#704717 (PyPy3) No.837 Noelちゃんと星々2

提出ソース

結果

問題	No.837 Noelちゃんと星々2
ユーザー	None
提出日時	2021-10-06 06:07:50
言語	PyPy3 (7.3.15)
結果	AC
実行時間	768 ms / 2,000 ms
コード長	12,517 bytes
コンパイル時間	345 ms
コンパイル使用メモリ	82,464 KB
実行使用メモリ	143,024 KB
最終ジャッジ日時	2024-06-11 14:31:51
合計ジャッジ時間	9,874 ms
ジャッジサーバーID （参考情報）	judge3 / judge4

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	742 ms 142,864 KB
testcase_01	AC	749 ms 142,992 KB
testcase_02	AC	768 ms 142,596 KB
testcase_03	AC	759 ms 142,872 KB
testcase_04	AC	757 ms 142,800 KB
testcase_05	AC	765 ms 142,616 KB
testcase_06	AC	742 ms 143,024 KB
testcase_07	AC	743 ms 142,604 KB
testcase_08	AC	747 ms 142,552 KB
testcase_09	AC	53 ms 65,536 KB
testcase_10	AC	47 ms 62,080 KB
testcase_11	AC	47 ms 62,848 KB
testcase_12	AC	41 ms 55,808 KB
testcase_13	AC	41 ms 55,168 KB
testcase_14	AC	51 ms 63,744 KB
testcase_15	AC	51 ms 63,616 KB
testcase_16	AC	40 ms 55,168 KB
testcase_17	AC	49 ms 63,744 KB
testcase_18	AC	41 ms 55,296 KB
testcase_19	AC	42 ms 55,680 KB
testcase_20	AC	49 ms 63,488 KB
testcase_21	AC	54 ms 66,432 KB
testcase_22	AC	52 ms 64,640 KB
testcase_23	AC	50 ms 63,744 KB
testcase_24	AC	41 ms 54,528 KB
testcase_25	AC	42 ms 55,296 KB
testcase_26	AC	40 ms 55,032 KB
testcase_27	AC	41 ms 55,296 KB
testcase_28	AC	41 ms 54,912 KB
testcase_29	AC	40 ms 54,784 KB
testcase_30	AC	39 ms 55,040 KB
testcase_31	AC	39 ms 54,960 KB
testcase_32	AC	40 ms 55,296 KB

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ソースコード

raw source code

class Bit:
    def __init__(self, n, array=[]):
        """
        :param n: number of elements
        """
        self.n = n
        self.tree = [0]*(n+1)
        self.depth = n.bit_length() - 1
        for i, a in enumerate(array):
            self.add(i, a)

    def get(self,i):
        """ return summation of elements in [0,i) """
        s = 0
        i -= 1
        while i >= 0:
            s += self.tree[i]
            i = (i & (i + 1) )- 1
        return s

    def build(self, array):
        """ bulid BIT from array """
        for i, a in enumerate(array):
            self.add(i, a)

    def add(self, i, x):
        """ add x to i-th element """
        while i < self.n:
            self.tree[i] += x
            i |= i + 1

    def get_range(self,i,j):
        """ return summation of elements in [i,j) """
        if i == 0:
            return self.get(j)
        return self.get(j)-self.get(i)

    def lower_bound(self, x, equal=False):
        """
        return tuple = (return maximum i s.t. a0+a1+...+ai < x (if not existing, -1 ) , a0+a1+...+ai )
        if one wants to include equal (i.e., a0+a1+...+ai <= x), please set equal = True
        (Cation) We must assume that A_i>=0
        """
        sum_ = 0
        pos = -1    # 1-indexed の時は pos = 0
        if not equal:
            for i in range(self.depth, -1, -1):
                k = pos + (1 << i)
                if k < self.n and sum_ + self.tree[k] < x:  # 1-indexed の時は k <= self.n
                    sum_ += self.tree[k]
                    pos += 1 << i
        if equal:
            for i in range(self.depth, -1, -1):
                k = pos + (1 << i)
                if k < self.n and sum_ + self.tree[k] <= x: # 1-indexed の時は k <= self.n
                    sum_ += self.tree[k]
                    pos += 1 << i
        return pos, sum_

    def __getitem__(self, i):
        """ [a0, a1, a2, ...] """
        if i<0: i=self.n+i
        return self.get_range(i,i+1)

    def __setitem__(self, i, x):
        self.add(i,x-self[i])

    def __iter__(self):
        """ [a0, a1, a2, ...] """
        for i in range(self.n):
            yield self.get_range(i,i+1)

    def __str__(self):
        text1 = " ".join(["element:            "] + list(map(str, self)))
        text2 = " ".join(["cumsum(1-indexed):  "]+list(str(self.get(i)) for i in range(1,self.n+1)))
        return "\n".join((text1, text2))

