結果

問題 No.2873 Kendall's Tau
ユーザー siganaisiganai
提出日時 2024-09-06 21:51:50
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 732 ms / 4,500 ms
コード長 8,574 bytes
コンパイル時間 2,582 ms
コンパイル使用メモリ 222,916 KB
実行使用メモリ 44,672 KB
最終ジャッジ日時 2024-09-06 21:52:05
合計ジャッジ時間 13,098 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
6,944 KB
testcase_04 AC 2 ms
6,944 KB
testcase_05 AC 2 ms
6,944 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 570 ms
30,208 KB
testcase_08 AC 719 ms
40,832 KB
testcase_09 AC 572 ms
29,824 KB
testcase_10 AC 732 ms
44,672 KB
testcase_11 AC 551 ms
28,672 KB
testcase_12 AC 669 ms
38,784 KB
testcase_13 AC 141 ms
12,288 KB
testcase_14 AC 526 ms
35,584 KB
testcase_15 AC 80 ms
10,368 KB
testcase_16 AC 79 ms
9,216 KB
testcase_17 AC 423 ms
24,960 KB
testcase_18 AC 310 ms
23,424 KB
testcase_19 AC 403 ms
26,624 KB
testcase_20 AC 80 ms
9,728 KB
testcase_21 AC 338 ms
20,224 KB
testcase_22 AC 117 ms
11,392 KB
testcase_23 AC 312 ms
21,248 KB
testcase_24 AC 32 ms
6,944 KB
testcase_25 AC 72 ms
9,856 KB
testcase_26 AC 368 ms
22,400 KB
testcase_27 AC 263 ms
19,968 KB
testcase_28 AC 523 ms
33,920 KB
testcase_29 AC 567 ms
31,616 KB
testcase_30 AC 56 ms
7,424 KB
testcase_31 AC 111 ms
11,008 KB
testcase_32 AC 324 ms
22,912 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 1 "main.cpp"
#include<bits/stdc++.h>
using namespace std;
// #pragma GCC target("avx,avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#ifdef LOCAL
#include <debug.hpp>
#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (static_cast<void>(0))
#endif
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll,ll>;
using pii = pair<int,int>;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vul = vector<ull>;
using vpii = vector<pii>;
using vvpii = vector<vpii>;
using vpll = vector<pll>;
using vs = vector<string>;
template<class T> using pq = priority_queue<T,vector<T>, greater<T>>;
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload3(a,b,c,name,...) name
#define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER)
#define rep2(i, n) for (ll i = 0; i < (n); ++i)
#define rep3(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--)
#define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define all1(i) begin(i) , end(i)
#define all2(i,a) begin(i) , begin(i) + a
#define all3(i,a,b) begin(i) + a , begin(i) + b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; }
template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; }
template<class T> auto min(const T& a){return *min_element(all(a));}
template<class T> auto max(const T& a){return *max_element(all(a));}
template<class... Ts> void in(Ts&... t);
#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)
#define VEC(type, name, size) vector<type> name(size); in(name)
#define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name)
ll intpow(ll a, ll b){ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;}
ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
bool is_clamp(ll val,ll low,ll high) {return low <= val && val < high;}
void Yes() {cout << "Yes\n";return;}
void No() {cout << "No\n";return;}
void YES() {cout << "YES\n";return;}
void NO() {cout << "NO\n";return;}
template <typename T>
T floor(T a, T b) {return a / b - (a % b && (a ^ b) < 0);}
template <typename T>
T ceil(T x, T y) {return floor(x + y - 1, y);}
template <typename T>
T bmod(T x, T y) {return x - y * floor(x, y);}
template <typename T>
pair<T, T> divmod(T x, T y) {T q = floor(x, y);return {q, x - q * y};}
namespace IO{
#define VOID(a) decltype(void(a))
struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(15);}} setting;
template<int I> struct P : P<I-1>{};
template<> struct P<0>{};
template<class T> void i(T& t){ i(t, P<3>{}); }
void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; }
template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; }
template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); }
template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){in(get<idx>(t)...);}
template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){ituple(t, make_index_sequence<tuple_size<T>::value>{});} 
