結果
問題 | No.2873 Kendall's Tau |
ユーザー |
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提出日時 | 2024-09-06 23:27:38 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 30 |
ソースコード
#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(); }}