class SortedList:
    def __init__(self, n, A=[]):
        """
        :param n: miximum value of A
        self.size: number of elements in BitSet
        """
        self.n = n
        self.p = Bit(self.n + 1)
        self.size = 0
        self.flip = 0
        self.S = Bit(self.n + 1)
        for a in A:
            self.add(a)

    def add(self,x):
        self.p.add(x, 1)
        self.S.add(x, x)
        self.size += 1

    def remove(self,x):
        self.p.add(x, -1)
        self.S.add(x, -x)
        self.size -= 1

    def bisect_left(self,x):
        """ return bisect_left(sorted(B),x) """
        if x <= self.n:
            return self.p.get(x)
        else:
            return self.size

    def bisect_right(self,x):
        """ return bisect_right(sorted(B),x) """
        x += 1
        if x <= self.n:
            return self.p.get(x)
        else:
            return self.size

    def flip_counter(self):
        return self.flip

    def count(self,x):
        return self.p[x]

    def count_range(self,l,r):
        """ return number of elements in open set [l,r)"""
        return self.bisect_left(r)-self.bisect_left(l)

    def get_range(self,l,r):
        """ return sum of elements in open set [l,r)"""
        Sl=self.S.get(l)
        if r <= self.n:
            Sr = self.S.get(r)
        else:
            Sr = self.S.get(self.n+1)
        return Sr-Sl

    def minimum(self,k=1):
        """ return k-th minimum value """
        if k <= self.size:
            return self.p.lower_bound(k)[0] + 1
        else:
            sys.stderr.write("minimum: list index out of range (k={0})\n".format(k))

    def min(self):
        return self.minimum(1)

    def max(self):
        return self.p.lower_bound(self.size)[0] + 1

    def upper_bound(self,x,equal=False):
        """ return maximum element lower than x """
        k = self.p.get(x+equal)
        if k:
            return self.minimum(k)
        else:
            sys.stderr.write("upper_bound: no element smaller than {0} in this BitSet\n".format(x))

    def lower_bound(self,x,equal=False):
        """ return minimum element greater than x """
        k =self.p.get(x+1-equal)+1
        if k <= self.size:
            return self.minimum(k)
        else:
            sys.stderr.write("lower_bound: no element larger than {0} in this BitSet\n".format(x))

    def median(self):
        return self.minimum(self.size//2 + 1)

    def absolute_minimum(self):
        """
        return min value of
            sum_i |B[i]-x|
        over any x
        """
        INF=10**18
        res=0
        m=self.median()
        res+=self.count_range(-INF,m)*m-self.get_range(-INF,m)
        res+=self.get_range(m,INF)-self.count_range(m,INF)*m
        return res

    def __getitem__(self, k):
        """
        return k-th minimum element (0-indexed)
        B[k] = sorted(A)[k]
        """
        if len(self)==0:
            sys.stderr.write("__getitem__: no elements exist in this BitSet\n")
        elif k >= len(self):
            sys.stderr.write("__getitem__: index (={0}) is larger than the maximum index (={1})\n".format(k,len(self)-1))
        elif k >= 0:
            return self.minimum(k+1)
        else:
            sys.stderr.write("__getitem__: index (={0}) is negative \n".format(k))

    def __len__(self):
        return self.size

    def __iter__(self):
        """ return sorted list """
        for i in range(self.n+1):
            if self.p[i]:
                for _ in range(self.p[i]):
                    yield i

    def __str__(self):
        """ return sorted list """
        text1 = " ".join(list(map(str, self)))
        return "[" + text1 + "]"

class SortedList2:
    """ if we need compress """
    def __init__(self, data, A=[]):
        """
        self.size: number of elements in BitSet
        """
        self.data = sorted(list(set(data)))
        self.n = len(self.data)
        self.p = Bit(self.n + 1)
        self.S = Bit(self.n + 1)
        self.size = 0
        self.code = {}
        self.decode = []
        for i, b in enumerate(self.data):
            self.code[b] = i
            self.decode.append(b)
        for a in A:
            self.add(a)

    def add(self,x):
        self.p.add(self.code[x], 1)
        self.S.add(self.code[x], x)
        self.size += 1

    def remove(self,x):
        self.p.add(self.code[x], -1)
        self.S.add(self.code[x], -x)
        self.size -= 1

    def bisect_left(self,x):
        """ return bisect_left(sorted(B),x) """
        if x in self.code.keys():
            return self.p.get(self.code[x])
        else:
            return self.p.get(bisect_right(self.data,x))

    def bisect_right(self,x):
        """ return bisect_right(sorted(B),x) """
        x += 1
        if x in self.code.keys():
            return self.p.get(self.code[x])
        else:
            return self.p.get(bisect_right(self.data,x))

    def count(self,x):
        return self.p[self.code[x]]

    def count_range(self,l,r):
        """ return number of elements in open set [l,r)"""
        return self.bisect_left(r)-self.bisect_left(l)

