cp-library

This documentation is automatically generated by online-judge-tools/verification-helper

View the Project on GitHub kobejean/cp-library

:heavy_check_mark: test/atcoder/abc/abc261_g_queries_mo_ops.test.py

Depends on

Code

# verification-helper: PROBLEM https://atcoder.jp/contests/abc293/tasks/abc293_g


def main():
    N, Q = read()
    A = read(list[int])
    ops, *opands = read(QueriesMoOps[Q, N])
    
    # State for counting triples
    cnt = [0]*200001        
    triples = 0           
    ans = [0]*Q
    
    for j in range(len(ops)):
        if ops[j] in MoOp.ADD:
            for i in range(opands[0][j], opands[1][j], opands[2][j]):
                v = A[i]
                c = cnt[v] 
                triples += c*(c-1)  
                cnt[v] += 1   
        elif ops[j] in MoOp.REMOVE:
            for i in range(opands[0][j], opands[1][j], opands[2][j]):
                v = A[i]
                cnt[v] -= 1       
                c = cnt[v]      
                triples -= c*(c-1)    
        else:
            i = opands[0][j]
            ans[i] = triples >> 1
    
    write(*ans, sep='\n')

from cp_library.ds.queries_mo_ops_cls import QueriesMoOps, MoOp
from cp_library.io.read_fn import read
from cp_library.io.write_fn import write

if __name__ == "__main__":
    main()
# verification-helper: PROBLEM https://atcoder.jp/contests/abc293/tasks/abc293_g


def main():
    N, Q = read()
    A = read(list[int])
    ops, *opands = read(QueriesMoOps[Q, N])
    
    # State for counting triples
    cnt = [0]*200001        
    triples = 0           
    ans = [0]*Q
    
    for j in range(len(ops)):
        if ops[j] in MoOp.ADD:
            for i in range(opands[0][j], opands[1][j], opands[2][j]):
                v = A[i]
                c = cnt[v] 
                triples += c*(c-1)  
                cnt[v] += 1   
        elif ops[j] in MoOp.REMOVE:
            for i in range(opands[0][j], opands[1][j], opands[2][j]):
                v = A[i]
                cnt[v] -= 1       
                c = cnt[v]      
                triples -= c*(c-1)    
        else:
            i = opands[0][j]
            ans[i] = triples >> 1
    
    write(*ans, sep='\n')

'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
             https://kobejean.github.io/cp-library               
'''

import typing
from collections import deque
from numbers import Number
from types import GenericAlias 
from typing import Callable, Collection, Iterator, Union
import os
import sys
from io import BytesIO, IOBase


class FastIO(IOBase):
    BUFSIZE = 8192
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        BUFSIZE = self.BUFSIZE
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        BUFSIZE = self.BUFSIZE
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    stdin: 'IOWrapper' = None
    stdout: 'IOWrapper' = None
    
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable

    def write(self, s):
        return self.buffer.write(s.encode("ascii"))
    
    def read(self):
        return self.buffer.read().decode("ascii")
    
    def readline(self):
        return self.buffer.readline().decode("ascii")

sys.stdin = IOWrapper.stdin = IOWrapper(sys.stdin)
sys.stdout = IOWrapper.stdout = IOWrapper(sys.stdout)
from typing import TypeVar
_T = TypeVar('T')

class TokenStream(Iterator):
    stream = IOWrapper.stdin

    def __init__(self):
        self.queue = deque()

    def __next__(self):
        if not self.queue: self.queue.extend(self._line())
        return self.queue.popleft()
    
    def wait(self):
        if not self.queue: self.queue.extend(self._line())
        while self.queue: yield
 
    def _line(self):
        return TokenStream.stream.readline().split()

    def line(self):
        if self.queue:
            A = list(self.queue)
            self.queue.clear()
            return A
        return self._line()
TokenStream.default = TokenStream()

class CharStream(TokenStream):
    def _line(self):
        return TokenStream.stream.readline().rstrip()
CharStream.default = CharStream()


