結果

問題 No.2873 Kendall's Tau
ユーザー Aging1986Aging1986
提出日時 2024-09-06 21:59:36
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 476 ms / 4,500 ms
コード長 10,060 bytes
コンパイル時間 2,729 ms
コンパイル使用メモリ 222,712 KB
実行使用メモリ 23,764 KB
最終ジャッジ日時 2024-09-06 21:59:47
合計ジャッジ時間 10,509 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,812 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 2 ms
6,940 KB
testcase_03 AC 2 ms
6,940 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 2 ms
6,944 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 371 ms
18,232 KB
testcase_08 AC 476 ms
22,732 KB
testcase_09 AC 376 ms
18,340 KB
testcase_10 AC 436 ms
23,764 KB
testcase_11 AC 389 ms
18,180 KB
testcase_12 AC 412 ms
22,536 KB
testcase_13 AC 91 ms
8,192 KB
testcase_14 AC 356 ms
20,404 KB
testcase_15 AC 52 ms
7,048 KB
testcase_16 AC 51 ms
6,940 KB
testcase_17 AC 285 ms
14,796 KB
testcase_18 AC 195 ms
13,944 KB
testcase_19 AC 246 ms
15,064 KB
testcase_20 AC 53 ms
6,940 KB
testcase_21 AC 200 ms
13,240 KB
testcase_22 AC 77 ms
8,192 KB
testcase_23 AC 205 ms
13,500 KB
testcase_24 AC 22 ms
6,940 KB
testcase_25 AC 47 ms
6,940 KB
testcase_26 AC 275 ms
14,408 KB
testcase_27 AC 147 ms
11,936 KB
testcase_28 AC 314 ms
18,284 KB
testcase_29 AC 352 ms
19,900 KB
testcase_30 AC 36 ms
6,944 KB
testcase_31 AC 69 ms
7,396 KB
testcase_32 AC 217 ms
13,244 KB
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 # 


#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
typedef pair<double, double> pdd;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vll> vvll;
typedef vector<vvll> vvvll;
typedef vector<pii> vpii;
typedef vector<vpii> vvpii;
typedef vector<pll> vpll;
typedef vector<vpll> vvpll;
typedef vector<pdd> vpdd;
typedef vector<vd> vvd;
#define yn(ans) printf("%s\n", (ans)?"Yes":"No");
#define YN(ans) printf("%s\n", (ans)?"YES":"NO");
    template<class T> bool chmax(T &a, T b) {
	if (a >= b) return false;
	a = b; return true;
}
template<class T> bool chmin(T &a, T b) {
	if (a <= b) return false;
	a = b; return true;
}
#define FOR(i, s, e, t) for ((i) = (s); (i) < (e); (i) += (t)) 
#define REP(i, e) for (int i = 0; i < (e); ++i) 
#define REP1(i, s, e) for (int i = (s); i < (e); ++i)
#define RREP(i, e) for (int i = (e); i >= 0; --i)
#define RREP1(i, e, s) for (int i = (e); i >= (s); --i)
#define all(v) v.begin(), v.end()
#define pb push_back
#define qb pop_back
#define pf push_front
#define qf pop_front
#define maxe max_element
#define mine min_element
ll inf = 1e18;
#define DEBUG printf("%d\n", __LINE__); fflush(stdout);
template<class T> void print(vector<T> &v, bool withSize = false) {
	if (withSize) cout << v.size() << endl;
	REP(i, v.size()) cout << v[i] << " "; 
	cout << endl;
}
mt19937_64 rng((unsigned int) chrono::steady_clock::now().time_since_epoch().count());

int __FAST_IO__ = []() {
	std::ios::sync_with_stdio(0);
	std::cin.tie(0);
	std::cout.tie(0);
	return 0;
}();

// Mint & Combinatorics
 
template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  return u;
}
 
template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;
 
  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }
 
  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }
 
  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }
 
  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
  template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
  template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) { Modular result(*this); *this += 1; return result; }
  Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
  Modular operator-() const { return Modular(-value); }
 
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
    asm(
      "divl %4; \n\t"
      : "=a" (d), "=d" (m)
      : "d" (xh), "a" (xl), "r" (mod())
    );
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) {
    long long q = static_cast<long long>(static_cast<long double>(value) * rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }
 
  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
 
  friend const Type& abs(const Modular& x) { return x.value; }
 
  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
 
  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
 
  template <typename V, typename U>
  friend V& operator>>(V& stream, Modular<U>& number);
 
 private:
  Type value;
};
 
template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
 
template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
 
template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
 
template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
 
template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
 
template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
 
template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
 
template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}
 
template <typename T>
bool IsZero(const Modular<T>& number) {
  return number() == 0;
}
 
template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}
 
// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
  return stream << number();
}
 
// U == std::istream? but done this way because of fastinput
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, long long>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
 
struct MOD {
    static int value;
};
int MOD::value = 998244353;
using Mint = Modular<MOD>;
typedef vector<Mint> vm;
typedef vector<vm> vvm;
typedef vector<vvm> vvvm;

class Fenw {
public:
	Fenw(ll _n): n(_n), v(n, 0) {}
	int lowbit(int x) {return x & -x;}
	ll query(int x) {
		ll ans = 0;
		for (int i = x; i > 0; i -= lowbit(i)) ans += v[i];
		return ans;
	}
	void update(int x, ll val) {
		for (int i = x; i < n; i += lowbit(i)) {
			v[i] += val;
		}
	}
private:
	int n;
	vector<ll> v;
};


template <typename T> struct Discrete {
	Discrete() {}
	Discrete(vector<T> &v): p(v) {init();}
	void add(T t) {
		p.pb(t);
	}
	
	void init() {
		sort(all(p));
		p.resize(unique(all(p)) - p.begin());
	}
	
	int size() {return p.size();}
	
	int id(T t) {
		return lower_bound(all(p), t) - p.begin();
	}
	
	T operator[](int id) {return p[id];}
 
    	vector<T> &get() {return p;}
	vector<T> p;
};

#define TESTS int t; cin >> t; while (t--)
#define TEST 
int main() {
    int N;
    cin >> N;
    vpii v(N);
    map<int, int> m, m2;
    Discrete<int> d, d2;
    REP(i, N) {
        cin >> v[i].first >> v[i].second;
        m[v[i].first]++, m2[v[i].second]++;
        d.add(v[i].first), d2.add(v[i].second);
    }
    
    ll R = 1ll * N * (N - 1) / 2, S = 1ll * N * (N - 1) / 2;
    for (auto &e: m) R -= 1ll * e.second * (e.second - 1) / 2;
    for (auto &e: m2) S -= 1ll * e.second * (e.second - 1) / 2;
    
    ll P = 0, Q = 0;
    {
        d2.init();
        sort(all(v));
        Fenw f(N + 1);
        for (int i = 0; i < N; ) {
            int j = i;
            vi q;
            while (j < N && v[i].first == v[j].first) {
                int id = d2.id(v[j].second);
                P += f.query(id);
                Q += f.query(N) - f.query(id + 1);
                q.pb(id);
                j++;
            }
            for (auto c: q) f.update(c + 1, 1);
            i = j;
        }
    }
    
    double ans = (double)(P - Q) / sqrt((double)R * S);
    
    //printf("%lld %lld %lld %lld\n", P, Q, R, S);
    printf("%.12lf\n", ans);
    return 0;
}
0