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/library-checker/linear-algebra/pow_of_matrix_matpow.test.py

Depends on

Code

# verification-helper: PROBLEM https://judge.yosupo.jp/problem/pow_of_matrix


def main():
    mod = 998244353
    N, K = read()
    if N < 10:
        from cp_library.math.linalg.mat.mat_pow_fn import mat_pow
        from cp_library.math.mod.mint_cls import mint
        mint.set_mod(998244353)

        A = read(list[list[mint],N])
        B = mat_pow(A, K)
    else:
        from cp_library.math.linalg.mat.mod.mat_pow_fn import mat_pow

        A = [read() for _ in range(N)]
        B = mat_pow(A, K, mod)

    for row in B:
        write(*row)

from cp_library.io.read_fn import read
from cp_library.io.write_fn import write

if __name__ == '__main__':
    main()
# verification-helper: PROBLEM https://judge.yosupo.jp/problem/pow_of_matrix


def main():
    mod = 998244353
    N, K = read()
    if N < 10:
        '''
        ╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
                     https://kobejean.github.io/cp-library               
        '''
        
        
        
        
        def mat_pow(A,K):
            R = A if K & 1 else mat_id(len(A))
            for i in range(1,K.bit_length()):
                A = mat_mul(A,A) 
                if K >> i & 1: R = mat_mul(R,A) 
            return R
        '''
        ╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
                     https://kobejean.github.io/cp-library               
        '''
        
        
        
        
        def mat_mul(A,B):
            assert len(A[0]) == len(B)
            R = [[0]*len(B[0]) for _ in range(len(A))] 
            for i,Ri in enumerate(R):
                for k,Aik in enumerate(A[i]):
                    for j,Bkj in enumerate(B[k]):
                        Ri[j] = Bkj*Aik + Ri[j]  
            return R
        '''
        ╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
                     https://kobejean.github.io/cp-library               
        '''
        
        
        
        
        def mat_id(N):
            return [[int(i==j) for j in range(N)] for i in range(N)]
        '''
        ╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
                     https://kobejean.github.io/cp-library               
        '''
        
        
            
        class mint(int):
            mod: int
            zero: 'mint'
            one: 'mint'
            two: 'mint'
            cache: list['mint']
            def __new__(cls, *args, **kwargs):
                if 0 <= (x := int(*args, **kwargs)) < 64: return cls.cache[x]
                else: return cls.fix(x)
            @classmethod
            def set_mod(cls, mod: int):
                mint.mod = cls.mod = mod
                mint.zero = cls.zero = cls.cast(0)
                mint.one = cls.one = cls.fix(1)
                mint.two = cls.two = cls.fix(2)
                mint.cache = cls.cache = [cls.zero, cls.one, cls.two]
                for x in range(3,64): mint.cache.append(cls.fix(x))
            @classmethod
            def fix(cls, x): return cls.cast(x%cls.mod)
            @classmethod
            def cast(cls, x): return super().__new__(cls,x)
            @classmethod
            def mod_inv(cls, x):
                a,b,s,t = int(x), cls.mod, 1, 0
                while b: a,b,s,t = b,a%b,t,s-a//b*t
                if a == 1: return cls.fix(s)
                raise ValueError(f"{x} is not invertible in mod {cls.mod}")
            @property
            def inv(self): return mint.mod_inv(self)
            def __add__(self, x): return mint.fix(super().__add__(x))
            def __radd__(self, x): return mint.fix(super().__radd__(x))
            def __sub__(self, x): return mint.fix(super().__sub__(x))
            def __rsub__(self, x): return mint.fix(super().__rsub__(x))
            def __mul__(self, x): return mint.fix(super().__mul__(x))
            def __rmul__(self, x): return mint.fix(super().__rmul__(x))
            def __floordiv__(self, x): return self * mint.mod_inv(x)
            def __rfloordiv__(self, x): return self.inv * x
            def __truediv__(self, x): return self * mint.mod_inv(x)
            def __rtruediv__(self, x): return self.inv * x
            def __pow__(self, x): return self.cast(super().__pow__(x, self.mod))
            def __neg__(self): return mint.mod-self
            def __pos__(self): return self
            def __abs__(self): return self
            def __class_getitem__(self, x: int): return self.cache[x]
        mint.set_mod(998244353)

        A = read(list[list[mint],N])
        B = mat_pow(A, K)
    else:
        '''
        ╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
                     https://kobejean.github.io/cp-library               
        '''
        
        
        
        
        
        def mat_pow(A,K,mod):
            N = len(A)
            ret = A if K & 1 else mat_id(N)
            for i in range(1,K.bit_length()):
                A = mat_mul(A,A,mod) 
                if K >> i & 1:
                    ret = mat_mul(ret,A,mod) 
            return ret 
        '''
        ╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
                     https://kobejean.github.io/cp-library               
        '''
        
        
        
