#866582 (PyPy3) No.2292 Interval Union Find

提出ソース

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	4,336 ms / 5,000 ms
コード長	8,328 bytes
コンパイル時間	877 ms
コンパイル使用メモリ	85,996 KB
実行使用メモリ	175,092 KB
最終ジャッジ日時	2023-08-30 19:58:01
合計ジャッジ時間	119,045 ms
ジャッジサーバーID （参考情報）	judge14 / judge11

このコードへのチャレンジ
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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	198 ms 81,396 KB
testcase_01	AC	201 ms 81,716 KB
testcase_02	AC	195 ms 81,408 KB
testcase_03	AC	195 ms 81,404 KB
testcase_04	AC	1,339 ms 138,212 KB
testcase_05	AC	2,437 ms 148,508 KB
testcase_06	AC	1,181 ms 138,024 KB
testcase_07	AC	1,897 ms 139,916 KB
testcase_08	AC	1,351 ms 133,104 KB
testcase_09	AC	1,305 ms 132,500 KB
testcase_10	AC	1,318 ms 136,028 KB
testcase_11	AC	1,326 ms 137,808 KB
testcase_12	AC	2,042 ms 141,164 KB
testcase_13	AC	1,211 ms 133,396 KB
testcase_14	AC	1,411 ms 140,604 KB
testcase_15	AC	1,442 ms 140,668 KB
testcase_16	AC	1,360 ms 136,616 KB
testcase_17	AC	1,337 ms 135,120 KB
testcase_18	AC	2,872 ms 161,108 KB
testcase_19	AC	3,571 ms 144,380 KB
testcase_20	AC	4,336 ms 175,092 KB
testcase_21	AC	3,269 ms 147,704 KB
testcase_22	AC	3,341 ms 150,444 KB
testcase_23	AC	3,238 ms 146,172 KB
testcase_24	AC	3,223 ms 146,332 KB
testcase_25	AC	3,346 ms 146,640 KB
testcase_26	AC	3,264 ms 147,376 KB
testcase_27	AC	3,271 ms 147,016 KB
testcase_28	AC	3,211 ms 147,476 KB
testcase_29	AC	3,201 ms 145,188 KB
testcase_30	AC	3,262 ms 147,276 KB
testcase_31	AC	3,254 ms 146,096 KB
testcase_32	AC	3,269 ms 148,348 KB
testcase_33	AC	3,259 ms 147,260 KB
testcase_34	AC	3,330 ms 147,864 KB
testcase_35	AC	3,315 ms 150,944 KB
testcase_36	AC	3,354 ms 148,332 KB
testcase_37	AC	3,342 ms 146,724 KB
testcase_38	AC	3,321 ms 145,460 KB
testcase_39	AC	3,373 ms 145,264 KB
testcase_40	AC	3,306 ms 145,680 KB
testcase_41	AC	555 ms 122,864 KB
testcase_42	AC	766 ms 128,596 KB
testcase_43	AC	1,477 ms 145,372 KB
testcase_44	AC	1,319 ms 137,904 KB
testcase_45	AC	1,417 ms 139,372 KB
testcase_46	AC	1,447 ms 140,968 KB
testcase_47	AC	1,393 ms 136,384 KB

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ソースコード

raw source code

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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結果

テストケース

ソースコード