#undef VOID
}
#define unpack(a) (void)initializer_list<int>{(a, 0)...}
template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); }
#undef unpack
constexpr long double PI = 3.141592653589793238462643383279L;
template <class F> struct REC {
    F f;
    REC(F &&f_) : f(forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }};

constexpr int mod = 998244353;
//constexpr int mod = 1000000007;
#line 2 "library/segtree/segtree.hpp"
template <typename T, typename OP>
struct segtree {
    int N;
    int size;
    vector<T> seg;
    const OP op;
    const T I;
    segtree(OP _op, const T I_) : N(0), size(0), op(_op), I(I_) {}
    explicit segtree(int _N, const OP _op, const T I_) : op(_op), I(I_) { init(_N); }
    explicit segtree(const vector<T> &v, const OP _op, const T I_) : op(_op), I(I_) {
        init(v.size());
        for (int i = 0; i < (int)v.size(); i++) {
            seg[i + size] = v[i];
        }
        build();
    }
    void init(int _N) {
        N = _N;
        size = 1;
        while (size < N) size <<= 1;
        seg.assign(2 * size, I);
    }
    void build() {
        for (int k = size - 1; k > 0; k--) {
            seg[k] = op(seg[2 * k], seg[2 * k + 1]);
        }
    }
    void set(int p, T x) {
        assert(0 <= p && p < N);
        p += size;
        seg[p] = x;
        while (p >>= 1) {
            seg[p] = op(seg[2 * p], seg[2 * p + 1]);
        }
    }
    void add(int p, T x) {
        assert(0 <= p && p < N);
        p += size;
        seg[p] += x;
        while (p >>= 1) {
            seg[p] = op(seg[2 * p], seg[2 * p + 1]);
        }
    }
    T get(int p) const {
        assert(0 <= p && p < N);
        return seg[p + size];
    }
    // query to [l, r)
    T prod(int l, int r) {
        assert(0 <= l && l <= r && r <= N);
        T L = I, R = I;
        for (l += size, r += size; l < r; l >>= 1, r >>= 1) {
            if (l & 1) L = op(L, seg[l++]);
            if (r & 1) R = op(seg[--r], R);
        }
        return op(L, R);
    }
    T all_prod() {return seg[1];}
    // check(a[l] * ...  * a[r-1]) が true となる最大の r
    // (右端まですべて true なら N を返す)
    template <class C>
    int max_right(int l, C check) {
        assert(0 <= l && l <= N);
        assert(check(I) == true);
        if (l == N) return N;
        l += size;
        T sm = I;
        do {
            while (l % 2 == 0) l >>= 1;
            if (!check(op(sm, seg[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (check(op(sm, seg[l]))) {
                        sm = op(sm, seg[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, seg[l]);
            l++;
        } while ((l & -l) != l);
        return N;
    }
    // check(a[l] * ... * a[r-1]) が true となる最小の l
    // (左端まで true なら 0 を返す)
    template <typename C>
    int min_left(int r, C check) {
        assert(0 <= r && r <= N);
        assert(check(I) == true);
        if (r == 0) return 0;
        r += size;
        T sm = I;
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!check(op(seg[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (check(op(seg[r], sm))) {
                        sm = op(seg[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(seg[r], sm);
        } while ((r & -r) != r);
        return 0;
    }
};
#line 100 "main.cpp"
using T = int;
T op(T x,T y) {return x + y;}
T e() {return 0;}
int main() {
	INT(n);
	vi x(n),y(n);
	rep(i,n) cin >> x[i] >> y[i];
	ll r = 1LL * n * (n - 1) / 2;
	ll s = r;
	map<int,int> mpx,mpy;
	rep(i,n) {
		r -= mpx[x[i]];
		++mpx[x[i]];
		s -= mpy[y[i]];
		++mpy[y[i]];
	}
	map<int,vi> mp;
	rep(i,n) mp[x[i]].emplace_back(i);
	ll p = 0,q = 0;
	vi Y = y;
	sort(all(Y));
	Y.erase(unique(all(Y)),Y.end());
	segtree<int,decltype(&op)> seg(Y.size(),op,e());
	for(auto &[_,v]:mp) {
		rep(i,v.size()) {
			int id = lower_bound(all(Y),y[v[i]]) - Y.begin();
			p += seg.prod(0,id);
			q += seg.prod(id+1,Y.size());
		}
		rep(i,v.size()) {
			int id = lower_bound(all(Y),y[v[i]]) - Y.begin();
			seg.add(id,1);
		}
	}
	cout << (p - q) / (sqrt(r) * sqrt(s)) << '\n';
}
0