ParseFn = Callable[[TokenStream],_T]
class Parser:
    def __init__(self, spec: Union[type[_T],_T]):
        self.parse = Parser.compile(spec)

    def __call__(self, ts: TokenStream) -> _T:
        return self.parse(ts)
    
    @staticmethod
    def compile_type(cls: type[_T], args = ()) -> _T:
        if issubclass(cls, Parsable):
            return cls.compile(*args)
        elif issubclass(cls, (Number, str)):
            def parse(ts: TokenStream): return cls(next(ts))              
            return parse
        elif issubclass(cls, tuple):
            return Parser.compile_tuple(cls, args)
        elif issubclass(cls, Collection):
            return Parser.compile_collection(cls, args)
        elif callable(cls):
            def parse(ts: TokenStream):
                return cls(next(ts))              
            return parse
        else:
            raise NotImplementedError()
    
    @staticmethod
    def compile(spec: Union[type[_T],_T]=int) -> ParseFn[_T]:
        if isinstance(spec, (type, GenericAlias)):
            cls = typing.get_origin(spec) or spec
            args = typing.get_args(spec) or tuple()
            return Parser.compile_type(cls, args)
        elif isinstance(offset := spec, Number): 
            cls = type(spec)  
            def parse(ts: TokenStream): return cls(next(ts)) + offset
            return parse
        elif isinstance(args := spec, tuple):      
            return Parser.compile_tuple(type(spec), args)
        elif isinstance(args := spec, Collection):  
            return Parser.compile_collection(type(spec), args)
        elif isinstance(fn := spec, Callable): 
            def parse(ts: TokenStream): return fn(next(ts))
            return parse
        else:
            raise NotImplementedError()

    @staticmethod
    def compile_line(cls: _T, spec=int) -> ParseFn[_T]:
        if spec is int:
            fn = Parser.compile(spec)
            def parse(ts: TokenStream): return cls([int(token) for token in ts.line()])
            return parse
        else:
            fn = Parser.compile(spec)
            def parse(ts: TokenStream): return cls([fn(ts) for _ in ts.wait()])
            return parse

    @staticmethod
    def compile_repeat(cls: _T, spec, N) -> ParseFn[_T]:
        fn = Parser.compile(spec)
        def parse(ts: TokenStream): return cls([fn(ts) for _ in range(N)])
        return parse

    @staticmethod
    def compile_children(cls: _T, specs) -> ParseFn[_T]:
        fns = tuple((Parser.compile(spec) for spec in specs))
        def parse(ts: TokenStream): return cls([fn(ts) for fn in fns])  
        return parse
            
    @staticmethod
    def compile_tuple(cls: type[_T], specs) -> ParseFn[_T]:
        if isinstance(specs, (tuple,list)) and len(specs) == 2 and specs[1] is ...:
            return Parser.compile_line(cls, specs[0])
        else:
            return Parser.compile_children(cls, specs)

    @staticmethod
    def compile_collection(cls, specs):
        if not specs or len(specs) == 1 or isinstance(specs, set):
            return Parser.compile_line(cls, *specs)
        elif (isinstance(specs, (tuple,list)) and len(specs) == 2 and isinstance(specs[1], int)):
            return Parser.compile_repeat(cls, specs[0], specs[1])
        else:
            raise NotImplementedError()

class Parsable:
    @classmethod
    def compile(cls):
        def parser(ts: TokenStream): return cls(next(ts))
        return parser

def elist(est_len: int) -> list: ...
try:
    from __pypy__ import newlist_hint
except:
    def newlist_hint(hint):
        return []
elist = newlist_hint
    

from enum import IntFlag, auto
from math import isqrt

class MoOp(IntFlag):
    ADD_LEFT = auto()
    ADD_RIGHT = auto()
    REMOVE_LEFT = auto()
    REMOVE_RIGHT = auto()
    ANSWER = auto()
    
