結果
問題 | No.2873 Kendall's Tau |
ユーザー | Rubikun |
提出日時 | 2024-09-06 21:30:26 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 230 ms / 4,500 ms |
コード長 | 13,667 bytes |
コンパイル時間 | 2,667 ms |
コンパイル使用メモリ | 218,280 KB |
実行使用メモリ | 10,812 KB |
最終ジャッジ日時 | 2024-09-06 21:30:35 |
合計ジャッジ時間 | 8,610 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge3 |
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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
6,944 KB |
testcase_02 | AC | 2 ms
6,940 KB |
testcase_03 | AC | 2 ms
6,944 KB |
testcase_04 | AC | 2 ms
6,940 KB |
testcase_05 | AC | 2 ms
6,940 KB |
testcase_06 | AC | 2 ms
6,944 KB |
testcase_07 | AC | 201 ms
10,036 KB |
testcase_08 | AC | 205 ms
10,636 KB |
testcase_09 | AC | 201 ms
9,988 KB |
testcase_10 | AC | 230 ms
10,812 KB |
testcase_11 | AC | 201 ms
9,864 KB |
testcase_12 | AC | 195 ms
10,440 KB |
testcase_13 | AC | 62 ms
6,940 KB |
testcase_14 | AC | 156 ms
9,528 KB |
testcase_15 | AC | 33 ms
6,940 KB |
testcase_16 | AC | 35 ms
6,940 KB |
testcase_17 | AC | 146 ms
8,312 KB |
testcase_18 | AC | 107 ms
7,500 KB |
testcase_19 | AC | 166 ms
8,516 KB |
testcase_20 | AC | 35 ms
6,944 KB |
testcase_21 | AC | 118 ms
7,720 KB |
testcase_22 | AC | 51 ms
6,940 KB |
testcase_23 | AC | 118 ms
7,604 KB |
testcase_24 | AC | 17 ms
6,940 KB |
testcase_25 | AC | 31 ms
6,944 KB |
testcase_26 | AC | 148 ms
8,312 KB |
testcase_27 | AC | 88 ms
6,976 KB |
testcase_28 | AC | 167 ms
9,348 KB |
testcase_29 | AC | 176 ms
9,544 KB |
testcase_30 | AC | 26 ms
6,940 KB |
testcase_31 | AC | 48 ms
6,940 KB |
testcase_32 | AC | 121 ms
7,588 KB |
ソースコード
#include <bits/stdc++.h> using namespace std; typedef long long ll; template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; } template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; } #define vi vector<int> #define vl vector<ll> #define vii vector<pair<int,int>> #define vll vector<pair<ll,ll>> #define vvi vector<vector<int>> #define vvl vector<vector<ll>> #define vvii vector<vector<pair<int,int>>> #define vvll vector<vector<pair<ll,ll>>> #define vst vector<string> #define pb push_back #define all(x) (x).begin(),(x).end() #define mkunique(x) sort(all(x));(x).erase(unique(all(x)),(x).end()) #define fi first #define se second #define mp make_pair #define si(x) int(x.size()) const int mod=998244353,MAX=300005,INF=15<<26; // BIT セグ木 遅延セグ木 のみ // from: https://gist.github.com/yosupo06/ddd51afb727600fd95d9d8ad6c3c80c9 // (based on AtCoder STL) #include <algorithm> #include <array> #ifdef _MSC_VER #include <intrin.h> #endif namespace atcoder { namespace internal { int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } } // namespace internal } // namespace atcoder #include <cassert> #include <numeric> #include <type_traits> namespace atcoder { namespace internal { #ifndef _MSC_VER template <class T> using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value, std::true_type, std::false_type>::type; template <class T> using make_unsigned_int128 = typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>; template <class T> using is_integral = typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_signed_int = typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional< is_signed_int128<T>::value, make_unsigned_int128<T>, typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type; #else template <class T> using is_integral = typename std::is_integral<T>; template <class T> using is_signed_int = typename std::conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type; #endif template <class T> using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>; template <class T> using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>; template <class T> using to_unsigned_t = typename to_unsigned<T>::type; } // namespace internal } // namespace atcoder #include <cassert> #include <vector> namespace atcoder { template <class T> struct fenwick_tree { using U = internal::to_unsigned_t<T>; public: fenwick_tree() : _n(0) {} fenwick_tree(int n) : _n(n), data(n) {} void add(int p, T x) { assert(0 <= p && p < _n); p++; while (p <= _n) { data[p - 1] += U(x); p += p & -p; } } T sum(int l, int r) { assert(0 <= l && l <= r && r <= _n); return sum(r) - sum(l); } private: int _n; std::vector<U> data; U sum(int r) { U s = 0; while (r > 0) { s += data[r - 1]; r -= r & -r; } return s; } }; } // namespace atcoder #include <algorithm> #include <cassert> #include <iostream> #include <vector> namespace atcoder { template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()> struct lazy_segtree { public: lazy_segtree() : lazy_segtree(0) {} lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {} lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector<S>(2 * size, e()); lz = std::vector<F>(size, id()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); return d[p]; } S prod(int l, int r) { assert(0 <= l && l <= r && r <= _n); if (l == r) return e(); l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push(r >> i); } S sml = e(), smr = e(); while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() { return d[1]; } void apply(int p, F f) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); d[p] = mapping(f, d[p]); for (int i = 1; i <= log; i++) update(p >> i); } void apply(int l, int r, F f) { assert(0 <= l && l <= r && r <= _n); if (l == r) return; l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } { int l2 = l, r2 = r; while (l < r) { if (l & 1) all_apply(l++, f); if (r & 1) all_apply(--r, f); l >>= 1; r >>= 1; } l = l2; r = r2; } for (int i = 1; i <= log; i++) { if (((l >> i) << i) != l) update(l >> i); if (((r >> i) << i) != r) update((r - 1) >> i); } } template <bool (*g)(S)> int max_right(int l) { return max_right(l, [](S x) { return g(x); }); } template <class G> int max_right(int l, G g) { assert(0 <= l && l <= _n); assert(g(e())); if (l == _n) return _n; l += size; for (int i = log; i >= 1; i--) push(l >> i); S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!g(op(sm, d[l]))) { while (l < size) { push(l); l = (2 * l); if (g(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while ((l & -l) != l); return _n; } template <bool (*g)(S)> int min_left(int r) { return min_left(r, [](S x) { return g(x); }); } template <class G> int min_left(int r, G g) { assert(0 <= r && r <= _n); assert(g(e())); if (r == 0) return 0; r += size; for (int i = log; i >= 1; i--) push((r - 1) >> i); S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!g(op(d[r], sm))) { while (r < size) { push(r); r = (2 * r + 1); if (g(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while ((r & -r) != r); return 0; } private: int _n, size, log; std::vector<S> d; std::vector<F> lz; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } void all_apply(int k, F f) { d[k] = mapping(f, d[k]); if (k < size) lz[k] = composition(f, lz[k]); } void push(int k) { all_apply(2 * k, lz[k]); all_apply(2 * k + 1, lz[k]); lz[k] = id(); } }; } // namespace atcoder #include <algorithm> #include <cassert> #include <vector> namespace atcoder { template <class S, S (*op)(S, S), S (*e)()> struct segtree { public: segtree() : segtree(0) {} segtree(int n) : segtree(std::vector<S>(n, e())) {} segtree(const std::vector<S>& v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector<S>(2 * size, e()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) { assert(0 <= p && p < _n); return d[p + size]; } S prod(int l, int r) { assert(0 <= l && l <= r && r <= _n); S sml = e(), smr = e(); l += size; r += size; while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() { return d[1]; } template <bool (*f)(S)> int max_right(int l) { return max_right(l, [](S x) { return f(x); }); } template <class F> int max_right(int l, F f) { assert(0 <= l && l <= _n); assert(f(e())); if (l == _n) return _n; l += size; S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!f(op(sm, d[l]))) { while (l < size) { l = (2 * l); if (f(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while ((l & -l) != l); return _n; } template <bool (*f)(S)> int min_left(int r) { return min_left(r, [](S x) { return f(x); }); } template <class F> int min_left(int r, F f) { assert(0 <= r && r <= _n); assert(f(e())); if (r == 0) return 0; r += size; S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!f(op(d[r], sm))) { while (r < size) { r = (2 * r + 1); if (f(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while ((r & -r) != r); return 0; } private: int _n, size, log; std::vector<S> d; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } }; } // namespace atcoder int main(){ std::ifstream in("text.txt"); std::cin.rdbuf(in.rdbuf()); cin.tie(0); ios::sync_with_stdio(false); ll N;cin>>N; vi use,X(N),Y(N); for(int i=0;i<N;i++){ int a,b;cin>>a>>b; use.pb(a); use.pb(b); X[i]=a; Y[i]=b; } mkunique(use); for(int i=0;i<N;i++){ X[i]=lower_bound(all(use),X[i])-use.begin(); Y[i]=lower_bound(all(use),Y[i])-use.begin(); } int K=si(use); vii SS(N); for(int i=0;i<N;i++) SS[i]=mp(X[i],Y[i]); sort(all(SS)); ll P=0,Q=0,R=0,S=0; R=N*(N-1)/2; S=R; atcoder::fenwick_tree<ll> BI(K); ll i=0; while(i<N){ ll j=i; while(j<N&&SS[i].fi==SS[j].fi){ P+=BI.sum(0,SS[j].se); Q+=BI.sum(SS[j].se+1,K); j++; } for(int k=i;k<j;k++){ BI.add(SS[k].se,1); } R-=(j-i)*(j-i-1)/2; i=j; } for(int i=0;i<N;i++) swap(SS[i].fi,SS[i].se); sort(all(SS)); i=0; while(i<N){ ll j=i; while(j<N&&SS[i].fi==SS[j].fi){ j++; } S-=(j-i)*(j-i-1)/2; i=j; } double ans=P-Q; ans/=sqrtl((double)R*(double)S); //cout<<P<<" "<<Q<<" "<<R<<" "<<S<<endl; cout<<fixed<<setprecision(25)<<ans<<endl; }