#1007654 (PyPy3) No.2873 Kendall's Tau

• 問題: No.2873 Kendall's Tau
• ユーザー: rlangevin
• 提出日時: 2024-09-06 22:08:37
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 1,106 ms / 4,500 ms
• コード長: 2,570 bytes
• コンパイル時間: 467 ms
• コンパイル使用メモリ: 82,248 KB
• 実行使用メモリ: 200,724 KB
• 最終ジャッジ日時: 2024-09-06 22:10:18
• 合計ジャッジ時間: 17,522 ms
• ジャッジサーバーID （参考情報）: judge1 / judge4

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
input = sys.stdin.readline
from collections import *
class Fenwick_Tree:
    def __init__(self, n):
        self._n = n
        self.data = [0] * n
    def add(self, p, x):
        assert 0 <= p < self._n
        p += 1
        while p <= self._n:
            self.data[p - 1] += x
            p += p & -p
    def sum(self, l, r):
        assert 0 <= l <= r <= self._n
        return self._sum(r) - self._sum(l)
    def _sum(self, r):
        s = 0
        while r > 0:
            s += self.data[r - 1]
            r -= r & -r
        return s
    # T.sum(0, x) <= kとなる最大のxを返す。
    def get(self, k):
        k += 1
        x, r = 0, 1
        while r < self._n:
            r <<= 1
        len = r
        while len:
            if x + len - 1 < self._n:
                if self.data[x + len - 1] < k:
                    k -= self.data[x + len - 1]
                    x += len
            len >>= 1
        return x
    def __str__(self):
        temp = []
        for i in range(self._n):
            temp.append(str(self.sum(i, i + 1)))
        return ' '.join(temp)
from bisect import *
from copy import deepcopy
def compress(lst):
    '''
    B: lstを座圧したリスト
    idx_to_val: indexから元の値を取得するリスト
    val_to_idx: 元の値からindexを取得する辞書
    '''
    B = []
    val_to_idx = {}
    idx_to_val = deepcopy(lst)
    idx_to_val = list(set(idx_to_val))
    idx_to_val.sort()
    for i in range(len(lst)):
        ind = bisect_left(idx_to_val, lst[i])
        B.append(ind)
    for i in range(len(B)):
        val_to_idx[lst[i]] = B[i]
    return B, idx_to_val, val_to_idx
N = int(input())
X, Y = [], []
D = []
for i in range(N):
    x, y = map(int, input().split())
    X.append(x)
    Y.append(y)
X, _, _ = compress(X)
Y, _, _ = compress(Y)
D = [[] for i in range(N)]
for i in range(N):
    D[X[i]].append(Y[i])
    
Cx = Counter(X)
Cy = Counter(Y)
R, S = N * (N - 1) // 2, N * (N - 1) // 2 
for k, v in Cx.items():
    R -= v * (v - 1) // 2
for k, v in Cy.items():
    S -= v * (v - 1) // 2
       
P = 0
T = Fenwick_Tree(N + 1)
for x in range(N):
    for y in D[x]:
        T.add(y, 1)
for x in range(N):
    for y in D[x]:
        T.add(y, -1)
    for y in D[x]:
        P += T.sum(y + 1, N + 1)
    
Q = 0
T = Fenwick_Tree(N + 1)
for x in range(N-1, -1, -1):
    for y in D[x]:
        T.add(y, 1)
        
for x in range(N-1, -1, -1):
    for y in D[x]:
        T.add(y, -1)
    for y in D[x]:
        Q += T.sum(y + 1, N + 1)
        
print((P - Q) / (R * S) ** 0.5)
 
 
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