結果
| 問題 | No.2829 GCD Divination |
| ユーザー |
 Navier_Boltzmann
|
| 提出日時 | 2024-08-03 19:08:41 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
MLE
|
| 実行時間 | - |
| コード長 | 13,241 bytes |
| コンパイル時間 | 445 ms |
| コンパイル使用メモリ | 82,008 KB |
| 実行使用メモリ | 569,780 KB |
| 最終ジャッジ日時 | 2024-08-03 19:08:50 |
| 合計ジャッジ時間 | 8,849 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
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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 | 51 ms
65,392 KB |
| testcase_01 | AC | 49 ms
59,016 KB |
| testcase_02 | MLE | - |
| testcase_03 | AC | 50 ms
58,856 KB |
| testcase_04 | TLE | - |
| testcase_05 | TLE | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
ソースコード
# import pypyjit
# pypyjit.set_param('max_unroll_recursion=-1')
from collections import *
from functools import *
from heapq import *
from itertools import *
import sys, math
def cle(a, D):
"""
Counts the number of elements in D that are less than or equal to a.
Parameters:
a (int): The value to compare against.
D (list): A sorted list of integers.
Returns:
int: The count of elements in D that are less than or equal to a.
"""
y = len(D) - 1
x = 0
if D[x] > a:
return 0
if D[y] <= a:
return y + 1
while y - x > 1:
mid = (y + x) // 2
if D[mid] <= a:
x = mid
else:
y = mid
return y
def mergecount(A):
"""
Counts the number of inversions in the array A using merge sort.
Parameters:
A (list): A list of integers.
Returns:
int: The number of inversions in the list.
"""
cnt = 0
n = len(A)
if n > 1:
A1 = A[: n >> 1]
A2 = A[n >> 1 :]
cnt += mergecount(A1)
cnt += mergecount(A2)
i1 = 0
i2 = 0
for i in range(n):
if i2 == len(A2):
A[i] = A1[i1]
i1 += 1
elif i1 == len(A1):
A[i] = A2[i2]
i2 += 1
elif A1[i1] <= A2[i2]:
A[i] = A1[i1]
i1 += 1
else:
A[i] = A2[i2]
i2 += 1
cnt += n // 2 - i1
return cnt
class cs_2d:
"""
2D cumulative sum class.
"""
def __init__(self, x):
"""
Initializes the 2D cumulative sum array.
Parameters:
x (list of list of int): A 2D list of integers.
"""
n = len(x)
m = len(x[0])
self.n = n
self.m = m
tmp = [0] * ((n + 1) * (m + 1))
for i in range(n):
for j in range(m):
tmp[m * (i + 1) + j + 1] = (
tmp[m * (i + 1) + j] + tmp[m * i + j + 1] - tmp[m * i + j] + x[i][j]
)
self.S = tmp
def query(self, ix, jx, iy, jy):
"""
Queries the sum of the submatrix from (ix, iy) to (jx, jy).
Parameters:
ix (int): Starting row index.
jx (int): Ending row index.
iy (int): Starting column index.
jy (int): Ending column index.
Returns:
int: The sum of the submatrix.
"""
return (
self.S[self.m * jx + jy]
- self.S[self.m * jx + iy]
- self.S[self.m * ix + jy]
+ self.S[self.m * ix + iy]
)
class prime_factorize:
"""
Class for prime factorization and related operations.
"""
def __init__(self, M=10**6):
"""
Initializes the sieve for prime factorization.
Parameters:
M (int): The maximum number to factorize.
"""
self.sieve = [-1] * (M + 1)
self.sieve[1] = 1
self.p = [False] * (M + 1)
self.mu = [1] * (M + 1)
for i in range(2, M + 1):
if self.sieve[i] == -1:
self.p[i] = True
i2 = i**2
for j in range(i2, M + 1, i2):
self.mu[j] = 0
for j in range(i, M + 1, i):
self.sieve[j] = i
self.mu[j] *= -1
def factors(self, x):
"""
Returns the prime factors of x.
Parameters:
x (int): The number to factorize.
Returns:
list: A list of prime factors of x.
