#1007768 (PyPy3) No.2873 Kendall's Tau

• 問題: No.2873 Kendall's Tau
• ユーザー: mkawa2
• 提出日時: 2024-09-06 22:36:09
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 1,580 ms / 4,500 ms
• コード長: 2,369 bytes
• コンパイル時間: 408 ms
• コンパイル使用メモリ: 82,196 KB
• 実行使用メモリ: 212,040 KB
• 最終ジャッジ日時: 2024-09-06 22:36:38
• 合計ジャッジ時間: 25,944 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

ファイルパターン	結果
sample	AC * 3
other	AC * 30

ソースコード

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import sys
# sys.setrecursionlimit(200005)
# sys.set_int_max_str_digits(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()
dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
# inf = -1-(-1 << 31)
inf = -1-(-1 << 62)
# md = 10**9+7
md = 998244353
class BitSum:
    def __init__(self, n):
        self._n = n+1
        self._table = [0]*self._n
        self._origin = [0]*n
    def __getitem__(self, item):
        return self._origin[item]
    def __setitem__(self, index, value):
        self.add(index, value-self._origin[index])
        self._origin[index] = value
    def add(self, i, x):
        if x == 0: return
        self._origin[i] += x
        i += 1
        while i < self._n:
            self._table[i] += x
            i += i & -i
    def sum(self, r):
        res = 0
        while r > 0:
            res += self._table[r]
            r -= r & -r
        return res
    def sumlr(self, l, r):
        if l >= r: return 0
        if l == 0: return self.sum(r)
        return self.sum(r)-self.sum(l)
    # return "min(i) of sum(a[0]..a[i])>=x" or "N"
    def bisect(self, x):
        idx = 0
        d = 1 << (self._n-1).bit_length()-1
        while d:
            if idx|d < self._n and self._table[idx|d] < x:
                idx |= d
                x -= self._table[idx]
            d >>= 1
        return idx
from collections import Counter
n=II()
xy=LLI(n)
enc={a:i for i,a in enumerate(sorted(set(y for x,y in xy)))}
xy=[[x,enc[y]] for x,y in xy]
cx=Counter()
cy=Counter()
r=s=n*(n-1)//2
bit=BitSum(n)
p=0
xy.sort(key=lambda x:(x[0],-x[1]))
for x,y in xy:
    r-=cx[x]
    s-=cy[y]
    cx[x]+=1
    cy[y]+=1
    p+=bit.sum(y)
    bit.add(y,1)
bit=BitSum(n)
q=0
xy=[[x,n-1-y] for x,y in xy]
xy.sort(key=lambda x:(x[0],-x[1]))
for x,y in xy:
    q+=bit.sum(y)
    bit.add(y,1)
# print(p,q,r,s)
print((p-q)/(r*s)**0.5)
 
 
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