結果
| 問題 | No.42 貯金箱の溜息 |
| ユーザー |
 Mao-beta
|
| 提出日時 | 2024-03-01 10:39:29 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 9,103 bytes |
| コンパイル時間 | 279 ms |
| コンパイル使用メモリ | 82,148 KB |
| 実行使用メモリ | 72,976 KB |
| 最終ジャッジ日時 | 2024-09-29 13:10:05 |
| 合計ジャッジ時間 | 1,005 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
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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 | RE | - |
| testcase_01 | RE | - |
| testcase_02 | RE | - |
ソースコード
import sys
import math
import bisect
from heapq import heapify, heappop, heappush
from collections import deque, defaultdict, Counter
from functools import lru_cache
from itertools import accumulate, combinations, permutations, product
sys.setrecursionlimit(1000000)
MOD = 10 ** 9 + 9
MOD99 = 998244353
input = lambda: sys.stdin.readline().strip()
NI = lambda: int(input())
NMI = lambda: map(int, input().split())
NLI = lambda: list(NMI())
SI = lambda: input()
SMI = lambda: input().split()
SLI = lambda: list(SMI())
EI = lambda m: [NLI() for _ in range(m)]
# ACL for python
class FFT():
def primitive_root_constexpr(self, m):
if m == 2: return 1
if m == 167772161: return 3
if m == 469762049: return 3
if m == 754974721: return 11
if m == 998244353: return 3
divs = [0] * 20
divs[0] = 2
cnt = 1
x = (m - 1) // 2
while (x % 2 == 0): x //= 2
i = 3
while (i * i <= x):
if (x % i == 0):
divs[cnt] = i
cnt += 1
while (x % i == 0):
x //= i
i += 2
if x > 1:
divs[cnt] = x
cnt += 1
g = 2
while (1):
ok = True
for i in range(cnt):
if pow(g, (m - 1) // divs[i], m) == 1:
ok = False
break
if ok:
return g
g += 1
def bsf(self, x):
res = 0
while (x % 2 == 0):
res += 1
x //= 2
return res
rank2 = 0
root = []
iroot = []
rate2 = []
irate2 = []
rate3 = []
irate3 = []
def __init__(self, MOD):
self.mod = MOD
self.g = self.primitive_root_constexpr(self.mod)
self.rank2 = self.bsf(self.mod - 1)
self.root = [0 for i in range(self.rank2 + 1)]
self.iroot = [0 for i in range(self.rank2 + 1)]
self.rate2 = [0 for i in range(self.rank2)]
self.irate2 = [0 for i in range(self.rank2)]
self.rate3 = [0 for i in range(self.rank2 - 1)]
self.irate3 = [0 for i in range(self.rank2 - 1)]
self.root[self.rank2] = pow(self.g, (self.mod - 1) >> self.rank2, self.mod)
self.iroot[self.rank2] = pow(self.root[self.rank2], self.mod - 2, self.mod)
for i in range(self.rank2 - 1, -1, -1):
self.root[i] = (self.root[i + 1] ** 2) % self.mod
self.iroot[i] = (self.iroot[i + 1] ** 2) % self.mod
prod = 1;
iprod = 1
for i in range(self.rank2 - 1):
self.rate2[i] = (self.root[i + 2] * prod) % self.mod
self.irate2[i] = (self.iroot[i + 2] * iprod) % self.mod
prod = (prod * self.iroot[i + 2]) % self.mod
iprod = (iprod * self.root[i + 2]) % self.mod
prod = 1;
iprod = 1
for i in range(self.rank2 - 2):
self.rate3[i] = (self.root[i + 3] * prod) % self.mod
self.irate3[i] = (self.iroot[i + 3] * iprod) % self.mod
prod = (prod * self.iroot[i + 3]) % self.mod
iprod = (iprod * self.root[i + 3]) % self.mod
def butterfly(self, a):
n = len(a)
h = (n - 1).bit_length()
LEN = 0
while (LEN < h):
if (h - LEN == 1):
p = 1 << (h - LEN - 1)
rot = 1
for s in range(1 << LEN):
offset = s << (h - LEN)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p] * rot
a[i + offset] = (l + r) % self.mod
a[i + offset + p] = (l - r) % self.mod
rot *= self.rate2[(~s & -~s).bit_length() - 1]
rot %= self.mod
LEN += 1
