結果
| 問題 | No.1300 Sum of Inversions |
| ユーザー |
 vwxyz
|
| 提出日時 | 2023-12-02 14:22:48 |
| 言語 | Python3 (3.12.2 + numpy 1.26.4 + scipy 1.12.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 20,146 bytes |
| コンパイル時間 | 201 ms |
| コンパイル使用メモリ | 14,976 KB |
| 実行使用メモリ | 57,484 KB |
| 最終ジャッジ日時 | 2024-09-26 16:35:49 |
| 合計ジャッジ時間 | 5,867 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
（要ログイン）
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 | 41 ms
18,304 KB |
| testcase_01 | AC | 43 ms
12,928 KB |
| testcase_02 | AC | 41 ms
12,928 KB |
| testcase_03 | TLE | - |
| testcase_04 | -- | - |
| testcase_05 | -- | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
ソースコード
import sys
readline=sys.stdin.readline
from collections import defaultdict,Counter
class UnionFind:
def __init__(self,N,label=None,f=None,weighted=False,rollback=False):
self.N=N
self.parents=[None]*self.N
self.size=[1]*self.N
self.roots={i for i in range(self.N)}
self.label=label
if self.label!=None:
self.label=[x for x in label]
self.f=f
self.weighted=weighted
if self.weighted:
self.weight=[0]*self.N
self.rollback=rollback
if self.rollback:
self.operate_list=[]
self.operate_set=[]
def Find(self,x):
stack=[]
while self.parents[x]!=None:
stack.append(x)
x=self.parents[x]
if not self.rollback:
if self.weighted:
w=0
for y in stack[::-1]:
self.parents[y]=x
w+=self.weight[y]
self.weight[y]=w
else:
for y in stack[::-1]:
self.parents[y]=x
return x
def Union(self,x,y,w=None):
root_x=self.Find(x)
root_y=self.Find(y)
if self.rollback:
self.operate_list.append([])
self.operate_set.append([])
if root_x==root_y:
if self.weighted:
if self.weight[y]-self.weight[x]==w:
return True
else:
return False
else:
if self.size[root_x]<self.size[root_y]:
x,y=y,x
root_x,root_y=root_y,root_x
if self.weighted:
w=-w
if self.rollback:
self.operate_list[-1].append((self.parents,root_y,self.parents[root_y]))
self.operate_list[-1].append((self.size,root_x,self.size[root_x]))
self.operate_set[-1].append(root_y)
if self.label!=None:
self.operate_list[-1]((self.label,root_x,self.label[root_x]))
if self.weighted:
self.operate_list[-1].append((self.weight,root_y,self.weight[root_y]))
self.parents[root_y]=root_x
self.size[root_x]+=self.size[root_y]
self.roots.remove(root_y)
if self.label!=None:
self.label[root_x]=self.f(self.label[root_x],self.label[root_y])
if self.weighted:
self.weight[root_y]=w+self.weight[x]-self.weight[y]
def Size(self,x):
return self.size[self.Find(x)]
def Same(self,x,y):
return self.Find(x)==self.Find(y)
def Label(self,x):
return self.label[self.Find(x)]
def Weight(self,x,y):
root_x=self.Find(x)
root_y=self.Find(y)
if root_x!=root_y:
return None
return self.weight[y]-self.weight[x]
def Roots(self):
return list(self.roots)
def Linked_Components_Count(self):
return len(self.roots)
def Linked_Components(self):
linked_components=defaultdict(list)
for x in range(self.N):
linked_components[self.Find(x)].append(x)
return linked_components
def Rollback(self):
assert self.rollback
if self.operate_list:
for lst,x,v in self.operate_list.pop():
lst[x]=v
for x in self.operate_set.pop():
self.roots.add(x)
