結果

問題 No.2873 Kendall's Tau
ユーザー pitP
提出日時 2024-09-06 22:09:19
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 474 ms / 4,500 ms
コード長 2,813 bytes
コンパイル時間 7,030 ms
コンパイル使用メモリ 337,628 KB
実行使用メモリ 44,476 KB
最終ジャッジ日時 2024-09-06 22:10:58
合計ジャッジ時間 14,107 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
istream &operator>>(istream &is, modint &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); }
istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); }
istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } 
typedef long long ll;
typedef vector<vector<int>> Graph;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define FOR(i,l,r) for (int i = l;i < (int)(r); i++)
#define rep(i,n) for (int i = 0;i < (int)(n); i++)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define my_sort(x) sort(x.begin(), x.end())
#define my_max(x) *max_element(all(x))
#define my_min(x) *min_element(all(x))
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const int INF = (1<<30) - 1;
const ll LINF = (1LL<<62) - 1;
const int MOD = 998244353;
const int MOD2 = 1e9+7;
const double PI = acos(-1);
vector<int> di = {1,0,-1,0};
vector<int> dj = {0,1,0,-1};
#ifdef LOCAL
#  include <debug_print.hpp>
#  define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#  define debug(...) (static_cast<void>(0))
#endif
int main(){
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    int N; cin >> N;
    vector<pii> xy(N);
    vector<int> z;
    rep(i, N) {
        int x, y; cin >> x >> y;
        z.push_back(x);
        z.push_back(y);
        xy[i] = make_pair(x, y);
    }
    sort(all(z));
    z.erase(unique(all(z)), z.end());
    int L = z.size();
    rep(i, N){
        xy[i].first = lower_bound(all(z), xy[i].first) - z.begin();
        xy[i].second = lower_bound(all(z), xy[i].second) - z.begin();
    }
    
    
    ll P = 0, Q = 0, R = 0, S = 0;
    map<int, ll> cx, cy;
    rep(i, N){
        R += i - cx[xy[i].first];
        cx[xy[i].first]++;
        S += i - cy[xy[i].second];
        cy[xy[i].second]++;
    }
    sort(all(xy));
    fenwick_tree<ll> fy(L);
    vector<vector<int>> events(L);
    rep(i, N) events[xy[i].first].push_back(xy[i].second);
    rep(z, L){
        for(auto y : events[z]){
            Q += fy.sum(y + 1, L);
            P += fy.sum(0, y);
        }
        for(auto y : events[z]){
            fy.add(y, 1);
        }
    }
    double tau = (double)(P - Q);
    tau /= (double)sqrt(R) * (double)sqrt(S);
    debug(P, Q, R, S);
    cout << fixed << setprecision(15) << tau << endl;
}
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