結果

問題 No.2873 Kendall's Tau
ユーザー Moss_LocalMoss_Local
提出日時 2024-09-06 22:37:15
言語 C++23(gcc13)
(gcc 13.2.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 18,728 bytes
コンパイル時間 5,692 ms
コンパイル使用メモリ 342,852 KB
実行使用メモリ 27,780 KB
最終ジャッジ日時 2024-09-06 22:37:53
合計ジャッジ時間 17,438 ms
ジャッジサーバーID
(参考情報)
judge3 / judge1
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
6,944 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
6,940 KB
testcase_07 WA -
testcase_08 WA -
testcase_09 WA -
testcase_10 WA -
testcase_11 WA -
testcase_12 WA -
testcase_13 AC 170 ms
9,540 KB
testcase_14 WA -
testcase_15 AC 97 ms
7,904 KB
testcase_16 AC 121 ms
7,148 KB
testcase_17 WA -
testcase_18 WA -
testcase_19 WA -
testcase_20 AC 101 ms
7,900 KB
testcase_21 WA -
testcase_22 AC 161 ms
10,640 KB
testcase_23 WA -
testcase_24 AC 38 ms
6,944 KB
testcase_25 AC 84 ms
7,176 KB
testcase_26 WA -
testcase_27 WA -
testcase_28 WA -
testcase_29 WA -
testcase_30 AC 69 ms
6,944 KB
testcase_31 AC 126 ms
8,204 KB
testcase_32 WA -
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 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない?
// #pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T> constexpr T infty = 0;
template <> constexpr int infty<int> = 1'000'000'000;
template <> constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <> constexpr u32 infty<u32> = infty<int>;
template <> constexpr u64 infty<u64> = infty<ll>;
template <> constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <> constexpr double infty<double> = infty<ll>;
template <> constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using vvvvvc = vector<vvvvc<T>>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...)                                                 \
    vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)                                             \
    vector<vector<vector<type>>> name(                                         \
        h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)                                         \
    vector<vector<vector<vector<type>>>> name(                                 \
        a, vector<vector<vector<type>>>(                                       \
               b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for(ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for(ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for(ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for(ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for(ll i = (a) - 1; i >= ll(0); --i)
#define FOR2_R(i, a) for(ll i = (a) - 1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for(ll i = (b) - 1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s)                                                       \
    for(ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

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};
}

template <typename T, typename U> T SUM(const vector<U> &A) {
    T sm = 0;
    for(auto &&a : A)
        sm += a;
    return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x)                                                              \
    sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T> T POP(deque<T> &que) {
    T a = que.front();
    que.pop_front();
    return a;
}
template <typename T> T POP(pq<T> &que) {
    T a = que.top();
    que.pop();
    return a;
}
template <typename T> T POP(pqg<T> &que) {
    T a = que.top();
    que.pop();
    return a;
}
template <typename T> T POP(vc<T> &que) {
    T a = que.back();
    que.pop_back();
    return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
    if(check_ok)
        assert(check(ok));
    while(abs(ok - ng) > 1) {
        auto x = (ng + ok) / 2;
        (check(x) ? ok : ng) = x;
    }
    return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
    FOR(iter) {
        double x = (ok + ng) / 2;
        (check(x) ? ok : ng) = x;
    }
    return (ok + ng) / 2;
}

template <class T, class S> inline bool chmax(T &a, const S &b) {
    return (a < b ? a = b, 1 : 0);
}
template <class T, class S> inline bool chmin(T &a, const S &b) {
    return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
    vc<int> A(S.size());
    FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
    return A;
}

template <typename T, typename U> vector<T> cumsum(vector<U> &A, int off = 1) {
    int N = A.size();
    vector<T> B(N + 1);
    FOR(i, N) { B[i + 1] = B[i] + A[i]; }
    if(off == 0)
        B.erase(B.begin());
    return B;
}

// stable sort
template <typename T> vector<int> argsort(const vector<T> &A) {
    vector<int> ids(len(A));
    iota(all(ids), 0);
    sort(all(ids),
         [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
    return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T> vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
    vc<T> B(len(I));
    FOR(i, len(I)) B[i] = A[I[i]];
    return B;
}
#endif
#line 1 "library/other/io.hpp"
#define FASTIO
#include <unistd.h>

// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
    char num[10000][4];
    constexpr Pre() : num() {
        for(int i = 0; i < 10000; i++) {
            int n = i;
            for(int j = 3; j >= 0; j--) {
                num[i][j] = n % 10 | '0';
                n /= 10;
            }
        }
    }
} constexpr pre;

inline void load() {
    memcpy(ibuf, ibuf + pil, pir - pil);
    pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
    pil = 0;
    if(pir < SZ)
        ibuf[pir++] = '\n';
}

inline void flush() {
    fwrite(obuf, 1, por, stdout);
    por = 0;
}

void rd(char &c) {
    do {
        if(pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while(isspace(c));
}

void rd(string &x) {
    x.clear();
    char c;
    do {
        if(pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while(isspace(c));
    do {
        x += c;
        if(pil == pir)
            load();
        c = ibuf[pil++];
    } while(!isspace(c));
}

template <typename T> void rd_real(T &x) {
    string s;
    rd(s);
    x = stod(s);
}

template <typename T> void rd_integer(T &x) {
    if(pil + 100 > pir)
        load();
    char c;
    do
        c = ibuf[pil++];
    while(c < '-');
    bool minus = 0;
    if constexpr(is_signed<T>::value || is_same_v<T, i128>) {
        if(c == '-') {
            minus = 1, c = ibuf[pil++];
        }
    }
    x = 0;
    while('0' <= c) {
        x = x * 10 + (c & 15), c = ibuf[pil++];
    }
    if constexpr(is_signed<T>::value || is_same_v<T, i128>) {
        if(minus)
            x = -x;
    }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U> void rd(pair<T, U> &p) {
    return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T> void rd_tuple(T &t) {
    if constexpr(N < std::tuple_size<T>::value) {
        auto &x = std::get<N>(t);
        rd(x);
        rd_tuple<N + 1>(t);
    }
}
template <class... T> void rd(tuple<T...> &tpl) { rd_tuple(tpl); }

template <size_t N = 0, typename T> void rd(array<T, N> &x) {
    for(auto &d : x)
        rd(d);
}
template <class T> void rd(vc<T> &x) {
    for(auto &d : x)
        rd(d);
}

void read() {}
template <class H, class... T> void read(H &h, T &...t) { rd(h), read(t...); }

void wt(const char c) {
    if(por == SZ)
        flush();
    obuf[por++] = c;
}
void wt(const string s) {
    for(char c : s)
        wt(c);
}
void wt(const char *s) {
    size_t len = strlen(s);
    for(size_t i = 0; i < len; i++)
        wt(s[i]);
}

template <typename T> void wt_integer(T x) {
    if(por > SZ - 100)
        flush();
    if(x < 0) {
        obuf[por++] = '-', x = -x;
    }
    int outi;
    for(outi = 96; x >= 10000; outi -= 4) {
        memcpy(out + outi, pre.num[x % 10000], 4);
        x /= 10000;
    }
    if(x >= 1000) {
        memcpy(obuf + por, pre.num[x], 4);
        por += 4;
    } else if(x >= 100) {
        memcpy(obuf + por, pre.num[x] + 1, 3);
        por += 3;
    } else if(x >= 10) {
        int q = (x * 103) >> 10;
        obuf[por] = q | '0';
        obuf[por + 1] = (x - q * 10) | '0';
        por += 2;
    } else
        obuf[por++] = x | '0';
    memcpy(obuf + por, out + outi + 4, 96 - outi);
    por += 96 - outi;
}

template <typename T> void wt_real(T x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << double(x);
    string s = oss.str();
    wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U> void wt(const pair<T, U> val) {
    wt(val.first);
    wt(' ');
    wt(val.second);
}
template <size_t N = 0, typename T> void wt_tuple(const T t) {
    if constexpr(N < std::tuple_size<T>::value) {
        if constexpr(N > 0) {
            wt(' ');
        }
        const auto x = std::get<N>(t);
        wt(x);
        wt_tuple<N + 1>(t);
    }
}
template <class... T> void wt(tuple<T...> tpl) { wt_tuple(tpl); }
template <class T, size_t S> void wt(const array<T, S> val) {
    auto n = val.size();
    for(size_t i = 0; i < n; i++) {
        if(i)
            wt(' ');
        wt(val[i]);
    }
}
template <class T> void wt(const vector<T> val) {
    auto n = val.size();
    for(size_t i = 0; i < n; i++) {
        if(i)
            wt(' ');
        wt(val[i]);
    }
}

void print() { wt('\n'); }
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
    wt(head);
    if(sizeof...(Tail))
        wt(' ');
    print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::flush;
using fastio::print;
using fastio::read;

#if defined(LOCAL)
#define SHOW(...)                                                              \
    SHOW_IMPL(__VA_ARGS__, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w)                                                      \
    print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#else
#define SHOW(...)
#endif

#define INT(...)                                                               \
    int __VA_ARGS__;                                                           \
    read(__VA_ARGS__)
#define LL(...)                                                                \
    ll __VA_ARGS__;                                                            \
    read(__VA_ARGS__)
#define U32(...)                                                               \
    u32 __VA_ARGS__;                                                           \
    read(__VA_ARGS__)
#define U64(...)                                                               \
    u64 __VA_ARGS__;                                                           \
    read(__VA_ARGS__)
#define STR(...)                                                               \
    string __VA_ARGS__;                                                        \
    read(__VA_ARGS__)
#define CHAR(...)                                                              \
    char __VA_ARGS__;                                                          \
    read(__VA_ARGS__)
#define DBL(...)                                                               \
    double __VA_ARGS__;                                                        \
    read(__VA_ARGS__)

