(self, x: int) -> T:
        "Return the x-th element, or IndexError if it doesn't exist."
        if x < 0: x += self.size
        if x < 0: raise IndexError
        for a in self.a:
            if x < len(a): return a[x]
            x -= len(a)
        raise IndexError

    def index(self, x: T) -> int:
        "Count the number of elements < x."
        ans = 0
        for a in self.a:
            if a[-1] >= x:
                return ans + bisect_left(a, x)
            ans += len(a)
        return ans

    def index_right(self, x: T) -> int:
        "Count the number of elements <= x."
        ans = 0
        for a in self.a:
            if a[-1] > x:
                return ans + bisect_right(a, x)
            ans += len(a)
        return ans


###セグメントツリー###

#####segfunc#####
def segfunc(x, y):
    return x + y
    # 最小値    min(x, y) 
    # 最大値    max(x, y)
    # 区間和    x + y
    # 区間積    x * y
    # 最大公約数  math.gcd(x, y)
    # 排他的論理和    x ^ y
#################

#####ide_ele#####
ide_ele = 0
    # 最小値    float('inf')
    # 最大値  -float('inf')
    # 区間和    0
    # 区間積    1
    # 最大公約数  0
    # 排他的論理和 0
#################

class SegTree:
    """
    init(init_val, ide_ele): 配列init_valで初期化 O(N)
    update(k, x): k番目の値をxに更新 O(logN)
    query(l, r): 区間[l, r)をsegfuncしたものを返す O(logN)
    """
    def __init__(self, init_val, segfunc, ide_ele):
        """
        init_val: 配列の初期値
        segfunc: 区間にしたい操作
        ide_ele: 単位元
        n: 要素数
        num: n以上の最小の2のべき乗
        tree: セグメント木(1-index)
        """
        n = len(init_val)
        self.segfunc = segfunc
        self.ide_ele = ide_ele
        self.num = 1 << (n - 1).bit_length()
        self.tree = [ide_ele] * 2 * self.num
        # 配列の値を葉にセット
        for i in range(n):
            self.tree[self.num + i] = init_val[i]
        # 構築していく
        for i in range(self.num - 1, 0, -1):
            self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])

    def update(self, k, x):
        """
        k番目の値をxに更新
        k: index(0-index)
        x: update value
        """
        k += self.num
        self.tree[k] = x
        while k > 1:
            self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
            k >>= 1

    def query(self, l, r):
        """
        [l, r)のsegfuncしたものを得る
        l: index(0-index)
        r: index(0-index)
        """
        res = self.ide_ele

        l += self.num
        r += self.num
        while l < r:
            if l & 1:
                res = self.segfunc(res, self.tree[l])
                l += 1
            if r & 1:
                res = self.segfunc(res, self.tree[r - 1])
            l >>= 1
            r >>= 1
        return res


###UnionFind###

class UnionFind:
    """0-indexed"""

    def __init__(self, n):
        self.n = n
        self.parent = [-1] * n
        self.__group_count = n  # 辺がないとき、連結成分はn個あります

    def unite(self, x, y):
        """xとyをマージ"""
        x = self.root(x)
        y = self.root(y)

        if x == y:
            return 0

        self.__group_count -= 1  # 木と木が合体するので、連結成分数が1減ります

        if self.parent[x] > self.parent[y]:
            x, y = y, x

        self.parent[x] += self.parent[y]
        self.parent[y] = x

        return self.parent[x]

    def is_same(self, x, y):
        """xとyが同じ連結成分か判定"""
        return self.root(x) == self.root(y)

    def root(self, x):
        """xの根を取得"""
        if self.parent[x] < 0:
            return x
        else:
            self.parent[x] = self.root(self.parent[x])
            return self.parent[x]

    def size(self, x):
        """xが属する連結成分のサイズを取得"""
        return -self.parent[self.root(x)]

    def all_sizes(self) -> List[int]:
        """全連結成分のサイズのリストを取得 O(N)
        """
        sizes = []
        for i in range(self.n):
            size = self.parent[i]
            if size < 0:
                sizes.append(-size)
        return sizes

    def groups(self) -> List[List[int]]:
        """全連結成分の内容のリストを取得 O(N・α(N))"""
        groups = dict()
        for i in range(self.n):
            p = self.root(i)
            if not groups.get(p):
                groups[p] = []
            groups[p].append(i)
        return list(groups.values())

    def group_count(self) -> int:
        """連結成分の数を取得 O(1)"""
        return self.__group_count  # 変数を返すだけなので、O(1)です


