結果

問題 No.2248 max(C)-min(C)
ユーザー 👑 Kazun
提出日時 2023-03-17 22:15:39
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,328 ms / 3,000 ms
コード長 11,218 bytes
コンパイル時間 383 ms
コンパイル使用メモリ 82,688 KB
実行使用メモリ 270,044 KB
最終ジャッジ日時 2024-09-27 04:58:11
合計ジャッジ時間 27,268 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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ファイルパターン 結果
sample AC * 3
other AC * 51
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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

class Segment_Tree():
    def __init__(self, L, calc, unit):
        """ calc を演算とするリスト L の Segment Tree を作成
        calc: 演算 (2変数関数, Monoid)
        unit: Monoid calc の単位元 (xe=ex=xを満たすe)
        """
        self.calc=calc
        self.unit=unit
        N=len(L); self.n=N
        d=max(1,(N-1).bit_length())
        k=1<<d
        self.data=data=[unit]*k+L+[unit]*(k-len(L))
        self.N=k
        self.depth=d
        for i in range(k-1,0,-1):
            data[i]=calc(data[i<<1], data[i<<1|1])
    def get(self, k):
        """ 第 k 要素を取得
        """
        assert 0<=k<self.N,"添字が範囲外"
        return self.data[k+self.N]
    def update(self, k, x):
        """第k要素をxに変え,更新を行う.
        k:数列の要素
        x:更新後の値
        """
        assert 0<=k<self.N,"添字が範囲外"
        m=k+self.N
        data=self.data; calc=self.calc
        data[m]=x
        while m>1:
            m>>=1
            data[m]=calc(data[m<<1], data[m<<1|1])
    def product(self, l, r, left_closed=True,right_closed=True):
        L=l+self.N+(not left_closed)
        R=r+self.N+(right_closed)
        vL=self.unit
        vR=self.unit
        data=self.data; calc=self.calc
        while L<R:
            if L&1:
                vL=calc(vL, data[L])
                L+=1
            if R&1:
                R-=1
                vR=calc(data[R], vR)
            L>>=1
            R>>=1
        return calc(vL,vR)
    def all_product(self):
        return self.data[1]
    def max_right(self, left, cond):
        """ 以下の2つをともに満たす x の1つを返す.\n
        (1) r=left or cond(data[left]*data[left+1]*...*data[r-1]): True
        (2) r=N or cond(data[left]*data[left+1]*...*data[r]): False
        ※ cond が単調減少の時, cond(data[left]*...*data[r-1]) を満たす最大の r となる.
        cond:関数(引数が同じならば結果も同じ)
        cond(unit): True
        0<=left<=N
        """
        assert 0<=left<=self.N,"添字が範囲外"
        assert cond(self.unit),"単位元が条件を満たさない."
        if left==self.N:
            return self.N
        left+=self.N
        sm=self.unit
        calc=self.calc; data=self.data
        first=True
        while first or (left & (-left))!=left:
            first=False
            while left%2==0:
                left>>=1
            if not cond(calc(sm, data[left])):
                while left<self.N:
                    left<<=1
                    if cond(calc(sm, data[left])):
                        sm=calc(sm, data[left])
                        left+=1
                return left-self.N
            sm=calc(sm, data[left])
            left+=1
        return self.N
    def min_left(self, right, cond):
        """ 以下の2つをともに満たす y の1つを返す.\n
        (1) l=right or cond(data[l]*data[l+1]*...*data[right-1]): True
        (2) l=0 or cond(data[l-1]*data[l]*...*data[right-1]): False
        ※ cond が単調増加の時, cond(data[l]*...*data[right-1]) を満たす最小の l となる.
        cond: 関数(引数が同じならば結果も同じ)
        cond(unit): True
        0<=right<=N
        """
        assert 0<=right<=self.N,"添字が範囲外"
        assert cond(self.unit),"単位元が条件を満たさない."
        if right==0:
            return 0
        right+=self.N
        sm=self.unit
        calc=self.calc; data=self.data
        first=1
        while first or (right & (-right))!=right:
            first=0
            right-=1
            while right>1 and right&1:
                right>>=1
            if not cond(calc(data[right], sm)):
                while right<self.N:
                    right=2*right+1
                    if cond(calc(data[right], sm)):
                        sm=calc(data[right], sm)
                        right-=1
                return right+1-self.N
            sm=calc(data[right], sm)
        return 0
    def __getitem__(self,k):
        return self.get(k)
    def __setitem__(self,k,x):
        return self.update(k,x)
    def __iter__(self):
        for i in range(self.n):
            yield self.get(i)
#==================================================
" Reference: https://qiita.com/tatyam/items/492c70ac4c955c055602"
