結果

問題 No.584 赤、緑、青の色塗り
ユーザー vwxyz
提出日時 2024-12-19 22:00:14
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 211 ms / 2,000 ms
コード長 3,346 bytes
コンパイル時間 336 ms
コンパイル使用メモリ 82,852 KB
実行使用メモリ 76,872 KB
最終ジャッジ日時 2024-12-19 22:00:17
合計ジャッジ時間 3,139 ms
ジャッジサーバーID
(参考情報)
judge3 / 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 * 6
other AC * 14
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 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,R,G,B=map(int,input().split())
mod=10**9+7
MD=MOD(mod)
MD.Build_Fact(N)
dp=[0]*(N+1)
dp[0]=1
for RGB in (R,G,B):
prev=dp
dp=[0]*(N+1)
for rgb in range(RGB//2+1):
for c in range(rgb,N+1):
dp[c]+=prev[c-rgb]*MD.Comb(c,rgb)%mod*MD.Comb(RGB,rgb*2)%mod*MD.Fact(rgb*2)%mod
dp[c]%=mod
ans=0
for c2 in range(N+1):
c1=R+G+B-c2*2
if 0<=c1<=N:
for c in range(c2+1):
if N-c1*2-c2*3+1>=0:
ans+=MD.Comb(N-c1-c2*2+(1 if c1+c2 else 0),c1+c2)*MD.Comb(c1+c2,c1)%mod*MD.Comb(c2,c)%mod*dp[c]*(-1)**c*MD.Fact(R+G+B-c*2)%mod
ans%=mod
for RGB in (R,G,B):
ans*=MD.Fact_Inve(RGB)
ans%=mod
print(ans)
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