        
        
        def mat_mul(A,B,mod):
            assert len(A[0]) == len(B)
            R = [[0]*len(B[0]) for _ in range(len(A))] 
            for i,Ri in enumerate(R):
                for k,Aik in enumerate(A[i]):
                    for j,Bkj in enumerate(B[k]):
                        Ri[j] = (Ri[j] + Aik*Bkj) % mod
            return R
        '''
        ╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
                     https://kobejean.github.io/cp-library               
        '''
        
        
        
        
        def mat_id(N):
            return [[int(i==j) for j in range(N)] for i in range(N)]

        A = [read() for _ in range(N)]
        B = mat_pow(A, K, mod)

    for row in B:
        write(*row)

'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
             https://kobejean.github.io/cp-library               
'''
from typing import Type, Union, overload
from typing import TypeVar

_S = TypeVar('S'); _T = TypeVar('T'); _U = TypeVar('U'); _T1 = TypeVar('T1'); _T2 = TypeVar('T2'); _T3 = TypeVar('T3'); _T4 = TypeVar('T4'); _T5 = TypeVar('T5'); _T6 = TypeVar('T6')


@overload
def read() -> list[int]: ...
@overload
def read(spec: Type[_T], char=False) -> _T: ...
@overload
def read(spec: _U, char=False) -> _U: ...
@overload
def read(*specs: Type[_T], char=False) -> tuple[_T, ...]: ...
@overload
def read(*specs: _U, char=False) -> tuple[_U, ...]: ...
def read(*specs: Union[Type[_T],_T], char=False):
    IO.stdin.char = char
    if not specs: return IO.stdin.readnumsinto([])
    parser: _T = Parser.compile(specs[0] if len(specs) == 1 else specs)
    return parser(IO.stdin)
from os import read as os_read, write as os_write, fstat as os_fstat
import sys
from __pypy__.builders import StringBuilder



def max2(a, b): return a if a > b else b

class IOBase:
    @property
    def char(io) -> bool: ...
    @property
    def writable(io) -> bool: ...
    def __next__(io) -> str: ...
    def write(io, s: str) -> None: ...
    def readline(io) -> str: ...
    def readtoken(io) -> str: ...
    def readtokens(io) -> list[str]: ...
    def readints(io) -> list[int]: ...
    def readdigits(io) -> list[int]: ...
    def readnums(io) -> list[int]: ...
    def readchar(io) -> str: ...
    def readchars(io) -> str: ...
    def readinto(io, lst: list[str]) -> list[str]: ...
    def readcharsinto(io, lst: list[str]) -> list[str]: ...
    def readtokensinto(io, lst: list[str]) -> list[str]: ...
    def readintsinto(io, lst: list[int]) -> list[int]: ...
    def readdigitsinto(io, lst: list[int]) -> list[int]: ...
    def readnumsinto(io, lst: list[int]) -> list[int]: ...
    def wait(io): ...
    def flush(io) -> None: ...
    def line(io) -> list[str]: ...

