結果

問題 No.2873 Kendall's Tau
ユーザー noya2noya2
提出日時 2024-09-06 23:27:38
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 649 ms / 4,500 ms
コード長 13,136 bytes
コンパイル時間 3,915 ms
コンパイル使用メモリ 283,992 KB
実行使用メモリ 59,156 KB
最終ジャッジ日時 2024-09-06 23:28:26
合計ジャッジ時間 14,256 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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
6,816 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 3 ms
6,940 KB
testcase_03 AC 2 ms
6,940 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 3 ms
6,940 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 614 ms
50,616 KB
testcase_08 AC 645 ms
57,816 KB
testcase_09 AC 594 ms
51,308 KB
testcase_10 AC 649 ms
59,156 KB
testcase_11 AC 554 ms
51,276 KB
testcase_12 AC 573 ms
55,524 KB
testcase_13 AC 140 ms
18,544 KB
testcase_14 AC 505 ms
51,956 KB
testcase_15 AC 80 ms
13,556 KB
testcase_16 AC 82 ms
13,160 KB
testcase_17 AC 375 ms
41,416 KB
testcase_18 AC 309 ms
32,176 KB
testcase_19 AC 381 ms
42,936 KB
testcase_20 AC 79 ms
13,888 KB
testcase_21 AC 296 ms
32,608 KB
testcase_22 AC 119 ms
17,056 KB
testcase_23 AC 330 ms
33,208 KB
testcase_24 AC 34 ms
7,764 KB
testcase_25 AC 73 ms
12,768 KB
testcase_26 AC 375 ms
44,752 KB
testcase_27 AC 229 ms
28,212 KB
testcase_28 AC 495 ms
47,116 KB
testcase_29 AC 530 ms
50,144 KB
testcase_30 AC 56 ms
10,084 KB
testcase_31 AC 113 ms
15,500 KB
testcase_32 AC 323 ms
32,796 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 # 

#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/offline_rectangle_sum.hpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/binary_indexed_tree.hpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/misc/concepts.hpp"

#include<concepts>

namespace noya2 {

template<class monoid>
concept Monoid = requires {
    typename monoid::value_type;
    {monoid::op(declval<typename monoid::value_type>(),declval<typename monoid::value_type>())} -> std::same_as<typename monoid::value_type>;
    {monoid::e()} -> std::same_as<typename monoid::value_type>;
};

template<class group>
concept Group = requires {
    requires Monoid<group>;
    {group::inv(declval<typename group::value_type>())} -> std::same_as<typename group::value_type>;
};

} // namespace noya2
#line 5 "/Users/noya2/Desktop/Noya2_library/data_structure/binary_indexed_tree.hpp"

namespace noya2{

template <Group G>
struct binary_indexed_tree {
    using T = typename G::value_type;
    binary_indexed_tree (int _n = 0) : n(_n), d(_n + 1, G::e()) {}
    void add(int i, T val) {
        for (int x = i+1; x <= n; x += x & -x) {
            d[x] = G::op(d[x],val);
        }
    }
    T prod(int r){
        return prefix_prod(r);
    }
    T prod(int l, int r) {
        return G::op(G::inv(prefix_prod(l)),prefix_prod(r));
    }
    T get(int i){
        return prod(i,i+1);
    }
    void set(int i, T val){
        add(i,G::op(G::inv(get(i)),val));
    }
  private:
    int n;
    std::vector<T> d;
    T prefix_prod(int i) {
        assert(0 <= i && i <= n);
        T ret = G::e();
        for (int x = i; x > 0; x -= x & -x) {
            ret = G::op(ret,d[x]);
        }
        return ret;
    }
};

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
#include<ranges>
#line 7 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"

namespace noya2::internal {

template<class E>
struct csr {
    csr () {}
    csr (int _n) : n(_n) {}
    csr (int _n, int m) : n(_n){
        start.reserve(m);
        elist.reserve(m);
    }
    // ACL style constructor (do not have to call build)
    csr (int _n, const std::vector<std::pair<int,E>> &idx_elem) : n(_n), start(_n + 2), elist(idx_elem.size()) {
        for (auto &[i, e] : idx_elem){
            start[i + 2]++;
        }
        for (int i = 1; i < n; i++){
            start[i + 2] += start[i + 1];
        }
        for (auto &[i, e] : idx_elem){
            elist[start[i + 1]++] = e;
        }
        prepared = true;
    }
    int add(int idx, E elem){
        int eid = start.size();
        start.emplace_back(idx);
        elist.emplace_back(elem);
        return eid;
    }
    void build(){
        if (prepared) return ;
        int m = start.size();
        std::vector<E> nelist(m);
        std::vector<int> nstart(n + 2, 0);
        for (int i = 0; i < m; i++){
            nstart[start[i] + 2]++;
        }
        for (int i = 1; i < n; i++){
            nstart[i + 2] += nstart[i + 1];
        }
        for (int i = 0; i < m; i++){
            nelist[nstart[start[i] + 1]++] = elist[i];
        }
        swap(elist,nelist);
        swap(start,nstart);
        prepared = true;
    }
    const auto operator[](int idx) const {
        return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
    }
    auto operator[](int idx){
        return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
    }
    const auto operator()(int idx, int l, int r) const {
        return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
    }
    auto operator()(int idx, int l, int r){
        return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
    }
    int n;
    std::vector<int> start;
    std::vector<E> elist;
    bool prepared = false;
};