    def get_range(self,l,r):
        if l in self.code.keys():
            Sl=self.S.get(self.code[l])
        else:
            Sl=self.S.get(bisect_right(self.data,l))

        if r in self.code.keys():
            Sr=self.S.get(self.code[r])
        else:
            Sr=self.S.get(bisect_right(self.data,r))

        return Sr-Sl

    def minimum(self,k=1):
        """ return k-th minimum value """
        if k <= self.size:
            return self.decode[self.p.lower_bound(k)[0] + 1]
        else:
            sys.stderr.write("minimum: list index out of range (k={0})\n".format(k))

    def min(self):
        return self.minimum(1)

    def max(self):
        return self.decode[self.p.lower_bound(self.size)[0] + 1]

    def upper_bound(self,x,equal=False):
        """ return maximum element lower than x """
        if x in self.code.keys():
            y = self.code[x] + equal
        else:
            y = bisect_right(self.data, x)
        k = self.p.get(y)
        if k:
            return self.minimum(k)
        else:
            sys.stderr.write("upper_bound: no element smaller than {0} in this BitSet\n".format(x))

    def lower_bound(self,x,equal=False):
        """ return minimum element greater than x """
        if x in self.code.keys():
            y = self.code[x] + 1 - equal
        else:
            y = bisect_left(self.data, x)
        k =self.p.get(y)+1
        if k <= self.size:
            return self.minimum(k)
        else:
            sys.stderr.write("lower_bound: no element larger than {0} in this BitSet\n".format(x))

    def nearest(self,x,k):
        """ return k-th nearest value to x """
        if k>len(self):
            sys.stderr.write("nearest: k (= {0}) is larger than the size of this BitSet\n".format(k))
            return

        def test(d):
            r=self.bisect_right(x+d)-1
            l=self.bisect_left(x-d)
            return r-l+1<=k

        ok,ng=0,10**18+1
        while abs(ok-ng)>1:
            mid=(ok+ng)//2
            if test(mid):
                ok=mid
            else:
                ng=mid
        d=ok

        r=self.bisect_right(x+d)-1
        l=self.bisect_left(x-d)
        if d==0:
            R=self.lower_bound(x,equal=True)
            L=self.upper_bound(x,equal=True)
            if abs(x-L)==abs(R-x):
                if self.count(L)>=k: return L
                else: return R
            elif abs(x-L)<abs(R-x): return L
            else: return R
        elif r-l+1==k:
            R=self[r]
            L=self[l]
            if abs(x-L)<=abs(R-x): return R
            else: return L
        else:
            if l<=0: return self[r+1]
            elif r>=len(self)-1: return self[l-1]
            else:
                R=self[r+1]
                L=self[l-1]
                if abs(x-L)==abs(R-x):
                    if self.count(L)>=k-(r-l+1):
                        return L
                    else: return R
                elif abs(x-L)<abs(R-x): return L
                else: return R

    def median(self):
        return self.minimum(self.size//2 + 1)

    def absolute_minimum(self):
        """
        return min value of
            sum_i |B[i]-x|
        over any x
        """
        INF=10**18
        res=0
        m=self.median()
        res+=self.count_range(-INF,m)*m-self.get_range(-INF,m)
        res+=self.get_range(m,INF)-self.count_range(m,INF)*m
        return res

    def __getitem__(self, k):
        """
        return k-th minimum element (0-indexed)
        B[k] = sorted(A)[k]
        """
        if len(self)==0:
            sys.stderr.write("__getitem__: no elements exist in this BitSet\n")
        elif k >= len(self):
            sys.stderr.write("__getitem__: index (={0}) is larger than the maximum index (={1})\n".format(k,len(self)-1))
        elif k >= 0:
            return self.minimum(k+1)
        else:
            sys.stderr.write("__getitem__: index (={0}) is negative \n".format(k))

    def __len__(self):
        return self.size

    def __iter__(self):
        """ return sorted list """
        for i in range(self.n+1):
            if self.p[i]:
                for _ in range(self.p[i]):
                    yield self.decode[i]

    def __str__(self):
        """ return sorted list """
        text1 = " ".join(list(map(str, self)))
        return "[" + text1 + "]"

###################################################
def example():
    global input
    example = iter(
        """
6
10 5 1 5 10 7
        """
            .strip().split("\n"))
    input = lambda: next(example)
###################################################

import sys
input = sys.stdin.readline
from bisect import bisect_left, bisect_right

# example()

N=int(input())
Y=list(map(int, input().split()))
Y.sort()
if Y[0]==Y[-1]:
    print(1)
    exit()

A=SortedList2(Y,[])
B=SortedList2(Y,Y)
INF=10**18
res=float("inf")
for y in Y[:N-1]:
    A.add(y)
    B.remove(y)
    res=min(res,A.absolute_minimum()+B.absolute_minimum())
print(res)

yukicoder

結果

テストケース

ソースコード