class IO(IOBase):
    BUFSIZE = 1 << 16; stdin: 'IO'; stdout: 'IO'
    __slots__ = 'f', 'file', 'B', 'O', 'V', 'S', 'l', 'p', 'char', 'sz', 'st', 'ist', 'writable', 'encoding', 'errors'
    def __init__(io, file):
        io.file = file
        try: io.f = file.fileno(); io.sz, io.writable = max2(io.BUFSIZE, os_fstat(io.f).st_size), ('x' in file.mode or 'r' not in file.mode)
        except: io.f, io.sz, io.writable = -1, io.BUFSIZE, False
        io.B, io.O, io.S = bytearray(), [], StringBuilder(); io.V = memoryview(io.B); io.l = io.p = 0
        io.char, io.st, io.ist, io.encoding, io.errors = False, [], [], 'ascii', 'ignore'
    def _dec(io, l, r): return io.V[l:r].tobytes().decode(io.encoding, io.errors)
    def readbytes(io, sz): return os_read(io.f, sz)
    def load(io):
        while io.l >= len(io.O):
            if not (b := io.readbytes(io.sz)):
                if io.O[-1] < len(io.B): io.O.append(len(io.B))
                break
            pos = len(io.B); io.B.extend(b)
            while ~(pos := io.B.find(b'\n', pos)): io.O.append(pos := pos+1)
    def __next__(io):
        if io.char: return io.readchar()
        else: return io.readtoken()
    def readchar(io):
        io.load(); r = io.O[io.l]
        c = chr(io.B[io.p])
        if io.p >= r-1: io.p = r; io.l += 1
        else: io.p += 1
        return c
    def write(io, s: str): io.S.append(s)
    def readline(io): io.load(); l, io.p = io.p, io.O[io.l]; io.l += 1; return io._dec(l, io.p)
    def readtoken(io):
        io.load(); r = io.O[io.l]
        if ~(p := io.B.find(b' ', io.p, r)): s = io._dec(io.p, p); io.p = p+1
        else: s = io._dec(io.p, r-1); io.p = r; io.l += 1
        return s
    def readtokens(io): io.st.clear(); return io.readtokensinto(io.st)
    def readints(io): io.ist.clear(); return io.readintsinto(io.ist)
    def readdigits(io): io.ist.clear(); return io.readdigitsinto(io.ist)
    def readnums(io): io.ist.clear(); return io.readnumsinto(io.ist)
    def readchars(io): io.load(); l, io.p = io.p, io.O[io.l]; io.l += 1; return io._dec(l, io.p-1)
    def readinto(io, lst):
        if io.char: return io.readcharsinto(lst)
        else: return io.readtokensinto(lst)
    def readcharsinto(io, lst): lst.extend(io.readchars()); return lst
    def readtokensinto(io, lst): 
        io.load(); r = io.O[io.l]
        while ~(p := io.B.find(b' ', io.p, r)): lst.append(io._dec(io.p, p)); io.p = p+1
        lst.append(io._dec(io.p, r-1)); io.p = r; io.l += 1; return lst
    def _readint(io, r):
        while io.p < r and io.B[io.p] <= 32: io.p += 1
        if io.p >= r: return None
        minus = x = 0
        if io.B[io.p] == 45: minus = 1; io.p += 1
        while io.p < r and io.B[io.p] >= 48: x = x * 10 + (io.B[io.p] & 15); io.p += 1
        io.p += 1
        return -x if minus else x
    def readintsinto(io, lst):
        io.load(); r = io.O[io.l]
        while io.p < r and (x := io._readint(r)) is not None: lst.append(x)
        io.l += 1; return lst
    def _readdigit(io): d = io.B[io.p] & 15; io.p += 1; return d
    def readdigitsinto(io, lst):
        io.load(); r = io.O[io.l]
        while io.p < r and io.B[io.p] > 32: lst.append(io._readdigit())
        if io.B[io.p] == 10: io.l += 1
        io.p += 1
        return lst
    def readnumsinto(io, lst):
        if io.char: return io.readdigitsinto(lst)
        else: return io.readintsinto(lst)
    def line(io): io.st.clear(); return io.readinto(io.st)
    def wait(io):
        io.load(); r = io.O[io.l]
        while io.p < r: yield
    def flush(io):
        if io.writable: os_write(io.f, io.S.build().encode(io.encoding, io.errors)); io.S = StringBuilder()
sys.stdin = IO.stdin = IO(sys.stdin); sys.stdout = IO.stdout = IO(sys.stdout)
import typing
from numbers import Number
from types import GenericAlias 
from typing import Callable, Collection

class Parsable:
    @classmethod
    def compile(cls):
        def parser(io: 'IOBase'): return cls(next(io))
        return parser
    @classmethod
    def __class_getitem__(cls, item): return GenericAlias(cls, item)

class Parser:
    def __init__(self, spec):  self.parse = Parser.compile(spec)
    def __call__(self, io: IOBase): return self.parse(io)
    @staticmethod
    def compile_type(cls, args = ()):
        if issubclass(cls, Parsable): return cls.compile(*args)
        elif issubclass(cls, (Number, str)):
            def parse(io: IOBase): return cls(next(io))              
            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(io: IOBase): return cls(next(io))              
            return parse
        else: raise NotImplementedError()
    @staticmethod
    def compile(spec=int):
        if isinstance(spec, (type, GenericAlias)):
            cls, args = typing.get_origin(spec) or spec, typing.get_args(spec) or tuple()
            return Parser.compile_type(cls, args)
        elif isinstance(offset := spec, Number): 
            cls = type(spec)  
            def parse(io: IOBase): return cls(next(io)) + 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(io: IOBase): return fn(next(io))
            return parse
        else: raise NotImplementedError()
    @staticmethod
    def compile_line(cls, spec=int):
        if spec is int:
            def parse(io: IOBase): return cls(io.readnums())
        elif spec is str:
            def parse(io: IOBase): return cls(io.line())
        else:
            fn = Parser.compile(spec)
            def parse(io: IOBase): return cls((fn(io) for _ in io.wait()))
        return parse
    @staticmethod
    def compile_repeat(cls, spec, N):
        fn = Parser.compile(spec)
        def parse(io: IOBase): return cls([fn(io) for _ in range(N)])
        return parse
    @staticmethod
    def compile_children(cls, specs):
        fns = tuple((Parser.compile(spec) for spec in specs))
        def parse(io: IOBase): return cls([fn(io) for fn in fns])  
        return parse
    @staticmethod
    def compile_tuple(cls, specs):
        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()

def write(*args, **kwargs):
    '''Prints the values to a stream, or to stdout_fast by default.'''
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", IO.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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