結果
| 問題 | No.2004 Incremental Coins |
| ユーザー |
 vwxyz
|
| 提出日時 | 2023-05-23 18:37:47 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 1,278 ms / 2,000 ms |
| コード長 | 10,084 bytes |
| コンパイル時間 | 464 ms |
| コンパイル使用メモリ | 81,876 KB |
| 実行使用メモリ | 365,176 KB |
| 最終ジャッジ日時 | 2023-11-05 22:40:32 |
| 合計ジャッジ時間 | 21,342 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge13 |
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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 | 44 ms
57,796 KB |
| testcase_01 | AC | 44 ms
57,796 KB |
| testcase_02 | AC | 44 ms
57,796 KB |
| testcase_03 | AC | 46 ms
57,796 KB |
| testcase_04 | AC | 61 ms
70,608 KB |
| testcase_05 | AC | 51 ms
59,848 KB |
| testcase_06 | AC | 135 ms
79,692 KB |
| testcase_07 | AC | 126 ms
78,764 KB |
| testcase_08 | AC | 921 ms
271,044 KB |
| testcase_09 | AC | 1,278 ms
277,412 KB |
| testcase_10 | AC | 668 ms
272,652 KB |
| testcase_11 | AC | 838 ms
281,824 KB |
| testcase_12 | AC | 1,062 ms
283,468 KB |
| testcase_13 | AC | 1,142 ms
365,176 KB |
| testcase_14 | AC | 1,251 ms
313,572 KB |
| testcase_15 | AC | 772 ms
283,568 KB |
| testcase_16 | AC | 953 ms
284,076 KB |
| testcase_17 | AC | 813 ms
282,856 KB |
| testcase_18 | AC | 1,033 ms
281,100 KB |
| testcase_19 | AC | 1,226 ms
285,508 KB |
| testcase_20 | AC | 1,178 ms
283,560 KB |
| testcase_21 | AC | 1,142 ms
286,296 KB |
ソースコード
import sys
readline=sys.stdin.readline
from collections import deque
mod = 998244353
imag = 911660635
iimag = 86583718
rate2 = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899)
irate2 = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960,
354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235)
rate3 = (372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099,
183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204)
irate3 = (509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500,
771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681)
def butterfly(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 % mod
a[i + offset] = (l + r) % mod
a[i + offset + p] = (l - r) % mod
if s + 1 != 1 << len_:
rot *= rate2[(~s & -~s).bit_length() - 1]
rot %= mod
len_ += 1
else:
p = 1 << (h - len_ - 2)
rot = 1
for s in range(1 << len_):
rot2 = rot * rot % mod
rot3 = rot2 * rot % mod
offset = s << (h - len_)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p] * rot
a2 = a[i + offset + p * 2] * rot2
a3 = a[i + offset + p * 3] * rot3
a1na3imag = (a1 - a3) % mod * imag
a[i + offset] = (a0 + a2 + a1 + a3) % mod
a[i + offset + p] = (a0 + a2 - a1 - a3) % mod
a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % mod
a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % mod
if s + 1 != 1 << len_:
rot *= rate3[(~s & -~s).bit_length() - 1]
rot %= mod
len_ += 2
def butterfly_inv(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) % mod
a[i + offset + p] = (l - r) * irot % mod
if s + 1 != (1 << (len_ - 1)):
irot *= irate2[(~s & -~s).bit_length() - 1]
irot %= mod
len_ -= 1
else:
p = 1 << (h - len_)
irot = 1
for s in range(1 << (len_ - 2)):
irot2 = irot * irot % mod
irot3 = irot2 * irot % mod
offset = s << (h - len_ + 2)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p]
a2 = a[i + offset + p * 2]
a3 = a[i + offset + p * 3]
a2na3iimag = (a2 - a3) * iimag % mod
a[i + offset] = (a0 + a1 + a2 + a3) % mod
a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % mod
a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % mod
a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % mod
if s + 1 != (1 << (len_ - 2)):
irot *= irate3[(~s & -~s).bit_length() - 1]
irot %= mod
len_ -= 2
def convolution_naive(a, b):
n = len(a)
m = len(b)
ans = [0] * (n + m - 1)
if n < m:
for j in range(m):
for i in range(n):
ans[i + j] = (ans[i + j] + a[i] * b[j]) % mod
else:
for i in range(n):
for j in range(m):
ans[i + j] = (ans[i + j] + a[i] * b[j]) % mod
return ans
def convolution_ntt(a, b):
a = a.copy()
b = b.copy()
n = len(a)
m = len(b)
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
butterfly(a)
b += [0] * (z - m)
butterfly(b)
for i in range(z):
a[i] = a[i] * b[i] % mod
butterfly_inv(a)
a = a[:n + m - 1]
iz = pow(z, mod - 2, mod)
for i in range(n + m - 1):
a[i] = a[i] * iz % mod
return a
def convolution_square(a):
a = a.copy()
n = len(a)
z = 1 << (2 * n - 2).bit_length()
a += [0] * (z - n)
butterfly(a)
for i in range(z):
a[i] = a[i] * a[i] % mod
butterfly_inv(a)
a = a[:2 * n - 1]
iz = pow(z, mod - 2, mod)
for i in range(2 * n - 1):
a[i] = a[i] * iz % mod
return a
def convolution(a, b):
"""It calculates (+, x) convolution in mod 998244353.
Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1],
it calculates the array c of length n + m - 1, defined by
> c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353.
It returns an empty list if at least one of a and b are empty.
Complexity
----------
> O(n log n), where n = len(a) + len(b).
"""
n = len(a)
m = len(b)
if n == 0 or m == 0:
return []
if min(n, m) <= 60:
return convolution_naive(a, b)
if a is b:
return convolution_square(a)
return convolution_ntt(a, b)
def Extended_Euclid(n,m):
stack=[]
while m:
stack.append((n,m))
n,m=m,n%m
if n>=0:
x,y=1,0
else:
x,y=-1,0
for i in range(len(stack)-1,-1,-1):
n,m=stack[i]
x,y=y,x-(n//m)*y
return x,y
class MOD:
def __init__(self,p,e=None):
self.p=p
self.e=e
if self.e==None:
self.mod=self.p
else:
self.mod=self.p**self.e
def Pow(self,a,n):
a%=self.mod
if n>=0:
return pow(a,n,self.mod)
else:
#assert math.gcd(a,self.mod)==1
x=Extended_Euclid(a,self.mod)[0]
return pow(x,-n,self.mod)
def Build_Fact(self,N):
assert N>=0
self.factorial=[1]
if self.e==None:
for i in range(1,N+1):
self.factorial.append(self.factorial[-1]*i%self.mod)
else:
self.cnt=[0]*(N+1)
for i in range(1,N+1):
self.cnt[i]=self.cnt[i-1]
ii=i
while ii%self.p==0:
ii//=self.p
self.cnt[i]+=1
self.factorial.append(self.factorial[-1]*ii%self.mod)
self.factorial_inve=[None]*(N+1)
self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1)
for i in range(N-1,-1,-1):
ii=i+1
while ii%self.p==0:
ii//=self.p
self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod
def Build_Inverse(self,N):
self.inverse=[None]*(N+1)
assert self.p>N
self.inverse[1]=1
for n in range(2,N+1):
if n%self.p==0:
continue
a,b=divmod(self.mod,n)
self.inverse[n]=(-a*self.inverse[b])%self.mod
def Inverse(self,n):
return self.inverse[n]
def Fact(self,N):
if N<0:
return 0
retu=self.factorial[N]
if self.e!=None and self.cnt[N]:
retu*=pow(self.p,self.cnt[N],self.mod)%self.mod
retu%=self.mod
return retu
def Fact_Inve(self,N):
if self.e!=None and self.cnt[N]:
return None
return self.factorial_inve[N]
def Comb(self,N,K,divisible_count=False):
if K<0 or K>N:
return 0
retu=self.factorial[N]*self.factorial_inve[K]%self.mod*self.factorial_inve[N-K]%self.mod
if self.e!=None:
cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K]
if divisible_count:
return retu,cnt
else:
retu*=pow(self.p,cnt,self.mod)
retu%=self.mod
return retu
N,K=map(int,readline().split())
A=list(map(int,readline().split()))
P=list(map(int,readline().split()))
child=[[] for x in range(N+1)]
for i in range(1,N+1):
child[P[i-1]].append(i)
dp=[deque([]) for x in range(N+1)]
MD=MOD(mod)
MD.Build_Fact(N+1)
fact=1
poly_K=[]
for i in range(N+1):
poly_K.append(fact*MD.Fact_Inve(i)%mod)
fact*=K-i
fact%=mod
for x in range(N,-1,-1):
if child[x]:
ma=max(len(dp[y]) for y in child[x])
for y in child[x]:
if len(dp[y])==ma:
yy=y
break
dp[x]=dp[yy]
for y in child[x]:
if y==yy:
continue
for i in range(len(dp[y])):
dp[x][i]+=dp[y][i]
dp[x][i]%=mod
dp[x].appendleft(A[x])
ans_lst=[None]*(N+1)
DP=[None]*(N+1)
le=len(dp[0])
DP[0]=deque(convolution(list(dp[0]),list(poly_K[:le][::-1]))[le-1:])
for x in range(N+1):
ans_lst[x]=DP[x].popleft()
for y in child[x]:
if dp[x] is dp[y]:
DP[y]=DP[x]
else:
le=len(dp[y])
DP[y]=deque(convolution(list(dp[y]),list(poly_K[:le][::-1]))[le-1:])
for i in range(le):
DP[x][i]-=DP[y][i]
DP[x][i]%=mod
print(*ans_lst,sep="\n")