結果

問題 No.2873 Kendall's Tau
ユーザー AyunaAyuna
提出日時 2024-09-06 22:20:00
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 5,409 bytes
コンパイル時間 4,913 ms
コンパイル使用メモリ 277,220 KB
実行使用メモリ 29,692 KB
最終ジャッジ日時 2024-09-06 22:20:14
合計ジャッジ時間 11,986 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 * 13 WA * 17
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 # 

#if 1

#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
using namespace atcoder;

using mint93 = modint998244353;
using mint17 = modint1000000007;
using mint = modint;

using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T, class S>
using p = pair<T, S>;
#define edec vector
template <class T>
using v = vector<T>;
template <class T>
using vv = v<v<T>>;
template <class T>
using vvv = v<vv<T>>;
template <class T, class S>
using vp = v<p<T, S>>;
using vl = v<ll>;
using vvl = vv<ll>;
using vvvl = vvv<ll>;
using vpl = v<pll>;
using vvpl = v<vpl>;
constexpr ll TEN(int n) { return (n == 0) ? 1ll : 10ll * TEN(n - 1); }

#define FOR(i, a, b) for (ll i = (ll)(a); i < (ll)(b); i++)
#define rep(i, N) for (int i = 0; i < (int)(N); i++)
#define rep1(i, N) for (int i = 1; i <= (int)(N); i++)
#define rrep(i, N) for (int i = N - 1; i >= 0; i--)
#define rrep1(i, N) for (int i = N; i > 0; i--)
#define fore(i, a) for (auto &i : a)
#define fs first
#define sc second
#define eb emplace_back
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define UNIQUE(x) (x).erase(unique((x).begin(), (x).end()), (x).end());
#define YES(x) cout << ((x) ? "YES" : "NO") << endl;
#define Yes(x) cout << ((x) ? "Yes" : "No") << endl;
#define yes(x) cout << ((x) ? "yes" : "no") << endl;
#define printans(x) cout << (x == infl ? -1 : x) << endl;
ll sum(vl &x) { return accumulate(all(x), 0ll); }
template <class T>
auto min(const T &a) {
  return *min_element(all(a));
}
template <class T>
auto max(const T &a) {
  return *max_element(all(a));
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
const int inf = (1 << 29);
const ll infl = (1ll << 60);
const ll mod93 = 998244353ll;
const ll mod17 = 1000000007ll;
int popcnt(uint x) { return __builtin_popcount(x); }
int popcnt(ull x) { return __builtin_popcountll(x); }
int bsr(uint x) { return 32 - __builtin_clz(x); }
int bsr(ull x) { return 64 - __builtin_clzll(x); }
int bsf(uint x) { return __builtin_ctz(x); }
int bsf(ull x) { return __builtin_ctzll(x); }

ostream &operator<<(ostream &os, const mint93 &x) { return os << x.val(); }
ostream &operator<<(ostream &os, const mint17 &x) { return os << x.val(); }
template <class T, class S>
istream &operator>>(istream &is, pair<T, S> &x) {
  return is >> x.fs >> x.sc;
}
template <class T, class S>
ostream &operator<<(ostream &os, pair<T, S> &x) {
  return os << x.fs << " " << x.sc;
}
template <class T>
istream &operator>>(istream &is, v<T> &x) {
  for (auto &y : x) is >> y;
  return is;
}
template <class T>
ostream &operator<<(ostream &os, v<T> &x) {
  for (unsigned int i = 0, size = x.size(); i < size; i++)
    os << x[i] << (i == size - 1 ? "" : " ");
  return os;
}
template <class T>
void print(T &t) {
  fore(H, t) cout << H << ' ';
  cout << endl;
}
struct StopWatch {
  bool f = false;
  clock_t st;
  void start() {
    f = true;
    st = clock();
  }
  int msecs() {
    assert(f);
    return (clock() - st) * 1000 / CLOCKS_PER_SEC;
  }
};
ll rand_int(ll l, ll r) {  // [l, r]
  static random_device rd;
  static mt19937 gen(rd());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <typename T>  // mint
struct Count {
  int N;
  v<T> fact, ifact;
  Count(int n) : N(n) {
    fact.resize(N + 1);
    ifact.resize(N + 1);
    fact[0] = 1;
    for (int i = 1; i <= N; i++) {
      fact[i] = fact[i - 1] * i;
    }
    ifact[N] = T(1) / fact[N];
    for (int i = N; i > 0; i--) {
      ifact[i - 1] = ifact[i] * i;
    }
  }
  void extend(int n) {
    int pn = fact.size();
    fact.resize(n + 1);
    ifact.resize(n + 1);
    for (int i = pn; i < n + 1; i++) {
      fact[i] = fact[i - 1] * i;
    }
    ifact[n] = T(1) / fact[n];
    for (int i = n; i > pn; i--) {
      ifact[i - 1] = ifact[i] * i;
    }
  }
  T nCk(int n, int k) {
    if (k > n || k < 0) return 0;
    if (n >= int(fact.size())) extend(n);
    return fact[n] * ifact[k] * ifact[n - k];
  }
  T nPk(int n, int k) {
    if (k > n || k < 0) return 0;
    if (n >= int(fact.size())) extend(n);
    return fact[n] * ifact[n - k];
  }
  T nHk(int n, int k) {
    if (n == 0 && k == 0) return 1;
    return nCk(n + k - 1, k);
  }
  T catalan(int n) { return nCk(2 * n, n) - nCk(2 * n, n + 1); }
  T catalan(int n, int m, int k) {
    if (n > m + k || k < 0)
      return 0;
    else
      return nCk(n + m, n) - nCk(n + m, m + k + 1);
  }
};
#endif

// #define _GLIBCXX_DEBUG


int main() {
  ll n;
  cin >> n;
  vpl xy(n);
  cin >> xy;
  sort(all(xy));
  map<ll, v<int>> mp;
  rep(i, n){
    mp[xy[i].sc].push_back(i);
  }
  v<int> yorder(n);
  int ymx = 0;
  ll s = n * (n - 1) / 2ll;
  fore(pa, mp) {
    fore(k, pa.sc){
      yorder[k] = ymx;
    }
    ymx++;
    s -= (ll)pa.sc.size() * (pa.sc.size() - 1) / 2ll;
  }
  mp.clear();
  rep(i, n){
    mp[xy[i].fs].push_back(i);
  }
  ll r = n * (n - 1) / 2ll;
  fore(pa, mp) {
    r -= (ll)pa.sc.size() * (pa.sc.size() - 1) / 2ll;
  }
  ll p = 0, q = 0;
  fenwick_tree<ll> bit(ymx);
  fore(pa, mp){
    fore(i, pa.sc){
      p += bit.sum(0, yorder[i]);
      q += bit.sum(yorder[i] + 1, ymx);
    }
    fore(i, pa.sc) bit.add(yorder[i], 1);
  }
  cout << setprecision(20) << (ld)(p - q) / sqrtl(r * s) << endl;
}
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