結果

問題 No.2873 Kendall's Tau
コンテスト
ユーザー 👑 p-adic
提出日時 2024-09-07 09:53:41
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,675 ms / 4,500 ms
コード長 7,557 bytes
コンパイル時間 547 ms
コンパイル使用メモリ 82,388 KB
実行使用メモリ 263,820 KB
最終ジャッジ日時 2024-09-07 09:54:09
合計ジャッジ時間 27,955 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 * 3
other AC * 30
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 # 

def rec_str(a):return"".join(["[",", ".join(rec_str(x)for x in a),"]"])if isinstance(a,list)else str(a)
class BIT:
	def __init__(self,x):
		if isinstance(x,int):
			self.N=x
			self.F=[0]*(x+1)
		else:
			self.N=len(x)
			self.F=[0]*(self.N+1)
			for j in R(1,self.N+1):
				i=j-1
				self.F[j]=x[i]
				k=j-(j&-j)
				while i>k:
					self.F[j]+=self.F[i]
					i-=i&-i
	def Add(self,i,u):
		i+=1
		while i<=self.N:
			self.F[i]+=u
			i+=i&-i
	def InitialSegmentSum(self,r):
		assert(r>-2)
		a=0
		i=min(r+1,self.N)
		while i:
			a+=self.F[i]
			i-=i&-i
		return a
class IntervalAddBIT:
	def __init__(self,N):
		self.N=N
		self.F=BIT(N+1)
		self.G=BIT(N+1)
	def IntervalAdd(self,l,r,u):
		self.F.Add(l,-(l-1)*u)
		self.F.Add(r+1,r*u)
		self.G.Add(l,u)
		self.G.Add(r+1,-u)
	def Add(self,i,u):self.IntervalAdd(i,i,u)
	def Set(self,i,u):self.Add(i,u-self.Get(i))
	def InitialSegmentSum(self,r):return self.F.InitialSegmentSum(r)+r*self.G.InitialSegmentSum(r)
	def IntervalSum(self,l,r):return self.InitialSegmentSum(r)-self.InitialSegmentSum(l-1)
	def Get(self,i):return self.IntervalSum(i,i)
	def list(self):return[self.Get(i)for i in R(self.N)]
	def __str__(self):return rec_str(self.list())

class NonNegativeLineMultiSubset:
	def __init__(self,ubound):
		assert(-1<=ubound)
		self.ubound=ubound
		self.bit=IntervalAddBIT(ubound+1)
	def copy(self):
		a=__class__([])
		a.ubound=self.ubound
		a.bit=self.bit.copy()
		return a
	def insert(self,i,c=1):assert(0<=i<=self.ubound);self.bit.Add(i,c)
	def IntervalInsert(self,i_start,i_final,c=1):assert(0<=i_start and i_final<=self.ubound);self.bit.IntervalAdd(i_start,i_final,c)
	def erase(self,i,c=1):self.bit.Add(i,-c)
	def EraseAll(self,i):self.bit.Set(i,0)
	def IntervalErase(self,i,c=1):self.bit.IntervalAdd(i_start,i_final,-c)
	def count(self,i):return self.bit.Get(i)if 0<=i<=self.ubound else 0
	def find(self,i):return self.count(i)>0
	def InitialSegmentCount(self,i_final):return self.bit.InitialSegmentSum(i_final)
	def IntervalCount(self,i_start,i_final):return self.bit.IntervalSum(i_start,i_final)

	#VVV Supported if multiplicities are non-negative
	def empty(self):return self.InitialSegmentCount(self.ubound)<1
	def MaximumLeq(self,i,k=0):#Returning lbound-1 if not exists
		num=self.InitialSegmentCount(i)-k
		i-=0
		def f(sum,j):return i<=j or num<=sum
		a=self.Search(f)
		return a if num>=0 and self.find(a)else 0-1
	def MaximumLt(self,i,k=0):return self.MaximumLeq(i-1,k)
	def MinimumGeq(self,i,k=0):return self.MinimumGt(i-1,k)
	def MinimumGt(self,i,k=0):#Returning ubound+1 if not exists
		num=self.InitialSegmentCount(i)+k
		i-=0
		def f(sum,j):return i<j and num<sum
		return self.Search(f)
	def Maximum(self,k=0):return self.MaximumLeq(self.ubound,k)
	def Minimum(self,k=0):return self.MinimumGeq(0,k)
	def RightEndPointOf(self,i,b=False):
		if not b and not self.find(i):return i-1
		c=i-self.InitialSegmentCount(i)
		def f(sum,j):return i<=j and sum+c<j
		return self.Search(f)-1
	def LeftEndPointOf(self,i,b=False):
		if not b and not self.find(i):return i+1
		c=i-self.InitialSegmentCount(i)
		def f(sum,j):return i<=j or(self.find(j)and sum+c==j)
		return self.Search(f)
	def ConnectedComponentOf(self,i,b=False):
		if not b:b=self.find(i)
		return[self.LeftEndPointOf(i,b),self.RightEndPointOf(i,b)]
	def GetConnectedComponent(self):
		a=[]
		l=self.Minimum()
		while l<=self.ubound:
			r=self.RightEndPointOf(l,True)
			a+=[[l,r]]
			l=self.MinimumGt(r)
		return a
	#AAA Supported if multiplicities are non-negative

	def __str__(self):
		s=[]
		for i in R(0,self.ubound+1):
			c=self.count(i)
			if c==1:s+=[str(i)]
			elif c>0:s+=[str(i)+'x'+str(c)]
			elif c<0:s+=[str(i)+"x("+str(c)+')']
		return '{{'+", ".join(s)+'}}'
	def lbound(self):return 0
	def ubound(self):return self.ubound