return True
else:
return False
def __str__(self):
linked_components=defaultdict(list)
for x in range(self.N):
linked_components[self.Find(x)].append(x)
return "\n".join(f"{r}: {linked_components[r]}" for r in sorted(list(linked_components.keys())))
class Graph:
def __init__(self,V,edges=None,graph=None,directed=False,weighted=False,inf=float("inf")):
self.V=V
self.directed=directed
self.weighted=weighted
self.inf=inf
if graph!=None:
self.graph=graph
"""
self.edges=[]
for i in range(self.V):
if self.weighted:
for j,d in self.graph[i]:
if self.directed or not self.directed and i<=j:
self.edges.append((i,j,d))
else:
for j in self.graph[i]:
if self.directed or not self.directed and i<=j:
self.edges.append((i,j))
"""
else:
self.edges=edges
self.graph=[[] for i in range(self.V)]
if weighted:
for i,j,d in self.edges:
self.graph[i].append((j,d))
if not self.directed:
self.graph[j].append((i,d))
else:
for i,j in self.edges:
self.graph[i].append(j)
if not self.directed:
self.graph[j].append(i)
def Warshall_Floyd(self,route_restoration=False):
dist=[[self.inf]*self.V for i in range(self.V)]
for i in range(self.V):
dist[i][i]=0
if route_restoration:
parents=[[j for j in range(self.V)] for i in range(self.V)]
for i,j,d in self.edges:
if i==j:
continue
if dist[i][j]>d:
dist[i][j]=d
if route_restoration:
parents[i][j]=i
if not self.directed and dist[j][i]>d:
dist[j][i]=d
if route_restoration:
parents[j][i]=j
for k in range(self.V):
for i in range(self.V):
for j in range(self.V):
if dist[i][j]>dist[i][k]+dist[k][j]:
dist[i][j]=dist[i][k]+dist[k][j]
if route_restoration:
parents[i][j]=parents[k][j]
for i in range(self.V):
if dist[i][i]<0:
for j in range(self.V):
if dist[i][j]!=self.inf:
dist[i][j]=-self.inf
if route_restoration:
for i in range(self.V):
if dist[i][i]==0:
parents[i][i]=None
return dist,parents
else:
return dist
def Kruskal(self,maximize=False,spanning_tree=False):
UF=UnionFind(self.V)
sorted_edges=sorted(self.edges if self.weighted else [(x,y,1) for x,y in self.edges],key=lambda tpl:tpl[2],reverse=maximize)
if spanning_tree:
st=[]
else:
cost=0
for x,y,d in sorted_edges:
if not UF.Same(x,y):
UF.Union(x,y)
if spanning_tree:
st.append((x,y,d))
else:
cost+=d
return st if spanning_tree else cost
def Inversion_Number(lst,weight=False,weakly=False):
compress,decompress=Compress(lst)
compressed_lst=[compress[x] for x in lst]
N=len(compress)
if not weight:
weight=[1]*len(lst)
ST=Segment_Tree(N,lambda x,y:x+y,0)
inversion_number=0
for c,x in zip(weight,compressed_lst):
inversion_number+=ST.Fold(x if weakly else x+1,N)*c
ST[x]+=c
return inversion_number
def Compress(lst):
decomp=sorted(list(set(lst)))
comp={x:i for i,x in enumerate(decomp)}
return comp,decomp
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:]))+"]"
class Cumsum:
def __init__(self,lst,mod=0):
self.N=len(lst)
self.mod=mod
self.cumsum=[0]*(self.N+1)
self.cumsum[0]=0
for i in range(1,self.N+1):
self.cumsum[i]=self.cumsum[i-1]+lst[i-1]
if self.mod:
self.cumsum[i]%=self.mod
def __getitem__(self,i):
if type(i)==int:
if 0<=i<self.N:
a,b=i,i+1
elif -self.N<=i<0:
a,b=i+self.N,i+self.N+1
else:
raise IndexError('list index out of range')
else:
a,b=i.start,i.stop
if a==None or a<-self.N:
a=0
elif self.N<=a:
a=self.N
elif a<0:
a+=self.N
if b==None or self.N<=b:
b=self.N
elif b<-self.N:
b=0
elif b<0:
b+=self.N
s=self.cumsum[b]-self.cumsum[a]
if self.mod:
s%=self.mod
return s
def __setitem__(self,i,x):
if -self.N<=i<0:
i+=self.N
elif not 0<=i<self.N:
raise IndexError('list index out of range')
self.cumsum[i+1]=self.cumsum[i]+x
if self.mod:
self.cumsum[i+1]%=self.mod
def __len__(self):
return self.N
def __str__(self):
lst=[self.cumsum[i+1]-self.cumsum[i] for i in range(self.N)]
if self.mod:
for i in range(self.N):
lst[i]%=self.mod
return "["+", ".join(map(str,lst))+"]"
def Swap_Count(N,A,B):
if sorted(A)==sorted(B):
idxA={tpl:i for i,tpl in enumerate(sorted([(A[i],i) for i in range(N)]))}
idxB={tpl:i for i,tpl in enumerate(sorted([(B[i],i) for i in range(N)]))}
for i in range(N):
A[i]=idxA[(A[i],i)]
B[i]=idxB[(B[i],i)]
idx={A[i]:i for i in range(N)}
for i in range(N):
B[i]=idx[B[i]]
retu=Inversion_Number(B)
else:
retu=-1
return retu
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
class Prime:
def __init__(self,N):
assert N<=10**8
self.smallest_prime_factor=[None]*(N+1)
for i in range(2,N+1,2):
self.smallest_prime_factor[i]=2
n=int(N**.5)+1
for p in range(3,n,2):
if self.smallest_prime_factor[p]==None:
self.smallest_prime_factor[p]=p
for i in range(p**2,N+1,2*p):
if self.smallest_prime_factor[i]==None:
self.smallest_prime_factor[i]=p
for p in range(n,N+1):
if self.smallest_prime_factor[p]==None:
self.smallest_prime_factor[p]=p
self.primes=[p for p in range(N+1) if p==self.smallest_prime_factor[p]]
def Factorize(self,N):
assert N>=1
factors=defaultdict(int)
if N<=len(self.smallest_prime_factor)-1:
while N!=1:
factors[self.smallest_prime_factor[N]]+=1
N//=self.smallest_prime_factor[N]
else:
for p in self.primes:
while N%p==0:
N//=p
factors[p]+=1
if N<p*p:
if N!=1:
factors[N]+=1
break
if N<=len(self.smallest_prime_factor)-1:
while N!=1:
factors[self.smallest_prime_factor[N]]+=1
N//=self.smallest_prime_factor[N]
break
else:
if N!=1:
factors[N]+=1
return factors
def Divisors(self,N):
assert N>0
divisors=[1]
for p,e in self.Factorize(N).items():
pow_p=[1]
for _ in range(e):
pow_p.append(pow_p[-1]*p)
divisors=[i*j for i in divisors for j in pow_p]
return divisors
def Is_Prime(self,N):
return N==self.smallest_prime_factor[N]
def Totient(self,N):
for p in self.Factorize(N).keys():
N*=p-1
N//=p
return N
def Mebius(self,N):
fact=self.Factorize(N)
for e in fact.values():
if e>=2:
return 0
else:
if len(fact)%2==0:
return 1
else:
return -1
N=int(input())
A=list(map(int,readline().split()))
mod=998244353
comp,decomp=Compress(A)
le=len(comp)
L1=Segment_Tree(le,lambda x,y:x+y,0)
R1=Segment_Tree(le,lambda x,y:x+y,0)
L2=Segment_Tree(le,lambda x,y:x+y,0)
R2=Segment_Tree(le,lambda x,y:x+y,0)
for a in A[::-1]:
a=comp[a]
R1[a]+=1
R2[a]+=R1.Fold(0,a)
ans=0
for a in A:
a=comp[a]
R1[a]-=1
R2[a]-=R1.Fold(0,a)
cnt=0
cnt+=L2.Fold(a+1,le)
cnt+=L1.Fold(a+1,le)*R1.Fold(0,a)
cnt+=R2.Fold(0,a)
ans+=cnt*decomp[a]%mod
ans%=mod
L1[a]+=1
L2[a]+=L1.Fold(a+1,le)
print(ans)