結果

問題 No.1835 Generalized Monty Hall Problem
ユーザー 👑 KazunKazun
提出日時 2022-02-11 21:35:14
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 77 ms / 1,000 ms
コード長 4,766 bytes
コンパイル時間 407 ms
コンパイル使用メモリ 86,912 KB
実行使用メモリ 71,684 KB
最終ジャッジ日時 2023-09-10 01:11:38
合計ジャッジ時間 2,479 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge13
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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 73 ms
71,420 KB
testcase_01 AC 73 ms
71,356 KB
testcase_02 AC 77 ms
71,464 KB
testcase_03 AC 72 ms
71,356 KB
testcase_04 AC 73 ms
71,348 KB
testcase_05 AC 74 ms
71,288 KB
testcase_06 AC 73 ms
71,468 KB
testcase_07 AC 74 ms
71,584 KB
testcase_08 AC 75 ms
71,684 KB
testcase_09 AC 76 ms
71,420 KB
testcase_10 AC 74 ms
71,472 KB
testcase_11 AC 74 ms
71,404 KB
testcase_12 AC 75 ms
71,384 KB
testcase_13 AC 74 ms
71,644 KB
testcase_14 AC 72 ms
71,284 KB
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ソースコード

diff # 

from math import gcd

class Fraction():
    __slots__=["a","b"]

    ##入力定義
    def __init__(self, Numerator=0, Denominator=1, expanded=False, reduction=False):
        """分数のオブジェクトを生成する.

        Numerator: 分子
        Denominator: 分母 (!=0)
        """
        assert Denominator or expanded,"分母が0"

        if Denominator<0:
            Numerator*=-1
            Denominator*=-1

        self.a=Numerator
        self.b=Denominator
        if reduction:
            g=gcd(Numerator, Denominator)
            self.a=Numerator//g
            self.b=Denominator//g

    #表示定義
    def __str__(self):
        if self.b==1:
            return str(self.a)
        else:
            return "{}/{}".format(self.a,self.b)

    __repr__=__str__

    #四則演算定義
    def __add__(self,other):
        if other.__class__==Fraction:
            x=self.a*other.b+self.b*other.a
            y=self.b*other.b
        elif other.__class__==int:
            x=self.a-self.b*other
            y=self.b
        else:
            assert 0,"型が違う"
        return Fraction(x,y)

    def __radd__(self,other):
        return self+other

    def __sub__(self,other):
        if other.__class__==Fraction:
            x=self.a*other.b-self.b*other.a
            y=self.b*other.b
        elif other.__class__==int:
            x=self.a+self.b*other
            y=self.b
        else:
            assert 0,"型が違う"
        return Fraction(x,y)

    def __rsub__(self,other):
        return -self+other

    def __mul__(self,other):
        if other.__class__==Fraction:
            x=self.a*other.a
            y=self.b*other.b
        elif other.__class__==int:
            x=self.a*other
            y=self.b
        else:
            assert 0,"型が違う"

        return Fraction(x,y)

    def __rmul__(self,other):
        return self*other

    def __floordiv__(self,other):
        if other==Fraction():
            raise ZeroDivisionError

        H=self/other
        return H.a//H.b

    def __rfloordiv__(self,other):
        if self==Fraction():
            raise ZeroDivisionError

        H=other/self
        return H.a//H.b

    def __truediv__(self,other):
        assert other,"除数が0"

        if other.__class__==Fraction:
            x=self.a*other.b
            y=self.b*other.a
        elif other.__class__==int:
            x=self.a
            y=self.b*other
        else:
            assert 0,"型が違う"

        return Fraction(x,y)

    def __rtruediv__(self,other):
        assert self,"除数が0"
        if other.__class__==Fraction:
            x=other.a*self.b
            y=other.b*self.a
        elif other.__class__==int:
            x=other*self.b
            y=self.a
        else:
            assert 0,"型が違う"
        return Fraction(x,y)

    def __pow__(self,m):
        alpha,beta=self.a,self.b
        if m<0:
            alpha,beta=beta,alpha
            m=-m

        return Fraction(pow(alpha,m),pow(beta,m))

    #丸め
    def __floor__(self):
        return self.a//self.b

    def __ceil__(self):
        return (self.a+self.b-1)//self.b

    #真偽値
    def __bool__(self):
        return bool(self.a)

    #比較
    def __eq__(self,other):
        if other.__class__==Fraction:
            return self.a*other.b==self.b*other.a
        elif other.__class__==int:
            return self.a==self.b*other
        else:
            assert 0,"型が違う"

    def __nq__(self,other):
        return not(self==other)

    def __lt__(self,other):
        return self<=other and self!=other

    def __le__(self,other):
        if other.__class__==Fraction:
            return self.a*other.b<=self.b*other.a
        elif other.__class__==int:
            return self.a<=self.b*other
        else:
            assert 0,"型が違う"

    def __gt__(self,other):
        return other<=self and other!=self

    def __ge__(self,other):
        return other<=self

    #その他
    def __float__(self):
        return self.a/self.b

    def sign(self):
        s=self.a*self.b
        if s>0:return 1
        elif s==0:return 0
        else:return -1

    #符号
    def __pos__(self):
        return self

    def __neg__(self):
        return Fraction(-self.a,self.b)

    def __abs__(self):
        if self.a>0:
            return self
        else:
            return -self

    #その他
    def is_unit(self):
        return self.a==1

    def __hash__(self):
        return hash(10**9*self.a+self.b)
#==================================================

N,M,K=map(int,input().split())

A=Fraction(M,N)


B=Fraction(M,N)*Fraction(M-1,N-K-1)+(Fraction(N-M,N))*Fraction(M,N-K-1)

C=max(A,B)
C=Fraction(C.a,C.b,reduction=True)
print(C.a,C.b)
0