#define VEC(type, name, size)                                                  \
    vector<type> name(size);                                                   \
    read(name)
#define VV(type, name, h, w)                                                   \
    vector<vector<type>> name(h, vector<type>(w));                             \
    read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }

#include <iomanip> // for precision
#include <iostream>
#include <set>
#include <vector>

using namespace std;

struct Point {
    long long x, y;
};

// カウント結果を保持する構造体
struct CountResult {
    long long P, Q;
};

using namespace std;

// 座標圧縮用関数
vector<int> compress_coordinates(const vector<long long> &values) {
    set<long long> s(values.begin(), values.end());
    vector<int> compressed(values.size());
    map<long long, int> compressed_map;
    int idx = 0;
    for(const auto &v : s) {
        compressed_map[v] = idx++;
    }
    for(size_t i = 0; i < values.size(); ++i) {
        compressed[i] = compressed_map[values[i]];
    }
    return compressed;
}

// セグメント木クラス
class SegmentTree {
  public:
    SegmentTree(int n) : n(n) { tree.assign(2 * n, 0); }

    // 値の加算
    void update(int pos, int value) {
        pos += n;
        tree[pos] += value;
        for(pos /= 2; pos > 0; pos /= 2) {
            tree[pos] = tree[2 * pos] + tree[2 * pos + 1];
        }
    }

    // 区間の合計を取得
    int query(int l, int r) { // 区間 [l, r) の合計を取得
        int res = 0;
        for(l += n, r += n; l < r; l /= 2, r /= 2) {
            if(l & 1)
                res += tree[l++];
            if(r & 1)
                res += tree[--r];
        }
        return res;
    }

  private:
    int n;
    vector<int> tree;
};

CountResult calculate_P_Q(const vector<Point> &points) {
    vector<long long> y_vals;
    for(const auto &p : points) {
        y_vals.push_back(p.y);
    }

    // Yの座標圧縮
    vector<int> compressed_y = compress_coordinates(y_vals);
    int max_y = *max_element(compressed_y.begin(), compressed_y.end());

    SegmentTree seg_tree(max_y + 1); // 座標圧縮後のY値に対応するセグメント木

    long long P = 0, Q = 0;
    long long prev_x = points[0].x;
    vector<int> y_values; // 圧縮されたY値のリスト

    for(size_t i = 0; i < points.size(); ++i) {
        const auto &p = points[i];
        int comp_y = compressed_y[i]; // 圧縮されたY値を取得

        if(p.x != prev_x) {
            // Xが変わったら、セグメント木にY値を追加
            for(const auto &y : y_values) {
                seg_tree.update(y, 1);
            }
            y_values.clear();
        }

        // 現在のp.yより小さい値のカウント (0からcomp_y-1までの区間)
        P += seg_tree.query(0, comp_y);

        // 現在のp.yより大きい値のカウント (comp_y+1からmax_yまでの区間)
        Q += seg_tree.query(comp_y + 1, max_y + 1);

        // Y値を保存して、次の段階でセグメント木に追加
        y_values.push_back(comp_y);

        prev_x = p.x;
    }

    return {P, Q};
}
int main() {
    int N;
    cin >> N;
    vector<Point> points(N);

    for(int i = 0; i < N; i++) {
        cin >> points[i].x >> points[i].y;
    }

    // Xの値で昇順にソート(Xが同じ場合はYでソート)
    sort(points.begin(), points.end(), [](const Point &a, const Point &b) {
        return a.x < b.x || (a.x == b.x && a.y < b.y);
    });

    // P と Q の計算
    CountResult result = calculate_P_Q(points);

    long long P = result.P;
    long long Q = result.Q;

    // 全ペア数
    // long long total_pairs = (long long)N * (N - 1) / 2;
    long long R = 0;
    long long S = 0;
    map<long long, long long> cnt_x;
    map<long long, long long> cnt_y;
    for(int i = 0; i < N; i++) {
        cnt_x[points[i].x]++;
        cnt_y[points[i].y]++;
    }

    // points for
    for(int i = 0; i < N; i++) {
        R += N - (cnt_x[points[i].x]);
        S += N - (cnt_y[points[i].y]);
    }
    R /= 2;
    S /= 2;
    // cout << P << " " << Q << " " << R << " " << S << endl;

    // ケンドールの順位相関係数 τ の計算
    double tau = (double)(P - Q) / sqrt(double(R * S));

    // 結果の出力(精度に注意)
    cout << fixed << setprecision(16) << tau << endl;

    return 0;
}
0