結果

問題 No.2292 Interval Union Find
ユーザー とりゐ
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
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 * 4
other AC * 44
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ソースコード

diff #
プレゼンテーションモードにする

from sys import stdin
input=lambda :stdin.readline()[:-1]
import math
from bisect import bisect_left, bisect_right
from typing import Generic, Iterable, Iterator, TypeVar, Union, List
T = TypeVar('T')
class SortedSet(Generic[T]):
BUCKET_RATIO = 50
REBUILD_RATIO = 170
def _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 j
def __reversed__(self) -> Iterator[T]:
for i in reversed(self.a):
for j in reversed(i): yield j
def __len__(self) -> int:
return self.size
def __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 a
return a
def __contains__(self, x: T) -> bool:
if self.size == 0: return False
a = self._find_bucket(x)
i = bisect_left(a, x)
return i != len(a) and a[i] == x
def add(self, x: T) -> bool:
"Add an element and return True if added. / O(√N)"
if self.size == 0:
self.a = [[x]]
self.size = 1
return True
a = self._find_bucket(x)
i = bisect_left(a, x)
if i != len(a) and a[i] == x: return False
a.insert(i, x)
self.size += 1
if len(a) > len(self.a) * self.REBUILD_RATIO:
self._build()
return True
def discard(self, x: T) -> bool:
"Remove an element and return True if removed. / O(√N)"
if self.size == 0: return False
a = self._find_bucket(x)
i = bisect_left(a, x)
if i == len(a) or a[i] != x: return False
a.pop(i)
self.size -= 1
if len(a) == 0: self._build()
return True
def 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.size
if x < 0: raise IndexError
for a in self.a:
if x < len(a): return a[x]
x -= len(a)
raise IndexError
def index(self, x: T) -> int:
"Count the number of elements < x."
ans = 0
for a in self.a:
if a[-1] >= x:
return ans + bisect_left(a, x)
ans += len(a)
return ans
def index_right(self, x: T) -> int:
"Count the number of elements <= x."
ans = 0
for a in self.a:
if a[-1] > x:
return ans + bisect_right(a, x)
ans += len(a)
return ans
from collections import defaultdict
class UnionFind():
def __init__(self,n):
self.n=n
self.parents=[-1]*n
def find(self,x):
if self.parents[x]<0:
return x
else:
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:
return
if self.parents[x]>self.parents[y]:
x,y=y,x
self.parents[x]+=self.parents[y]
self.parents[y]=x
def 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_members
def solve(n,q,queries):
inf=1<<30
ANS=[]
S=SortedSet()
for qi in range(q):
query=queries[qi]
if query[0]==1:
l,r=query[1:]
L,R=l,r
x=S.le([l,inf])
if x!=None and x[0]<=l and r<=x[1]:
continue
if 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:
break
S.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:
break
elif query[0]==3:
u,v=query[1:]
u,v=min(u,v),max(u,v)
if u==v:
ANS.append(1)
continue
x=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 ANS
def 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=uf2
if 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=0
for i in range(n+1):
if uf.same(i,u):
cnt+=1
ANS.append(cnt)
return ANS
import random
while 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))
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