} // namespace noya2::internal
#line 2 "/Users/noya2/Desktop/Noya2_library/misc/monoids.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/misc/monoids.hpp"

namespace noya2{

template<typename T>
struct max_monoid {
    using value_type = T;
    static constexpr T op(const T &a, const T &b){ return max(a,b); }
    static constexpr T e(){ return std::numeric_limits<T>::min(); }
    static constexpr T inv(const T &a){ return e(); }
};
template<typename T>
struct min_monoid {
    using value_type = T;
    static constexpr T op(const T &a, const T &b){ return min(a,b); }
    static constexpr T e(){ return std::numeric_limits<T>::max(); }
    static constexpr T inv(const T &a){ return e(); }
};
template<typename T>
struct plus_group {
    using value_type = T;
    static constexpr T op(const T &a, const T &b){ return a + b; }
    static constexpr T e(){ return T(0); }
    static constexpr T inv(const T &a){ return -a; }
};
template<typename T>
struct xor_group {
    using value_type = T;
    static constexpr T op(const T &a, const T &b){ return a ^ b; }
    static constexpr T e(){ return T(0); }
    static constexpr T inv(const T &a){ return a; }
};
    
} // namespace noya2
#line 6 "/Users/noya2/Desktop/Noya2_library/data_structure/offline_rectangle_sum.hpp"

namespace noya2 {

template<Group G = plus_group<ll>>
struct offline_rectangle_sum {
    using T = typename G::value_type;
    int h, w, query_id;
    internal::csr<pair<int,T>> elems;
    internal::csr<tuple<int,int,int>> queries;
    offline_rectangle_sum () {}
    offline_rectangle_sum (int h_, int w_) : h(h_), w(w_), query_id(0), elems(h_), queries(h_+1) {}
    offline_rectangle_sum (int h_, int w_, int m) : h(h_), w(w_), query_id(0), elems(h_,m), queries(h_+1) {}
    offline_rectangle_sum (int h_, int w_, int m, int q) : h(h_), w(w_), query_id(0), elems(h_,m), queries(h_+1,q*2) {}
    void add_elem(int x, int y, T e){
        elems.add(x,pair<int,T>(y,e));
    }
    void add_query(int lx, int rx, int ly, int ry){
        queries.add(lx,tuple<int,int,int>(ly,ry,-1-query_id));
        queries.add(rx,tuple<int,int,int>(ly,ry,query_id));
        query_id++;
    }
    vector<T> run(){
        elems.build();
        queries.build();
        binary_indexed_tree<G> fen(w);
        vector<T> ans(query_id,G::e());
        for (int x = 0; ; x++){
            for (auto [ly, ry, qid] : queries[x]){
                if (qid >= 0){
                    ans[qid] = G::op(ans[qid],fen.prod(ly,ry));
                }
                else {
                    ans[-1-qid] = G::op(ans[-1-qid],G::inv(fen.prod(ly,ry)));
                }
            }
            if (x == h) break;
            for (auto [y, e] : elems[x]){
                fen.add(y,e);
            }
        }
        return ans;
    }
};

} // namespace noya2
#line 4 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/compress.hpp"

#line 5 "/Users/noya2/Desktop/Noya2_library/data_structure/compress.hpp"

namespace noya2{

template<typename T>
struct compress {
    std::vector<T> raws;
    compress () {}
    compress (const vector<T> &_raws) : raws(_raws){ build(); }
    void build(){
        std::sort(raws.begin(), raws.end());
        raws.erase(std::unique(raws.begin(), raws.end()), raws.end());
    }
    int id(const T &raw){ return lb(raw); }
    T raw(const int &id){ return raws[id]; }
    void add(const T &raw){ raws.emplace_back(raw); }
    void reserve(size_t sz){ raws.reserve(sz); }
    size_t size(){ return raws.size(); }
    int lb(const T &raw){ return lower_bound(all(raws),raw) - raws.begin(); }
    int ub(const T &raw){ return upper_bound(all(raws),raw) - raws.begin(); }
    bool contains(const T &raw){
        int jd = lb(raw);
        if (jd < (int)size()) return raws[jd] == raw;
        return false;
    }
    int contains_id(const T &raw){
        int jd = lb(raw);
        if (jd < (int)size() && raws[jd] == raw) return jd;
        return -1;
    }
};

} // namespace noya2
#line 6 "c.cpp"

void solve(){
    ll n; in(n);
    vector<ll> xs(n), ys(n);
    rep(i,n) in(xs[i],ys[i]);
    ll tot = n*(n-1)/2;
    map<ll,ll> mpx, mpy;
    compress<ll> cpx(xs), cpy(ys);
    rep(i,n){
        mpx[xs[i]]++;
        mpy[ys[i]]++;
    }
    ll r = tot;
    for (auto [x, c] : mpx){
        r -= c*(c-1)/2;
    }
    ll s = tot;
    for (auto [y, c] : mpy){
        s -= c*(c-1)/2;
    }
    offline_rectangle_sum<plus_group<ll>> ors(cpx.size(),cpy.size());
    rep(i,n){
        ors.add_elem(cpx.id(xs[i]),cpy.id(ys[i]),1);
    }
    rep(i,n){
        ors.add_query(0,cpx.id(xs[i]),0,cpy.id(ys[i]));
        ors.add_query(0,cpx.id(xs[i]),cpy.id(ys[i])+1,cpy.size());
    }
    auto rem = ors.run();
    ll p = 0, q = 0;
    rep(i,n){
        p += rem[i*2];
        q += rem[i*2+1];
    }
    ld ans = ld(p-q)/sqrtl(ld(r)*ld(s));
    out(ans);
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}
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