結果

問題 No.2873 Kendall's Tau
ユーザー 👑 amentorimaru
提出日時 2024-09-06 22:04:05
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 434 ms / 4,500 ms
コード長 4,621 bytes
コンパイル時間 4,853 ms
コンパイル使用メモリ 249,192 KB
実行使用メモリ 32,508 KB
最終ジャッジ日時 2024-09-06 22:04:19
合計ジャッジ時間 11,695 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

#define ATCODER
#define _USE_MATH_DEFINES
#include<stdio.h>
#include<iostream>
#include<fstream>
#include<algorithm>
#include<vector>
#include<string>
#include <cassert>
#include <numeric>
#include <unordered_map>
#include <unordered_set>
#include <queue>
#include <math.h>
#include <climits>
#include <set>
#include <map>
#include <list>
#include <random>
#include <iterator>
#include <bitset>
#include <chrono>
#include <type_traits>
using namespace std;
using ll = long long;
using ld = long double;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
//template<claLR T> using pq = priority_queue<T, vector<T>, greater<T>>;
#define FOR(i, a, b) for(ll i=(a); i<(b);i++)
#define REP(i, n) for(ll i=0; i<(n);i++)
#define ROF(i, a, b) for(ll i=(b-1); i>=(a);i--)
#define PER(i, n) for(ll i=n-1; i>=0;i--)
#define REPREP(i,j,a,b) for(ll i=0;i<a;i++)for(ll j=0;j<b;j++)
#define VV(type) vector< vector<type> >
#define VV2(type,n,m,val) vector< vector<type> > val;val.resize(n);for(ll i;i<n;i++)val[i].resize(m)
#define vec(type) vector<type>
#define VEC(type,n,val) vector<type> val;val.resize(n)
#define VL vector<ll>
#define VVL vector< vector<ll> >
#define VP vector< pair<ll,ll> >
#define SZ size()
#define all(i) begin(i),end(i)
#define SORT(i) sort(all(i))
#define BITI(i) (1<<i)
#define BITSET(x,i) x | (ll(1)<<i)
#define BITCUT(x,i) x & ~(ll(1)<<i)
#define EXISTBIT(x,i) (((x>>i) & 1) != 0)
#define ALLBIT(n) (ll(1)<<n-1)
#define CHMAX(n,v) n=n<v?v:n
#define CHMIN(n,v) n=n>v?v:n
#define MP(a,b) make_pair(a,b)
#define DET2(x1,y1,x2,y2) (x1)*(y2)-(x2)*(y1)
#define DET3(x1,y1,z1,x2,y2,z2,x3,y3,z3) (x1)*(y2)*(z3)+(x2)*(y3)*(z1)+(x3)*(y1)*(z2)-(z1)*(y2)*(x3)-(z2)*(y3)*(x1)-(z3)*(y1)*(x2)
#define INC(a) for(auto& v:a)v++;
#define DEC(a) for(auto& v:a)v--;
#define SQU(x) (x)*(x)
#define L0 ll(0)
#ifdef ATCODER
#include <atcoder/all>
using namespace atcoder;
using mint = modint1000000007;
using mint2 = modint998244353;
#endif
template<typename T = ll>
vector<T> read(size_t n) {
  vector<T> ts(n);
  for (size_t i = 0; i < n; i++) cin >> ts[i];
  return ts;
}
template<typename TV, const ll N> void read_tuple_impl(TV&) {}
template<typename TV, const ll N, typename Head, typename... Tail>
void read_tuple_impl(TV& ts) {
  get<N>(ts).emplace_back(*(istream_iterator<Head>(cin)));
  read_tuple_impl<TV, N + 1, Tail...>(ts);
}
template<typename... Ts> decltype(auto) read_tuple(size_t n) {
  tuple<vector<Ts>...> ts;
  for (size_t i = 0; i < n; i++) read_tuple_impl<decltype(ts), 0, Ts...>(ts);
  return ts;
}
using val = ll;
using func = pair<ll, ll>;
val opm(val a, val b) {
  return min(a, b);
}
val em() { return 1e18; }
val opM(val a, val b) {
  return max(a, b);
}
val eM() { return 0; }
//val mp(func f, val a)
//{
//  if (f.first < 0)
//    return a;
//  return f;
//}
//func comp(func f, func g) {
//  if (g.first < 0)
//    return f;
//  return g;
//}
//
//func id() {
//  return MP(-1, -1);
//}
ll di[4] = { 1,0,-1,0 };
ll dj[4] = { 0,1,0,-1 };
ll si[4] = { 0,3,3,0 };
ll sj[4] = { 0,0,3,3 };
//ll di[4] = { -1,-1,1,1 };
//ll dj[4] = { -1,1,-1,1 };
ll di8[8] = { 0,-1,-1,-1,0,1,1,1 };
ll dj8[8] = { -1,-1,0,1,1,1,0,-1 };
class BIT {
public:
  BIT(ll s) {
    size = 1;
    while (size < s)
      size *= 2;
    bit.assign(size, 0); // def unit
  }
  void update(ll k, ll var) {
    k += 1;
    while (k <= size) {
      bit[k - 1] += var;  // def func
      k += k & -k;
    }
  }
  ll query(ll a) {
    ll s = 0;
    a++;
    while (a > 0) {
      s += bit[a - 1];  // def func
      a -= a & -a;
    }
    return s;
  }
  ll size;
  vector<ll> bit;
};
void solve() {
  ll n;
  cin >> n;
  auto [x, y] = read_tuple<ll, ll>(n);
  unordered_map<ll, ll> xc, yc;
  VP xy(n);
  REP(i, n) {
    xc[x[i]]++;
    yc[y[i]]++;
    xy[i] = MP(x[i], y[i]);
  }
  SORT(xy);
  y.push_back(-2000000000);
  y.push_back(2000000000);
  SORT(y);
  y.erase(unique(all(y)), y.end());
  unordered_map<ll, ll> ry;
  REP(i, y.size()) {
    ry[y[i]] = i;
  }
  BIT bit(y.size());
  ll p = 0, q = 0, r = n * (n - 1) / 2, s = n * (n - 1) / 2;
  for (auto& [k, c] : xc) {
    r -= c * (c - 1) / 2;
  }
  for (auto& [k, c] : yc) {
    s -= c * (c - 1) / 2;
  }
  ll add = 0;
  REP(i, n) {
    if (i > 0 && xy[i - 1].first != xy[i].first) {
      FOR(j, add, i) {
        bit.update(ry[xy[j].second], 1);
      }
      add = i;
    }
    p += bit.query(ry[xy[i].second] - 1);
    q += bit.query(y.size() - 1) - bit.query(ry[xy[i].second]);
  }
  printf("%.15f", double(p - q) / sqrt(double(r) * double(s)));
  return;
}
int main() {
  ll t = 1;
  //cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}
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