    ADD = ADD_LEFT | ADD_RIGHT
    REMOVE = REMOVE_LEFT | REMOVE_RIGHT

# def hilbert(x: int, y: int, n: int) -> int:
#     '''Convert (x,y) to Hilbert curve distance for given n (power of 2).'''
#     d = 0
#     for s in range(n.bit_length() - 1, -1, -1):
#         rx = (x >> s) & 1
#         ry = (y >> s) & 1
#         d += n * n * ((3 * rx) ^ ry) >> 2
#         if ry == 0:
#             if rx == 1:
#                 x = n-1 - x
#                 y = n-1 - y
#             x, y = y, x
#     return d

class QueriesMoOps(tuple[list[int], ...],Parsable):
    '''
    QueriesMoOps[Q: int, N: int, T: type = tuple[int, int]]
    Orders queries using Mo's algorithm and generates a sequence of operations to process them efficiently.
    Each operation is either moving pointers or answering a query.
    
    Uses half-interval convention: [left, right)
    '''
    
    def __new__(cls, L: list[int], R: list[int], N: int, B: int = None):
        Q = len(L)
        qbits = Q.bit_length()
        nbits = (N+1).bit_length()
        qmask = qmask = (1 << qbits)-1
        nmask = (1 << nbits)-1
        B = max(1,N//isqrt(max(1,Q)) )if B is None else B
        order = [0]*Q
        for i in range(Q):
            l, r = L[i], R[i]
            b = l//B
            r = nmask - r if b & 1 else r
            order[i] = (((b << nbits) + r) << qbits) + i
        # n = 1 << nbits
        # for i in range(Q):
        #     l, r = L[i], R[i]
        #     # Use Hilbert curve mapping for the 2D point (l,r)
        #     h = hilbert(l, r, n)
        #     order[i] = (h << qbits) + i
        order.sort()
        
        ops = elist(3*Q)
        A1 = elist(3*Q)
        A2 = elist(3*Q)
        A3 = elist(3*Q)

        nl = nr = 0
        
        for i in order:
            i &= qmask
            l, r = L[i], R[i]
            if l < nl:
                ops.append(MoOp.ADD_LEFT)
                A1.append(nl-1)
                A2.append(l-1)
                A3.append(-1)
                
            elif l > nl:
                ops.append(MoOp.REMOVE_LEFT)
                A1.append(nl)
                A2.append(l)
                A3.append(1)
                
            if r > nr:
                ops.append(MoOp.ADD_RIGHT)
                A1.append(nr)
                A2.append(r)
                A3.append(1)
                
            elif r < nr:
                ops.append(MoOp.REMOVE_RIGHT)
                A1.append(nr-1)
                A2.append(r-1)
                A3.append(-1)
                
            ops.append(MoOp.ANSWER)
            A1.append(i)
            A2.append(l)
            A3.append(r)
            
            nl, nr = l, r
        return super().__new__(cls, (ops, A1, A2, A3))

    @classmethod
    def compile(cls, Q: int, N: int, T: type = tuple[-1, int], B: int = None):
        if T == tuple[-1, int]:
            query = Parser.compile(T)
            def parse(ts: TokenStream):
                L, R = [0]*Q, [0]*Q
                for i in range(Q):
                    L[i], R[i] = map(int,ts.line())
                    L[i] -= 1
                return cls(L, R, N, B)
            return parse
        else:
            query = Parser.compile(T)
            def parse(ts: TokenStream):
                L, R = [0]*Q, [0]*Q
                for i in range(Q):
                    L[i], R[i] = query(ts)
                return cls(L, R, N, B)
            return parse

from typing import Iterable, Type, Union, overload

@overload
def read() -> Iterable[int]: ...
@overload
def read(spec: int) -> list[int]: ...
@overload
def read(spec: Union[Type[_T],_T], char=False) -> _T: ...
def read(spec: Union[Type[_T],_T] = None, char=False):
    if not char and spec is None: return map(int, TokenStream.default.line())
    parser: _T = Parser.compile(spec)
    return parser(CharStream.default if char else TokenStream.default)

def write(*args, **kwargs):
    '''Prints the values to a stream, or to stdout_fast by default.'''
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", IOWrapper.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()

if __name__ == "__main__":
    main()
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