	#private:
	def Search(self,f):#Computing minimum of j satisfying f(bit.InitialSegmentSum(j),j) or j==bit.N
		l,r=-1,self.bit.N
		while l+1<r:
			m=(l+r)>>1
			if f(self.bit.InitialSegmentSum(m),m):r=m
			else:l=m
		return r

class CompressedLineMultiSubset:
	def __init__(self,X):
		self.sorted_list=sorted(set(X))
		N=len(self.sorted_list)
		self.compressed_coordinate={self.sorted_list[i]:i for i in R(N)}
		self.nnls=NonNegativeLineMultiSubset(N-1)
	def copy(self):
		a=__class__([])
		a.sorted_list=self.sorted_list[:]
		a.compressed_coordinate=self.copy()
		a.nnls=self.nnls.copy()
		return a
	def insert(self,i,c=1):self.nnls.insert(self.compressed_coordinate[i],c)
	def IntervalInsert(self,i_start,i_final,c=1):self.nnls.insert(self.compressed_coordinate[i_start],self.compressed_coordinate[i_final],c)
	def erase(self,i,c=1):self.nnls.erase(self.compressed_coordinate[i],c)
	def EraseAll(self,i):self.nnls.EraseAll(self.compressed_coordinate[i])
	def IntervalErase(self,i_start,i_final,c=1):self.nnls.erase(self.compressed_coordinate[i_start],self.compressed_coordinate[i_final],c)
	def count(self,i):return self.nnls.count(self.compressed_coordinate[i])if i in self.compressed_coordinate else 0
	def find(self,i):return self.count(i)>0
	def InitialSegmentCount(self,i_final):return self.nnls.InitialSegmentCount(self.compressed_coordinate[i_final])
	def IntervalCount(self,i_start,i_final):return self.nnls.IntervalCount(self.compressed_coordinate[i_start],self.compressed_coordinate[i_final])

	#VVV Supported if multiplicities are non-negative
	def empty(self):return self.InitialSegmentCount(self.nnls.bit.N-1)<1
	def MaximumLeq(self,i,k=0):
		t=self.nnls.MaximumLeq(self.compressed_coordinate[i],k)
		return self.sorted_list[t]if t>=0 else None
	def MaximumLt(self,i,k=0):
		t=self.nnls.MaximumLt(self.compressed_coordinate[i],k)
		return self.sorted_list[t]if t>=0 else None
	def MinimumGeq(self,i,k=0):
		t=self.nnls.MinimumGeq(self.compressed_coordinate[i],k)
		return self.sorted_list[t]if t<self.nnls.bit.N else None
	def MinimumGt(self,i,k=0):
		t=self.nnls.MinimumGt(self.compressed_coordinate[i],k)
		return self.sorted_list[t]if t<self.nnls.bit.N else None
	def Maximum(self,k=0):return self.MaximumLeq(self.sorted_list[-1],k)
	def Minimum(self,k=0):return self.MinimumGeq(self.sorted_list[0],k)
	def RightEndPointOf(self,i,b=False):
		j=self.compressed_coordinate[i]
		t=self.nnls.RightEndPointOf(j,b)
		return self.sorted_list[t]if j<=t else i-1
	def LeftEndPointOf(self,i,b=False):
		j=self.compressed_coordinate[i]
		t=self.nnls.LeftEndPointOf(j,b)
		return self.sorted_list[t]if t<=j else i+1
	def ConnectedComponentOf(self,i,b=False):
		if not b:b=self.find(i)
		return[self.LeftEndPointOf(i,b),self.RightEndPointOf(i,b)]
	def GetConnectedComponent(self):
		a=[]
		l=self.Minimum()
		while l is not None:
			r=self.RightEndPointOf(l,True)
			a+=[[l,r]]
			l=self.MinimumGt(r)
		return a
	#AAA Supported if multiplicities are non-negative

	def __str__(self):
		s=[]
		for i in self.sorted_list:
			c=self.count(i)
			if c==1:s+=[str(i)]
			elif c>0:s+=[str(i)+'x'+str(c)]
			elif c<0:s+=[str(i)+"x("+str(c)+')']
		return '{{'+", ".join(s)+'}}'

R=range
J=lambda:map(int,input().split())
N,*_=J()
Dxy={}
Dyx={}
X=set()
Y=set()
for i in R(N):
	x,y=J()
	X.add(x)
	Y.add(y)
	if x in Dxy:Dxy[x]+=[y]
	else:Dxy[x]=[y]
	if y in Dyx:Dyx[y]+=[x]
	else:Dyx[y]=[x]
X=sorted(list(X))
for x in X:Dxy[x].sort()
query=[10**9]
i=0
for x in X:
	for y in Dxy[x]:
		query+=[y-1,y,y+1]
		i+=1
cl=CompressedLineMultiSubset(query)
p=q=r=s=0
i=0
for x in X:
	for y in Dxy[x]:
		p+=cl.InitialSegmentCount(y-1)
		q+=cl.IntervalCount(y+1,10**9)
	for y in Dxy[x]:
		cl.insert(y)
		i+=1
for x in X:
	L=len(Dxy[x])
	r+=(N-L)*L
for y in Y:
	L=len(Dyx[y])
	s+=(N-L)*L
print((p-q)/(r*s)**0.5*2)
0