結果
問題 | No.2292 Interval Union Find |
ユーザー |
![]() |
提出日時 | 2023-05-05 22:39:49 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 4,413 ms / 5,000 ms |
コード長 | 8,328 bytes |
コンパイル時間 | 407 ms |
コンパイル使用メモリ | 82,576 KB |
実行使用メモリ | 169,412 KB |
最終ジャッジ日時 | 2024-12-20 16:48:14 |
合計ジャッジ時間 | 119,571 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 44 |
ソースコード
from sys import stdininput=lambda :stdin.readline()[:-1]import mathfrom bisect import bisect_left, bisect_rightfrom typing import Generic, Iterable, Iterator, TypeVar, Union, ListT = TypeVar('T')class SortedSet(Generic[T]):BUCKET_RATIO = 50REBUILD_RATIO = 170def _build(self, a=None) -> None:"Evenly divide `a` into buckets."if a is None: a = list(self)size = self.size = len(a)bucket_size = int(math.ceil(math.sqrt(size / self.BUCKET_RATIO)))self.a = [a[size * i // bucket_size : size * (i + 1) // bucket_size] for i in range(bucket_size)]def __init__(self, a: Iterable[T] = []) -> None:"Make a new SortedSet from iterable. / O(N) if sorted and unique / O(N log N)"a = list(a)if not all(a[i] < a[i + 1] for i in range(len(a) - 1)):a = sorted(set(a))self._build(a)def __iter__(self) -> Iterator[T]:for i in self.a:for j in i: yield jdef __reversed__(self) -> Iterator[T]:for i in reversed(self.a):for j in reversed(i): yield jdef __len__(self) -> int:return self.sizedef __repr__(self) -> str:return "SortedSet" + str(self.a)def __str__(self) -> str:s = str(list(self))return "{" + s[1 : len(s) - 1] + "}"def _find_bucket(self, x: T) -> List[T]:"Find the bucket which should contain x. self must not be empty."for a in self.a:if x <= a[-1]: return areturn adef __contains__(self, x: T) -> bool:if self.size == 0: return Falsea = self._find_bucket(x)i = bisect_left(a, x)return i != len(a) and a[i] == xdef add(self, x: T) -> bool:"Add an element and return True if added. / O(√N)"if self.size == 0:self.a = [[x]]self.size = 1return Truea = self._find_bucket(x)i = bisect_left(a, x)if i != len(a) and a[i] == x: return Falsea.insert(i, x)self.size += 1if len(a) > len(self.a) * self.REBUILD_RATIO:self._build()return Truedef discard(self, x: T) -> bool:"Remove an element and return True if removed. / O(√N)"if self.size == 0: return Falsea = self._find_bucket(x)i = bisect_left(a, x)if i == len(a) or a[i] != x: return Falsea.pop(i)self.size -= 1if len(a) == 0: self._build()return Truedef lt(self, x: T) -> Union[T, None]:"Find the largest element < x, or None if it doesn't exist."for a in reversed(self.a):if a[0] < x:return a[bisect_left(a, x) - 1]def le(self, x: T) -> Union[T, None]:"Find the largest element <= x, or None if it doesn't exist."for a in reversed(self.a):if a[0] <= x:return a[bisect_right(a, x) - 1]def gt(self, x: T) -> Union[T, None]:"Find the smallest element > x, or None if it doesn't exist."for a in self.a:if a[-1] > x:return a[bisect_right(a, x)]def ge(self, x: T) -> Union[T, None]:"Find the smallest element >= x, or None if it doesn't exist."for a in self.a:if a[-1] >= x:return a[bisect_left(a, x)]def __getitem__(self, x: int) -> T:"Return the x-th element, or IndexError if it doesn't exist."if x < 0: x += self.sizeif x < 0: raise IndexErrorfor a in self.a:if x < len(a): return a[x]x -= len(a)raise IndexErrordef index(self, x: T) -> int:"Count the number