"""
tmp = []
while self.sieve[x] != x:
tmp.append(self.sieve[x])
x //= self.sieve[x]
tmp.append(self.sieve[x])
return tmp
def divisors(self, x):
"""
Returns all divisors of x.
Parameters:
x (int): The number to find divisors for.
Returns:
list: A sorted list of all divisors of x.
"""
C = Counter(self.factors(x))
tmp = []
for p in product(*[[pow(k, i) for i in range(v + 1)] for k, v in C.items()]):
res = 1
for pp in p:
res *= pp
tmp.append(res)
tmp.sort()
return tmp
def is_prime(self, x):
"""
Checks if x is a prime number.
Parameters:
x (int): The number to check.
Returns:
bool: True if x is prime, False otherwise.
"""
return self.p[x]
def mobius(self, x):
"""
Returns the Möbius function value of x.
Parameters:
x (int): The number to find the Möbius function value for.
Returns:
int: The Möbius function value of x.
"""
return self.mu[x]
class combination:
"""
Class for computing combinations (nCr) modulo p.
"""
def __init__(self, N, p):
"""
Initializes the combination class.
Parameters:
N (int): The maximum value of n.
p (int): The modulus.
"""
self.fact = [1, 1] # fact[n] = (n! mod p)
self.factinv = [1, 1] # factinv[n] = ((n!)^(-1) mod p)
self.inv = [0, 1] # factinv calculation
self.p = p
for i in range(2, N + 1):
self.fact.append((self.fact[-1] * i) % p)
self.inv.append((-self.inv[p % i] * (p // i)) % p)
self.factinv.append((self.factinv[-1] * self.inv[-1]) % p)
def cmb(self, n, r):
"""
Computes the combination (nCr) modulo p.
Parameters:
n (int): The total number of items.
r (int): The number of items to choose.
Returns:
int: The value of nCr modulo p.
"""
if (r < 0) or (n < r):
return 0
r = min(r, n - r)
return self.fact[n] * self.factinv[r] * self.factinv[n - r] % self.p
def md(n):
"""
Returns all divisors of n.
Parameters:
n (int): The number to find divisors for.
Returns:
list: A sorted list of all divisors of 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]
class DSU:
"""
Disjoint Set Union (Union-Find) class.
"""
def __init__(self, n):
"""
Initializes the DSU.
Parameters:
n (int): The number of elements.
"""
self._n = n
self.parent_or_size = [-1] * n
self.member = [[i] for i in range(n)]
def merge(self, a, b):
"""
Merges the sets containing a and b.
Parameters:
a (int): An element in the first set.
b (int): An element in the second set.
Returns:
int: The leader of the merged set.
"""
assert 0 <= a < self._n
assert 0 <= b < self._n
x, y = self.leader(a), self.leader(b)
if x == y:
return x
if -self.parent_or_size[x] < -self.parent_or_size[y]:
x, y = y, x
self.parent_or_size[x] += self.parent_or_size[y]
for tmp in self.member[y]:
self.member[x].append(tmp)
self.parent_or_size[y] = x
return x
def members(self, a):
"""
Returns the members of the set containing a.
Parameters:
a (int): An element in the set.
Returns:
list: A list of members in the set containing a.
"""
return self.member[self.leader(a)]
def same(self, a, b):
"""
Checks if a and b are in the same set.
Parameters:
a (int): An element in the first set.
b (int): An element in the second set.
Returns:
bool: True if a and b are in the same set, False otherwise.
"""
assert 0 <= a < self._n
assert 0 <= b < self._n
return self.leader(a) == self.leader(b)
def leader(self, a):
"""
Finds the leader of the set containing a.
Parameters:
a (int): An element in the set.
Returns:
int: The leader of the set containing a.
"""
assert 0 <= a < self._n
if self.parent_or_size[a] < 0:
return a
self.parent_or_size[a] = self.leader(self.parent_or_size[a])
return self.parent_or_size[a]
def size(self, a):
"""
Returns the size of the set containing a.
Parameters:
a (int): An element in the set.
Returns:
int: The size of the set containing a.
