結果
| 問題 |
No.2616 中央番目の中央値
|
| コンテスト | |
| ユーザー |
 vwxyz
|
| 提出日時 | 2024-01-27 17:28:51 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 487 ms / 2,000 ms |
| コード長 | 8,085 bytes |
| コンパイル時間 | 317 ms |
| コンパイル使用メモリ | 82,424 KB |
| 実行使用メモリ | 149,304 KB |
| 最終ジャッジ日時 | 2024-09-28 09:44:38 |
| 合計ジャッジ時間 | 10,510 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 37 |
ソースコード
import sys
readline=sys.stdin.readline
class Segment_Tree:
def __init__(self,N,f,e,lst=None,dynamic=False):
self.f=f
self.e=e
self.N=N
if dynamic:
self.segment_tree=defaultdict(lambda:self.e)
else:
if lst==None:
self.segment_tree=[self.e]*2*self.N
else:
assert len(lst)<=self.N
self.segment_tree=[self.e]*self.N+[x for x in lst]+[self.e]*(N-len(lst))
for i in range(self.N-1,0,-1):
self.segment_tree[i]=self.f(self.segment_tree[i<<1],self.segment_tree[i<<1|1])
def __getitem__(self,i):
if type(i)==int:
if -self.N<=i<0:
return self.segment_tree[i+self.N*2]
elif 0<=i<self.N:
return self.segment_tree[i+self.N]
else:
raise IndexError("list index out of range")
else:
a,b,c=i.start,i.stop,i.step
if a==None:
a=self.N
else:
a+=self.N
if b==None:
b=self.N*2
else:
b+=self.N
return self.segment_tree[slice(a,b,c)]
def __setitem__(self,i,x):
if -self.N<=i<0:
i+=self.N*2
elif 0<=i<self.N:
i+=self.N
else:
raise IndexError("list index out of range")
self.segment_tree[i]=x
while i>1:
i>>= 1
self.segment_tree[i]=self.f(self.segment_tree[i<<1],self.segment_tree[i<<1|1])
def Build(self,lst):
for i,x in enumerate(lst,self.N):
self.segment_tree[i]=x
for i in range(self.N-1,0,-1):
self.segment_tree[i]=self.f(self.segment_tree[i<<1],self.segment_tree[i<<1|1])
def Fold(self,L=None,R=None):
if L==None:
L=self.N
else:
L+=self.N
if R==None:
R=self.N*2
else:
R+=self.N
vL=self.e
vR=self.e
while L<R:
if L&1:
vL=self.f(vL,self.segment_tree[L])
L+=1
if R&1:
R-=1
vR=self.f(self.segment_tree[R],vR)
L>>=1
R>>=1
return self.f(vL,vR)
def Fold_Index(self,L=None,R=None):
if L==None:
L=self.N
else:
L+=self.N
if R==None:
R=self.N*2
else:
R+=self.N
if L==R:
return None
x=self.Fold(L-self.N,R-self.N)
while L<R:
if L&1:
if self.segment_tree[L]==x:
i=L
break
L+=1
if R&1:
R-=1
if self.segment_tree[R]==x:
i=R
break
L>>=1
R>>=1
while i<self.N:
if self.segment_tree[i]==self.segment_tree[i<<1]:
i<<=1
else:
i<<=1
i|=1
i-=self.N
return i
def Bisect_Right(self,L=None,f=None):
if L==self.N:
return self.N
if L==None:
L=0
L+=self.N
vl=self.e
vr=self.e
l,r=L,self.N*2
while l<r:
if l&1:
vl=self.f(vl,self.segment_tree[l])
l+=1
if r&1:
r-=1
vr=self.f(self.segment_tree[r],vr)
l>>=1
r>>=1
if f(self.f(vl,vr)):
return self.N
v=self.e
while True:
while L%2==0:
L>>=1
vv=self.f(v,self.segment_tree[L])
if f(vv):
v=vv
L+=1
else:
while L<self.N:
L<<=1
vv=self.f(v,self.segment_tree[L])
if f(vv):
v=vv
L+=1
return L-self.N
def Bisect_Left(self,R=None,f=None):
if R==0:
return 0
if R==None:
R=self.N
R+=self.N
vl=self.e
vr=self.e
l,r=self.N,R
while l<r:
if l&1:
vl=self.f(vl,self.segment_tree[l])
l+=1
if r&1:
r-=1
vr=self.f(self.segment_tree[r],vr)
l>>=1
r>>=1
if f(self.f(vl,vr)):
return 0
v=self.e
while True:
R-=1
while R>1 and R%2:
R>>=1
vv=self.f(self.segment_tree[R],v)
if f(vv):
v=vv
else:
while R<self.N:
R=2*R+1
vv=self.f(self.segment_tree[R],v)
if f(vv):
v=vv
R-=1
return R+1-self.N
def __str__(self):
return "["+", ".join(map(str,self.segment_tree[self.N:]))+"]"
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=int(input())
P=list(map(int,input().split()))
for i in range(N):
P[i]-=1
mod=998244353
MD=MOD(mod)
MD.Build_Fact(N)
ST=Segment_Tree(N,lambda x,y:x+y,0)
ans=0
for i in range(N):
l0=ST.Fold(0,P[i])
l1=i-l0
r0=P[i]-l0
r1=N-(P[i]+1)-l1
ans+=MD.Comb(l0+r1,l0)*MD.Comb(l1+r0,l1)%mod
ans%=mod
ST[P[i]]+=1
print(ans)