of elements < x."ans = 0for a in self.a:if a[-1] >= x:return ans + bisect_left(a, x)ans += len(a)return ansdef index_right(self, x: T) -> int:"Count the number of elements <= x."ans = 0for a in self.a:if a[-1] > x:return ans + bisect_right(a, x)ans += len(a)return ansfrom collections import defaultdictclass UnionFind():def __init__(self,n):self.n=nself.parents=[-1]*ndef find(self,x):if self.parents[x]<0:return xelse:self.parents[x]=self.find(self.parents[x])return self.parents[x]def union(self,x,y):x=self.find(x)y=self.find(y)if x==y:returnif self.parents[x]>self.parents[y]:x,y=y,xself.parents[x]+=self.parents[y]self.parents[y]=xdef size(self,x):return -self.parents[self.find(x)]def same(self,x,y):return self.find(x)==self.find(y)def members(self,x):root=self.find(x)return [i for i in range(self.n) if self.find(i)==root]def roots(self):return [i for i, x in enumerate(self.parents) if x< 0]def group_count(self):return len(self.roots())def all_group_members(self):group_members=defaultdict(list)for member in range(self.n):group_members[self.find(member)].append(member)return group_membersdef solve(n,q,queries):inf=1<<30ANS=[]S=SortedSet()for qi in range(q):query=queries[qi]if query[0]==1:l,r=query[1:]L,R=l,rx=S.le([l,inf])if x!=None and x[0]<=l and r<=x[1]:continueif x!=None and l<=x[1]<=r:L=min(L,x[0])y=S.le([r,-inf])if y!=None and l<=y[0]<=r:R=max(R,y[1])while True:x=S.ge([L,L])if x!=None and L<=x[0]<=R:R=max(R,x[1])S.discard(x)else:breakS.add([L,R])elif query[0]==2:l,r=query[1:]x=S.le([l-1,inf])if x!=None and x[1]>=l+1:S.discard(x)S.add([x[0],l])if x[1]>=r:S.add([r,x[1]])y=S.le([r,inf])if y!=None and y[1]>=r:S.discard(y)S.add([r,y[1]])if y[0]<=l:S.add([y[0],l])while True:x=S.ge([l,l])if x!=None and l<=x[0]<=x[1]<=r:S.discard(x)else:breakelif query[0]==3:u,v=query[1:]u,v=min(u,v),max(u,v)if u==v:ANS.append(1)continuex=S.le([u,inf])if x!=None and x[0]<=u<=v<=x[1]:ANS.append(1)else:ANS.append(0)elif query[0]==4:u=query[1]x=S.le([u,inf])if x!=None and x[0]<=u<=x[1]:ANS.append(x[1]-x[0]+1)else:ANS.append(1)return ANSdef naive(n,q,queries):uf=UnionFind(n+1)ANS=[]for qi in range(q):query=queries[qi]if query[0]==1:l,r=query[1:]for i in range(l,r+1):uf.union(l,i)if query[0]==2:l,r=query[1:]uf2=UnionFind(n+1)for i in range(1,l+1):for j in range(1,l+1):if uf.same(i,j):uf2.union(i,j)for i in range(r,n+1):for j in range(r,n+1):if uf.same(i,j):uf2.union(i,j)uf=uf2if query[0]==3:u,v=query[1:]if uf.same(u,v):ANS.append(1)else:ANS.append(0)if query[0]==4:u=query[1]cnt=0for i in range(n+1):if uf.same(i,u):cnt+=1ANS.append(cnt)return ANSimport randomwhile False:n=random.randint(2,10)q=random.randint(2,10)queries=[]print(n,q)for _ in range(q):t=random.randint(1,4)if t==1:l=random.randint(1,n-1)r=random.randint(l+1,n)queries.append([1,l,r])if t==2:l=random.randint(1,n-1)r=random.randint(l+1,n)queries.append([2,l,r])if t==3:u=random.randint(1,n)v=random.randint(1,n)queries.append([3,u,v])if t==4:u=random.randint(1,n)queries.append([4,u])if solve(n,q,queries)!=naive(n,q,queries):print(n,q,queries)print(solve(n,q,queries))print(naive(n,q,queries))exit()n,q=map(int,input().split())queries=[]for _ in range(q):query=list(map(int,input().split()))queries.append(query)print(*solve(n,q,queries),sep='\n')#print(naive(n,q,queries))