結果

問題 No.2303 Frog on Grid
ユーザー kys
提出日時 2023-05-13 18:16:41
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 980 ms / 2,000 ms
コード長 6,782 bytes
コンパイル時間 351 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 159,964 KB
最終ジャッジ日時 2024-11-29 09:52:09
合計ジャッジ時間 12,794 ms
ジャッジサーバーID
(参考情報)
judge4 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 20
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

def main():
from sys import stdin, setrecursionlimit
# setrecursionlimit(1000000)
input = stdin.readline
def iinput(): return int(input())
def sinput(): return input().rstrip()
def i0input(): return int(input()) - 1
def linput(): return list(input().split())
def liinput(): return list(map(int, input().split()))
def miinput(): return map(int, input().split())
def li0input(): return list(map(lambda x: int(x) - 1, input().split()))
def mi0input(): return map(lambda x: int(x) - 1, input().split())
INF = 1000000000000000000
MOD = 998244353
def modinv(a):
b = MOD
u, v = 1, 0
while b > 0:
t = a // b
a -= t * b
a, b = b, a
u -= t * v
u, v = v, u
return u % MOD
class Combination:
def __init__(self, N, MOD):
self.factorial = [1]
self.inv_factorial = [1]
self.mod = MOD
for i in range(1, N+1):
self.factorial.append(self.factorial[-1] * i % MOD)
self.inv_factorial.append(self.inv_factorial[-1] * modinv(i) % MOD)
def combi(self, n, k):
return self.factorial[n] * self.inv_factorial[k] % self.mod * self.inv_factorial[n-k] % self.mod
cmb = Combination(404040, MOD)
def counter(N):
ans = dict()
for k in range((N+1)//2, N+1):
ans[k] = cmb.combi(k, N-k)
return ans
H, W = miinput()
def solve_naive(H, W):
ans = 0
for h in range((H+1)//2, H+1):
for w in range((W+1)//2, W+1):
ans += cmb.factorial[h+w] * cmb.inv_factorial[H-h] % MOD * cmb.inv_factorial[2*h-H] % MOD * cmb.inv_factorial[W-w] % MOD * cmb
                    .inv_factorial[2*w-W] % MOD
ans %= MOD
return ans
def solve(H, W):
fft = FFT(MOD)
ans = 0
Wlist = []
for w in range((W+1)//2, W+1):
Wlist.append(cmb.inv_factorial[W-w] * cmb.inv_factorial[2*w-W] % MOD)
HWlist = []
for hw in range((H+1)//2 + (W+1)//2, H+W+1):
HWlist.append(cmb.factorial[hw])
Sum = fft.convolution(Wlist[::-1], HWlist)
for i, h in enumerate(range((H+1)//2, H+1)):
ans += Sum[i+len(Wlist)-1] % MOD * cmb.inv_factorial[H-h] % MOD * cmb.inv_factorial[2*h-H] % MOD
ans %= MOD
return ans
# print(solve_naive(H, W))
print(solve(H, W))
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
butterfly_first=True
butterfly_inv_first=True
sum_e=[0]*30
sum_ie=[0]*30
def __init__(self,MOD):
self.mod=MOD
self.g=self.primitive_root_constexpr(self.mod)
def butterfly(self,a):
n=len(a)
h=(n-1).bit_length()
if self.butterfly_first:
self.butterfly_first=False
es=[0]*30
ies=[0]*30
cnt2=self.bsf(self.mod-1)
e=pow(self.g,(self.mod-1)>>cnt2,self.mod)
ie=pow(e,self.mod-2,self.mod)
for i in range(cnt2,1,-1):
es[i-2]=e
ies[i-2]=ie
e=(e*e)%self.mod
ie=(ie*ie)%self.mod
now=1
for i in range(cnt2-2):
self.sum_e[i]=((es[i]*now)%self.mod)
now*=ies[i]
now%=self.mod
for ph in range(1,h+1):
w=1<<(ph-1)
p=1<<(h-ph)
now=1
for s in range(w):
offset=s<<(h-ph+1)
for i in range(p):
l=a[i+offset]
r=a[i+offset+p]*now
r%=self.mod
a[i+offset]=l+r
a[i+offset]%=self.mod
a[i+offset+p]=l-r
a[i+offset+p]%=self.mod
now*=self.sum_e[(~s & -~s).bit_length()-1]
now%=self.mod
def butterfly_inv(self,a):
n=len(a)
h=(n-1).bit_length()
if self.butterfly_inv_first:
self.butterfly_inv_first=False
es=[0]*30
ies=[0]*30
cnt2=self.bsf(self.mod-1)
e=pow(self.g,(self.mod-1)>>cnt2,self.mod)
ie=pow(e,self.mod-2,self.mod)
for i in range(cnt2,1,-1):
es[i-2]=e
ies[i-2]=ie
e=(e*e)%self.mod
ie=(ie*ie)%self.mod
now=1
for i in range(cnt2-2):
self.sum_ie[i]=((ies[i]*now)%self.mod)
now*=es[i]
now%=self.mod
for ph in range(h,0,-1):
w=1<<(ph-1)
p=1<<(h-ph)
inow=1
for s in range(w):
offset=s<<(h-ph+1)
for i in range(p):
l=a[i+offset]
r=a[i+offset+p]
a[i+offset]=l+r
a[i+offset]%=self.mod
a[i+offset+p]=(l-r)*inow
a[i+offset+p]%=self.mod
inow*=self.sum_ie[(~s & -~s).bit_length()-1]
inow%=self.mod
def convolution(self,a,b):
n=len(a);m=len(b)
if not(a) or not(b):
return []
if min(n,m)<=40:
if n<m:
n,m=m,n
a,b=b,a
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=[0]*z
for i in range(z):
c[i]=(a[i]*b[i])%self.mod
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]
main()
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