# ※ 計算量が O(sqrt(N)) per query なので, 過度な期待はしないこと.
from bisect import bisect_left, bisect_right, insort
class Sorted_Multiset:
    BUCKET_RATIO=50
    REBUILD_RATIO=170
    def __init__(self, A=[]):
        A=list(A)
        if not all(A[i]<=A[i+1] for i in range(len(A)-1)):
            A=sorted(A)
        self.__build(A)
        return
    def __build(self, A=None):
        if A is None:
            A=list(self)
        self.N=N=len(A)
        K=1
        while self.BUCKET_RATIO*K*K<N:
            K+=1
        self.list=[A[N*i//K: N*(i+1)//K] for i in range(K)]
    def __iter__(self):
        for A in self.list:
            for a in A:
                yield a
    def __reversed__(self):
        for A in reversed(self.list):
            for a in reversed(A):
                yield a
    def __len__(self):
        return self.N
    def __bool__(self):
        return bool(self.N)
    def __str__(self):
        string=str(list(self))
        return "{"+string[1:-1]+"}"
    def __repr__(self):
        return "Sorted Multiset: "+str(self)
    def __find_bucket(self, x):
        for A in self.list:
            if x<=A[-1]:
                return A
        else:
            return A
    def __contains__(self, x):
        if self.N==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):
        if self.N==0:
            self.list=[[x]]
            self.N+=1
            return
        A=self.__find_bucket(x)
        insort(A, x)
        self.N+=1
        if len(A)>len(self.list)*self.REBUILD_RATIO:
            self.__build()
    def discard(self, x):
        if self.N==0:
            return False
        A=self.__find_bucket(x)
        i=bisect_left(A, x)
        if not(i!=len(A) and A[i]==x):
            return False # x が存在しないので...
        A.pop(i)
        self.N-=1
        if len(A)==0:
            self.__build()
        return True
    def remove(self, x):
        if not self.discard(x):
            raise KeyError(x)
    #=== get, pop
    def __getitem__(self, index):
        if index<0:
            index+=self.N
            if index<0:
                raise IndexError("index out of range")
        for A in self.list:
            if index<len(A):
                return A[index]
            index-=len(A)
        else:
            raise IndexError("index out of range")
    def get_min(self):
        if self.N==0:
            raise ValueError("This is empty set.")
        return self.list[0][0]
    def pop_min(self):
        if self.N==0:
            raise ValueError("This is empty set.")
        A=self.list[0]
        value=A.pop(0)
        self.N-=1
        if len(A)==0:
            self.__build()
        return value
    def get_max(self):
        if self.N==0:
            return ValueError("This is empty set.")
        return self.list[-1][-1]
    def pop_max(self):
        if self.N==0:
            raise ValueError("This is empty set.")
        A=self.list[-1]
        value=A.pop(-1)
        self.N-=1
        if len(A)==0:
            self.__build()
        return value
    #=== previous, next
    def previous(self, value, mode=False):
        """ S にある value 未満で最大の要素を返す (存在しない場合は None)
        mode: True のときは "未満" が "以下" になる.
        """
        if self.N==0:
            return None
        if mode:
            for A in reversed(self.list):
                if A[0]<=value:
                    return A[bisect_right(A,value)-1]
        else:
            for A in reversed(self.list):
                if A[0]<value:
                    return A[bisect_left(A,value)-1]
    def next(self, value, mode=False):
        """ S にある value より大きい最小の要素を返す (存在しない場合は None)
        mode: True のときは "より大きい" が "以上" になる.
        """
        if self.N==0:
            return None
        if mode:
            for A in self.list:
                if A[-1]>=value:
                    return A[bisect_left(A,value)]
        else:
            for A in self.list:
                if A[-1]>value:
                    return A[bisect_right(A,value)]
    #=== count
    def less_count(self, value, equal=False):
        """ a < value となる S の元 a の個数を求める.
        equal=True ならば, a < value が a <= value になる.
        """
        count=0
        if equal:
            for A in self.list:
                if A[-1]>value:
                    return count+bisect_right(A, value)
                count+=len(A)
        else:
            for A in self.list:
                if A[-1]>=value:
                    return count+bisect_left(A, value)
                count+=len(A)
        return count
    def more_count(self, value, equal=False):
        """ a > value となる S の元 a の個数を求める.
        equal=True ならば, a > value が a >= value になる.
        """
        return self.N-self.less_count(value, not equal)
    #===
    def is_upper_bound(self, x, equal=True):
        if self.N:
            a=self.list[-1][-1]
            return (a<x) or (bool(equal) and a==x)
        else:
            return True
    def is_lower_bound(self, x, equal=True):
        if self.N:
            a=self.list[0][0]
            return (x<a) or (bool(equal) and a==x)
        else:
            return True
    #=== index
    def index(self, value):
        index=0
        for A in self.list:
            if A[-1]>value:
                i=bisect_left(A, value)
                if A[i]==value:
                    return index+i
                else:
                    raise ValueError("{} is not in Multiset".format(value))
            index+=len(A)
        raise ValueError("{} is not in Multiset".format(value))
#==================================================
def solve():
    N=int(input())
    A=list(map(int,input().split()))
    B=list(map(int,input().split()))
    D=[(A[i]+B[i])//2 for i in range(N)]
    for i in range(N):
        A[i],B[i]=min(A[i],B[i]), max(A[i],B[i])
    S=Segment_Tree([(B[i],i) for i in range(N)], max, (-1, 0))
    E=Sorted_Multiset()
    for i in range(N):
        E.add(B[i])
    remain=[2]*N
    ans=E.get_max()-E.get_min()
    while True:
        x,i=S.all_product()
        if remain[i]==2:
            S.update(i,(D[i],i))
            E.remove(B[i])
            E.add(D[i])
        elif remain[i]==1:
            S.update(i,(A[i],i))
            E.remove(D[i])
            E.add(A[i])
        else:
            break
        remain[i]-=1
        ans=min(ans, E.get_max()-E.get_min())
    return ans
#==================================================
print(solve())
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