結果

問題 No.888 約数の総和
ユーザー McGregorshMcGregorsh
提出日時 2023-04-13 22:33:30
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 174 ms / 2,000 ms
コード長 12,138 bytes
コンパイル時間 166 ms
コンパイル使用メモリ 82,304 KB
実行使用メモリ 91,636 KB
最終ジャッジ日時 2024-10-09 18:32:47
合計ジャッジ時間 7,284 ms
ジャッジサーバーID
(参考情報)
judge2 / judge1
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

######
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
######
#####segfunc#####
def segfunc(x, y):
return x + y
#     min(x, y) 
#     max(x, y)
#     x + y
#     x * y
#   math.gcd(x, y)
#     x ^ y
#################
#####ide_ele#####
ide_ele = 0
# float('inf')
#   -float('inf')
#     0
#     1
#   0
#  0
#################
class SegTree:
"""
init(init_val, ide_ele): init_val O(N)
update(k, x): kx O(logN)
query(l, r): [l, r)segfunc O(logN)
"""
def __init__(self, init_val, segfunc, ide_ele):
"""
init_val:
segfunc:
ide_ele:
n:
num: n2
tree: (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
#
for i in range(n):
self.tree[self.num + i] = init_val[i]
#
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):
"""
kx
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)segfunc
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 # n
def unite(self, x, y):
"""xy"""
x = self.root(x)
y = self.root(y)
if x == y:
return 0
self.__group_count -= 1 # 1
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):
"""xy"""
return self.root(x) == self.root(y)
def root(self, x):
"""x"""
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"""
return -self.parent[self.root(x)]
def all_sizes(self) -> List[int]:
""" 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]]:
""" O(Nα(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:
""" O(1)"""
return self.__group_count # O(1)
######
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
###n10###
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
###10n###
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 str_n[::-1]
######
from functools import reduce
#
def gcd_list(num_list: list) -> int:
return reduce(gcd, num_list)
#
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)
######
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]
######
def nPr(n, r):
npr = 1
for i in range(n, n-r, -1):
npr *= i
return npr
######
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
###MOD###
def comb(n,k):
nCk = 1
MOD = 10**9+7
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
######
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
######
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, re
from fractions import Fraction
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
from decimal import Decimal, getcontext, ROUND_HALF_UP
def i_input(): return int(input())
def i_map(): return map(int, input().split())
def i_list(): return list(i_map())
def i_row(N): return [i_input() for _ in range(N)]
def i_row_list(N): return [i_list() for _ in range(N)]
def s_input(): return input()
def s_map(): return input().split()
def s_list(): return list(s_map())
def s_row(N): return [s_input for _ in range(N)]
def s_row_str(N): return [s_list() for _ in range(N)]
def s_row_list(N): return [list(s_input()) for _ in range(N)]
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
def main():
N = int(input())
nums = make_divisors(N)
print(sum(nums))
if __name__ == '__main__':
main()
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