結果
| 問題 | No.2873 Kendall's Tau |
| ユーザー |
 Moss_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 |
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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 | - |
ソースコード
#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;
}