###素因数分解###

def prime_factorize(n: int) -> list:
   return_list = []
   while n % 2 == 0:
   	  return_list.append(2)
   	  n //= 2
   f = 3
   while f * f <= n:
   	  if n % f == 0:
   	  	  return_list.append(f)
   	  	  n //= f
   	  else:
   	  	  f += 2
   if n != 1:
   	  return_list.append(n)
   return return_list


###n進数から10進数変換###

def base_10(num_n,n):
	  num_10 = 0
	  for s in str(num_n):
	  	  num_10 *= n
	  	  num_10 += int(s)
	  return num_10


###10進数からn進数変換###

def base_n(num_10,n):
	  str_n = ''
	  while num_10:
	  	  if num_10%n>=10:
	  	  	  return -1
	  	  str_n += str(num_10%n)
	  	  num_10 //= n
	  return int(str_n[::-1])


###複数の数の最大公約数、最小公倍数###

from functools import reduce

# 最大公約数
def gcd_list(num_list: list) -> int:
	  return reduce(gcd, num_list)

# 最小公倍数
def lcm_base(x: int, y: int) -> int:
	  return (x * y) // gcd(x, y)
def lcm_list(num_list: list):
	  return reduce(lcm_base, num_list, 1)


###約数列挙###

def make_divisors(n):
	  lower_divisors, upper_divisors = [], []
	  i = 1
	  while i * i <= n:
	  	  if n % i == 0:
	  	  	  lower_divisors.append(i)
	  	  	  if i != n // i:
	  	  	  	  upper_divisors.append(n//i)
	  	  i += 1
	  return lower_divisors + upper_divisors[::-1]


###順列###

def nPr(n, r):
	  npr = 1
	  for i in range(n, n-r, -1):
	  	  npr *= i
	  return npr


###組合せ###

def nCr(n, r):
	  factr = 1
	  r = min(r, n - r)
	  for i in range(r, 1, -1):
	  	  factr *= i
	  return nPr(n, r)//factr


###組合せMOD###

def comb(n,k):
    nCk = 1
    MOD = 99824353

    for i in range(n-k+1, n+1):
        nCk *= i
        nCk %= MOD

    for i in range(1,k+1):
        nCk *= pow(i,MOD-2,MOD)
        nCk %= MOD
    return nCk


###回転行列###

def RotationMatrix(before_x, before_y, d):
	  d = math.radians(d)
	  new_x = before_x * math.cos(d) - before_y * math.sin(d)
	  new_y = before_x * math.sin(d) + before_y * math.cos(d)
	  return new_x, new_y


###ダイクストラ###

def daikusutora(N, G, s):
	  dist = [INF] * N
	  que = [(0, s)]
	  dist[s] = 0
	  while que:
	  	  c, v = heappop(que)
	  	  if dist[v] < c:
	  	  	  continue
	  	  for t, cost in G[v]:
	  	  	  if dist[v] + cost < dist[t]:
	  	  	  	  dist[t] = dist[v] + cost
	  	  	  	  heappush(que, (dist[t], t))
	  return dist


import sys
from sys import stdin
from fractions import Fraction
import math
from math import ceil, floor, sqrt, pi, factorial, gcd
from copy import deepcopy
from collections import Counter, deque, defaultdict
from heapq import heapify, heappop, heappush
from itertools import accumulate, product, combinations, combinations_with_replacement, permutations
from bisect import bisect, bisect_left, bisect_right
from functools import reduce, lru_cache
from decimal import Decimal, getcontext, ROUND_HALF_UP
def i_input(): return int(stdin.readline())
def i_map(): return map(int, stdin.readline().split())
def i_list(): return list(i_map())
def s_input(): return stdin.readline()[:-1]
def s_map(): return s_input().split()
def s_list(): return list(s_map())
def lcm(a, b): return a * b // gcd(a, b)
def get_distance(x1, y1, x2, y2):
	  d = sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)
	  return d
def rotate(table):
   	  n_fild = []
   	  for x in zip(*table[::-1]):
   	  	  n_fild.append(x)
   	  return n_fild
sys.setrecursionlimit(10 ** 7)
INF = float('inf')
MOD = 10 ** 9 + 7
MOD2 = 998244353
alpa = 'abcdefghijklmnopqrstuvwxyz'
ALPA = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'


def main():
   
   N = int(input())
   nums = prime_factorize(N)
   if N == 1:
   	  print('No')
   	  exit()
   
   ret = set()
   for i in nums:
   	  ret.add(i)
   
   if len(ret) == 2 or len(ret) == 1:
   	  print('Yes')
   else:
   	  print('No')
   
if __name__ == '__main__':
    main()

yukicoder

結果

テストケース

ソースコード