結果

問題 No.2873 Kendall's Tau
ユーザー fuppy_kyoprofuppy_kyopro
提出日時 2024-09-06 21:48:30
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 523 ms / 4,500 ms
コード長 7,924 bytes
コンパイル時間 3,196 ms
コンパイル使用メモリ 233,788 KB
実行使用メモリ 43,416 KB
最終ジャッジ日時 2024-09-06 21:49:05
合計ジャッジ時間 11,742 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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 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
6,944 KB
testcase_07 AC 449 ms
34,636 KB
testcase_08 AC 484 ms
41,132 KB
testcase_09 AC 443 ms
34,316 KB
testcase_10 AC 523 ms
43,416 KB
testcase_11 AC 439 ms
33,740 KB
testcase_12 AC 465 ms
40,444 KB
testcase_13 AC 132 ms
13,412 KB
testcase_14 AC 380 ms
36,920 KB
testcase_15 AC 72 ms
10,596 KB
testcase_16 AC 77 ms
9,656 KB
testcase_17 AC 345 ms
28,500 KB
testcase_18 AC 251 ms
23,736 KB
testcase_19 AC 319 ms
28,604 KB
testcase_20 AC 76 ms
10,332 KB
testcase_21 AC 265 ms
22,804 KB
testcase_22 AC 110 ms
12,972 KB
testcase_23 AC 269 ms
23,540 KB
testcase_24 AC 34 ms
6,940 KB
testcase_25 AC 67 ms
9,600 KB
testcase_26 AC 333 ms
28,348 KB
testcase_27 AC 201 ms
20,136 KB
testcase_28 AC 383 ms
34,620 KB
testcase_29 AC 421 ms
35,388 KB
testcase_30 AC 54 ms
7,760 KB
testcase_31 AC 104 ms
11,612 KB
testcase_32 AC 263 ms
23,804 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 # 

/*
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
//*/

// #include <atcoder/all>
// #include <atcoder/segtree>
#include <bits/stdc++.h>

using namespace std;
// using namespace atcoder;

// #define _GLIBCXX_DEBUG

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                        \
    cerr << #v << ":";                                      \
    for (int iiiiiiii = 0; iiiiiiii < v.size(); iiiiiiii++) \
        cerr << " " << v[iiiiiiii];                         \
    cerr << endl;
#define DEBUG_MAT(v)                                \
    cerr << #v << endl;                             \
    for (int iv = 0; iv < v.size(); iv++) {         \
        for (int jv = 0; jv < v[iv].size(); jv++) { \
            cerr << v[iv][jv] << " ";               \
        }                                           \
        cerr << endl;                               \
    }
typedef long long ll;
// #define int ll

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
    return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template <class S, class T>
ostream &operator<<(ostream &os, pair<S, T> p) {
    os << "(" << p.first << ", " << p.second << ")";
    return os;
}
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n) - 1; i >= 0; i--)
#define rrep1(i, n) for (int i = (int)(n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), c.end()
void YES(bool t = true) {
    cout << (t ? "YES" : "NO") << endl;
}
void Yes(bool t = true) { cout << (t ? "Yes" : "No") << endl; }
void yes(bool t = true) { cout << (t ? "yes" : "no") << endl; }
void NO(bool t = true) { cout << (t ? "NO" : "YES") << endl; }
void No(bool t = true) { cout << (t ? "No" : "Yes") << endl; }
void no(bool t = true) { cout << (t ? "no" : "yes") << endl; }
template <class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T, class U>
T ceil_div(T a, U b) {
    return (a + b - 1) / b;
}
template <class T>
T safe_mul(T a, T b) {
    if (a == 0 || b == 0) return 0;
    if (numeric_limits<T>::max() / a < b) return numeric_limits<T>::max();
    return a * b;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const long double pi = 3.1415926535897932384626433832795028841971L;
int popcount(ll t) { return __builtin_popcountll(t); }
vector<int> gen_perm(int n) {
    vector<int> ret(n);
    iota(all(ret), 0);
    return ret;
}
// int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
// int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
vi dx = {0, 0, -1, 1}, dy = {-1, 1, 0, 0};
vi dx2 = {1, 1, 0, -1, -1, -1, 0, 1}, dy2 = {0, 1, 1, 1, 0, -1, -1, -1};
struct Setup_io {
    Setup_io() {
        ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        cout << fixed << setprecision(25);
        cerr << fixed << setprecision(25);
    }
} setup_io;
// constexpr ll MOD = 1000000007;
constexpr ll MOD = 998244353;
// #define mp make_pair

template <typename T>
class Zaatsu {
    bool is_build;
    vector<T> elements;

  public:
    Zaatsu() : is_build(false) {}

    void add(T x) {
        elements.push_back(x);
    }

    void add(vector<T> x) {
        for (int i = 0; i < (int)x.size(); i++) {
            elements.push_back(x[i]);
        }
    }

    int build() {
        sort(elements.begin(), elements.end());
        UNIQUE(elements);
        is_build = true;
        return elements.size();
    }

    int operator[](T x) {
        assert(is_build);
        return lower_bound(elements.begin(), elements.end(), x) - elements.begin();
    }

