#1008031 (PyPy3) No.2873 Kendall's Tau

• 問題: No.2873 Kendall's Tau
• ユーザー: 👑 rin204
• 提出日時: 2024-09-07 00:31:04
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 1,010 ms / 4,500 ms
• コード長: 1,769 bytes
• コンパイル時間: 378 ms
• コンパイル使用メモリ: 82,400 KB
• 実行使用メモリ: 156,672 KB
• 最終ジャッジ日時: 2024-09-07 00:31:23
• 合計ジャッジ時間: 18,114 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

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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class BIT:
    def __init__(self, n):
        self.n = n
        self.data = [0] * (n + 1)
        if n == 0:
            self.n0 = 0
        else:
            self.n0 = 1 << (n.bit_length() - 1)
    def sum_(self, i):
        s = 0
        while i > 0:
            s += self.data[i]
            i -= i & -i
        return s
    def sum(self, l, r=-1):
        if r == -1:
            return self.sum_(l)
        else:
            return self.sum_(r) - self.sum_(l)
    def get(self, i):
        return self.sum(i, i + 1)
    def add(self, i, x):
        i += 1
        while i <= self.n:
            self.data[i] += x
            i += i & -i
    def lower_bound(self, x):
        if x <= 0:
            return 0
        i = 0
        k = self.n0
        while k > 0:
            if i + k <= self.n and self.data[i + k] < x:
                x -= self.data[i + k]
                i += k
            k //= 2
        return i + 1
n = int(input())
xy = [list(map(int, input().split())) for _ in range(n)]
xy.sort(key=lambda x: x[0])
Y_ = sorted(set(y for _, y in xy))
dic = {y: i for i, y in enumerate(Y_)}
add = []
b = xy[0][0]
bit = BIT(len(Y_))
p = 0
q = 0
for x, y in xy:
    y = dic[y]
    if b == x:
        add.append(y)
    else:
        for y_ in add:
            bit.add(y_, 1)
        add = [y]
        b = x
    p += bit.sum(y)
    q += bit.sum(y + 1, len(Y_))
X = [x for x, _ in xy]
X.sort()
r = n * (n - 1) // 2
row = 0
b = X[0]
for x in X:
    if b == x:
        r -= row
        row += 1
    else:
        row = 1
        b = x
Y = [y for _, y in xy]
Y.sort()
s = n * (n - 1) // 2
row = 0
b = Y[0]
for y in Y:
    if b == y:
        s -= row
        row += 1
    else:
        row = 1
        b = y
ans = (p - q) / ((r * s) ** 0.5)
print(ans)
 
 
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