"""
assert 0 <= a < self._n
return -self.parent_or_size[self.leader(a)]
def groups(self):
"""
Returns all sets as a list of lists.
Returns:
list: A list of lists, where each list contains the members of a set.
"""
leader_buf = [self.leader(i) for i in range(self._n)]
result = [[] for _ in range(self._n)]
for i in range(self._n):
result[leader_buf[i]].append(i)
return [r for r in result if r != []]
class SegTree:
"""
Segment Tree class.
"""
def __init__(self, init_val, segfunc, ide_ele):
"""
Initializes the Segment Tree.
Parameters:
init_val (list): The initial values for the leaves of the tree.
segfunc (function): The function to use for segment operations.
ide_ele (any): The identity element for the segment function.
"""
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
# Set the initial values to the leaves
for i in range(n):
self.tree[self.num + i] = init_val[i]
# Build the tree
for i in range(self.num - 1, 0, -1):
self.tree[i] = segfunc(self.tree[2 * i], self.tree[2 * i + 1])
def update(self, k, x):
"""
Updates the k-th value to x.
Parameters:
k (int): The index to update (0-indexed).
x (any): The new value.
"""
k += self.num
self.tree[k] = x
while k > 1:
tk = k >> 1
self.tree[tk] = self.segfunc(self.tree[tk << 1], self.tree[(tk << 1) + 1])
k >>= 1
def get(self, x):
return self.tree[x + self.num]
def query(self, l, r):
"""
Queries the segment function result for the range [l, r).
Parameters:
l (int): The start index (0-indexed).
r (int): The end index (0-indexed).
Returns:
any: The result of the segment function for the range [l, r).
"""
res_l = self.ide_ele
res_r = self.ide_ele
l += self.num
r += self.num
while l < r:
if l & 1:
res_l = self.segfunc(res_l, self.tree[l])
l += 1
if r & 1:
res_r = self.segfunc(self.tree[r - 1], res_r)
l >>= 1
r >>= 1
res = self.segfunc(res_l, res_r)
return res
def dijkstra(s, e):
INF = 1 << 60
N = len(e)
dist = [INF] * N
dist[s] = 0
h = []
heappush(h, s)
while h:
nw, v = divmod(heappop(h), N)
if dist[v] != nw:
continue
for iv, ic in e[v]:
nc = ic + nw
if nc < dist[iv]:
dist[iv] = nc
heappush(h, nc * N + iv)
return dist
class RSQandRAQ():
"""区間加算、区間取得クエリをそれぞれO(logN)で答える
add: 区間[l, r)にvalを加える
query: 区間[l, r)の和を求める
l, rは0-indexed
"""
def __init__(self, n):
self.n = n
self.bit0 = [0] * (n + 1)
self.bit1 = [0] * (n + 1)
def _add(self, bit, i, val):
i = i + 1
while i <= self.n:
bit[i] += val
i += i & -i
def _get(self, bit, i):
s = 0
while i > 0:
s += bit[i]
i -= i & -i
return s
def add(self, l, r, val):
"""区間[l, r)にvalを加える"""
self._add(self.bit0, l, -val * l)
self._add(self.bit0, r, val * r)
self._add(self.bit1, l, val)
self._add(self.bit1, r, -val)
def query(self, l, r):
"""区間[l, r)の和を求める"""
return self._get(self.bit0, r) + r * self._get(self.bit1, r) \
- self._get(self.bit0, l) - l * self._get(self.bit1, l)
input = sys.stdin.readline
# pf = prime_factorize(10**7)
N = int(input())
mem = defaultdict(lambda:-1)
mem[1] = 0
P = defaultdict(list)
P[N] = md(N)
P[N].sort(reverse=True)
for p in P:
if p==N:
continue
P[p] = md(p)
P[p].sort(reverse=True)
def f(n):
if mem[n]!=-1:
return mem[n]
cnt = defaultdict(int)
for p in P[n]:
s = (n//p)
for j in range(2*p,N+1,p):
s = (s - cnt[j])
cnt[p] = s
mem[n] = (sum(f(p)*cnt[p] for p in P[n][1:]) + n)/(n-1)
return mem[n]
print(f(N))