    T original(int i) {
        assert(is_build);
        return elements[i];
    }
};

template <typename T>
class SegmentTree {
  public:
    using F = function<T(T &, T &)>;
    int n;
    vector<T> dat;
    T e;
    F query_func;
    F update_func;

    SegmentTree(vector<T> a, F query_func, F update_func, T e) : n(a.size()), query_func(query_func), update_func(update_func), e(e) {
        if (n == 0) {
            a.push_back(e);
            n++;
        }
        dat.resize(4 * n);
        init(0, 0, n, a);
    }

    void init(int k, int l, int r, vector<T> &a) {
        if (r - l == 1) {
            dat[k] = a[l];
        } else {
            int lch = 2 * k + 1, rch = 2 * k + 2;
            init(lch, l, (l + r) / 2, a);
            init(rch, (l + r) / 2, r, a);
            dat[k] = query_func(dat[lch], dat[rch]);
        }
    }

    void update(int k, T a, int v, int l, int r) {
        if (r - l == 1) {
            dat[v] = update_func(dat[v], a);
        } else {
            if (k < (l + r) / 2)
                update(k, a, 2 * v + 1, l, (l + r) / 2);
            else {
                update(k, a, 2 * v + 2, (l + r) / 2, r);
            }
            dat[v] = query_func(dat[v * 2 + 1], dat[v * 2 + 2]);
        }
    }

    void update(int k, T a) {
        update(k, a, 0, 0, n);
    }

    T query(int a, int b, int k, int l, int r) {
        if (r <= a || b <= l) {
            return e;
        }
        if (a <= l && r <= b) {
            return dat[k];
        } else {
            T ul = query(a, b, k * 2 + 1, l, (l + r) / 2);
            T ur = query(a, b, k * 2 + 2, (l + r) / 2, r);
            return query_func(ul, ur);
        }
    }

    T query(int a, int b) {
        return query(a, b, 0, 0, n);
    }

    int find(int a, int b, int k, int l, int r, int x) {
        if (dat[k] < x || r <= a || b <= l) return -1;
        if (l + 1 == r) {
            if (dat[k] >= x)
                return l;
            else
                return -1;
        }
        int rv = find(a, b, 2 * k + 2, (l + r) / 2, r, x);
        if (rv != -1) return rv;
        return find(a, b, 2 * k + 1, l, (l + r) / 2, x);
    }
};

ll f(ll a, ll b) {
    return a + b;
}
ll g(ll a, ll b) {
    return a + b;
}

ll get_r(vl x, int cnt, ll n) {
    vl num(cnt);
    for (ll i : x) {
        num[i]++;
    }

    ll ret = 0;
    rep(i, cnt) {
        ret += num[i] * (n - num[i]);
    }

    return ret / 2;
}

ll get_p(vector<pll> xy, int cnt, ll n) {
    sort(all(xy));
    vll x2y(cnt);
    for (pll p : xy) {
        x2y[p.first].push_back(p.second);
    }

    SegmentTree<ll> st(vl(cnt), f, g, 0);
    ll ret = 0;
    rep(x, cnt) {
        for (ll y : x2y[x]) {
            ret += st.query(0, y);
        }
        for (ll y : x2y[x]) {
            st.update(y, 1);
        }
    }

    return ret;
}

signed main() {
    int n;
    cin >> n;

    vector<pll> xy(n);
    Zaatsu<ll> za;
    rep(i, n) {
        cin >> xy[i].first >> xy[i].second;
        za.add(xy[i].first);
        za.add(xy[i].second);
    }

    int cnt = za.build();
    rep(i, n) {
        xy[i].first = za[xy[i].first];
        xy[i].second = za[xy[i].second];
    }

    vl xs, ys;
    rep(i, n) {
        xs.push_back(xy[i].first);
        ys.push_back(xy[i].second);
    }

    ll r = get_r(xs, cnt, n);
    ll s = get_r(ys, cnt, n);

    ll p = get_p(xy, cnt, n);
    rep(i, n) {
        xy[i].second = cnt - 1 - xy[i].second;
    }
    ll q = get_p(xy, cnt, n);

    cout << (p - q) / (sqrtl(r) * sqrtl(s)) << endl;
}
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