else:
p = 1 << (h - LEN - 2)
rot = 1
imag = self.root[2]
for s in range(1 << LEN):
rot2 = (rot * rot) % self.mod
rot3 = (rot2 * rot) % self.mod
offset = s << (h - LEN)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p] * rot
a2 = a[i + offset + 2 * p] * rot2
a3 = a[i + offset + 3 * p] * rot3
a1na3imag = (a1 - a3) % self.mod * imag
a[i + offset] = (a0 + a2 + a1 + a3) % self.mod
a[i + offset + p] = (a0 + a2 - a1 - a3) % self.mod
a[i + offset + 2 * p] = (a0 - a2 + a1na3imag) % self.mod
a[i + offset + 3 * p] = (a0 - a2 - a1na3imag) % self.mod
rot *= self.rate3[(~s & -~s).bit_length() - 1]
rot %= self.mod
LEN += 2
def butterfly_inv(self, a):
n = len(a)
h = (n - 1).bit_length()
LEN = h
while (LEN):
if (LEN == 1):
p = 1 << (h - LEN)
irot = 1
for s in range(1 << (LEN - 1)):
offset = s << (h - LEN + 1)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p]
a[i + offset] = (l + r) % self.mod
a[i + offset + p] = (l - r) * irot % self.mod
irot *= self.irate2[(~s & -~s).bit_length() - 1]
irot %= self.mod
LEN -= 1
else:
p = 1 << (h - LEN)
irot = 1
iimag = self.iroot[2]
for s in range(1 << (LEN - 2)):
irot2 = (irot * irot) % self.mod
irot3 = (irot * irot2) % self.mod
offset = s << (h - LEN + 2)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p]
a2 = a[i + offset + 2 * p]
a3 = a[i + offset + 3 * p]
a2na3iimag = (a2 - a3) * iimag % self.mod
a[i + offset] = (a0 + a1 + a2 + a3) % self.mod
a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % self.mod
a[i + offset + 2 * p] = (a0 + a1 - a2 - a3) * irot2 % self.mod
a[i + offset + 3 * p] = (a0 - a1 - a2na3iimag) * irot3 % self.mod
irot *= self.irate3[(~s & -~s).bit_length() - 1]
irot %= self.mod
LEN -= 2
def convolution(self, a, b):
n = len(a);
m = len(b)
if not (a) or not (b):
return []
if min(n, m) <= 40:
res = [0] * (n + m - 1)
for i in range(n):
for j in range(m):
res[i + j] += a[i] * b[j]
res[i + j] %= self.mod
return res
z = 1 << ((n + m - 2).bit_length())
a = a + [0] * (z - n)
b = b + [0] * (z - m)
self.butterfly(a)
self.butterfly(b)
c = [(a[i] * b[i]) % self.mod for i in range(z)]
self.butterfly_inv(c)
iz = pow(z, self.mod - 2, self.mod)
for i in range(n + m - 1):
c[i] = (c[i] * iz) % self.mod
return c[:n + m - 1]
# 要FFT
def mul_fft(f, g, fft):
"""FFT畳み込み"""
# fft = FFT(mod)
res = fft.convolution(f, g)
return res
fft = FFT(MOD)
def bostan_mori_fft(P: list, Q: list, fft: FFT, n: int):
"""
d+1項間線形漸化式Qをもつ数列の第n項 modをもとめる
A = P / Q
O(M(d)logN) M(d)はd次多項式同士の積の計算量(O(dlogd logN))
d <= 15000くらいは2秒以内で計算できそう
http://q.c.titech.ac.jp/docs/progs/polynomial_division.html
:param P: 母関数の分子を表すd項以下のlist
:param Q: 母関数の分母をあらわすd+1項のlist
(フィボナッチなら An - An-1 - An-2 = 0 なので Q=[1, -1, -1])
:param n: 求めたい第n項(0-index)
:return: A[n]
"""
while n > 0:
Qm = [-q if i % 2 else q for i, q in enumerate(Q)]
V = mul_fft(Q, Qm, fft)
Q = V[::2]
PQm = mul_fft(P, Qm, fft)
if n % 2 == 0:
P = PQm[::2]
n >>= 1
else:
P = PQm[1::2]
n >>= 1
return P[0]
def mul_sparse(f: list, a, b, k, M):
"""(a + b * x^k)倍 x^Mまで"""
res = f.copy()
for i in range(M+1):
res[i] += f[i] * (a-1)
if i+k <= M:
res[i+k] += f[i] * b
res[i] %= MOD
return res
def main():
C = [1, 5, 10, 50, 100, 500]
D = sum(C)
Q = [0] * (D+1)
Q[0] = 1
for c in C:
Q = mul_sparse(Q, 1, -1, c, D)
T = NI()
for _ in range(T):
M = NI()
P = [0] * D
P[0] = 1
X = bostan_mori_fft(P, Q, fft, M)
print(X)
if __name__ == "__main__":
main()