結果
問題 | No.2977 Kth Xor Pair |
ユーザー |
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提出日時 | 2024-12-01 17:06:35 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2,387 ms / 3,000 ms |
コード長 | 17,472 bytes |
コンパイル時間 | 1,519 ms |
コンパイル使用メモリ | 140,404 KB |
実行使用メモリ | 170,036 KB |
最終ジャッジ日時 | 2024-12-01 17:07:50 |
合計ジャッジ時間 | 45,012 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 34 |
ソースコード
#include<iostream>#include<string>#include<vector>#include<algorithm>#include<numeric>#include<cmath>#include<utility>#include<tuple>#include<array>#include<cstdint>#include<cstdio>#include<iomanip>#include<map>#include<set>#include<unordered_map>#include<unordered_set>#include<queue>#include<stack>#include<deque>#include<bitset>#include<cctype>#include<chrono>#include<random>#include<cassert>#include<cstddef>#include<iterator>#include<string_view>#include<type_traits>#include<functional>#ifdef LOCAL# include "debug_print.hpp"# define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)#else# define debug(...) (static_cast<void>(0))#endifusing namespace std;namespace io {template <typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p) {is >> p.first >> p.second;return is;}template <typename T>istream &operator>>(istream &is, vector<T> &v) {for (auto &x : v) is >> x;return is;}template <typename T, size_t N = 0>istream &operator>>(istream &is, array<T, N> &v) {for (auto &x : v) is >> x;return is;}template <size_t N = 0, typename T>istream& cin_tuple_impl(istream &is, T &t) {if constexpr (N < std::tuple_size<T>::value) {auto &x = std::get<N>(t);is >> x;cin_tuple_impl<N + 1>(is, t);}return is;}template <class... T>istream &operator>>(istream &is, tuple<T...> &t) {return cin_tuple_impl(is, t);}template<typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p) {os << p.first << " " << p.second;return os;}template<typename T>ostream &operator<<(ostream &os, const vector<T> &v) {int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template<typename T, size_t N>ostream &operator<<(ostream &os, const array<T, N> &v) {size_t n = v.size();for (size_t i = 0; i < n; i++) {if (i) os << " ";os << v[i];}return os;}template <size_t N = 0, typename T>ostream& cout_tuple_impl(ostream &os, const T &t) {if constexpr (N < std::tuple_size<T>::value) {if constexpr (N > 0) os << " ";const auto &x = std::get<N>(t);os << x;cout_tuple_impl<N + 1>(os, t);}return os;}template <class... T>ostream &operator<<(ostream &os, const tuple<T...> &t) {return cout_tuple_impl(os, t);}void in() {}template<typename T, class... U>void in(T &t, U &...u) {cin >> t;in(u...);}void out() { cout << "\n"; }template<typename T, class... U, char sep = ' '>void out(const T &t, const U &...u) {cout << t;if (sizeof...(u)) cout << sep;out(u...);}void outr() {}template<typename T, class... U, char sep = ' '>void outr(const T &t, const U &...u) {cout << t;outr(u...);}void __attribute__((constructor)) _c() {ios_base::sync_with_stdio(false);cin.tie(nullptr);cout << fixed << setprecision(15);}} // namespace iousing io::in;using io::out;using io::outr;using ll = long long;using D = double;using LD = long double;using P = pair<ll, ll>;using u8 = uint8_t;using u16 = uint16_t;using u32 = uint32_t;using u64 = uint64_t;using i128 = __int128;using u128 = unsigned __int128;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>>;#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__))))template<typename T> using PQ = priority_queue<T,vector<T>>;template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;#define rep1(a) for(ll i = 0; i < a; i++)#define rep2(i, a) for(ll i = 0; i < a; 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 overload4(a, b, c, d, e, ...) e#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)#define rrep1(a) for(ll i = (a)-1; i >= 0; i--)#define rrep2(i, a) for(ll i = (a)-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 = (b)-1; i >= a; i -= c)#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)#define for_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))#define ALL(v) v.begin(), v.end()#define RALL(v) v.rbegin(), v.rend()#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() )#define SZ(v) ll(v.size())#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)))template <typename T, typename U>T SUM(const vector<U> &v) {T res = 0;for(auto &&a : v) res += a;return res;}template <typename T>vector<pair<T,int>> RLE(const vector<T> &v) {if (v.empty()) return {};T cur = v.front();int cnt = 1;vector<pair<T,int>> res;for (int i = 1; i < (int)v.size(); i++) {if (cur == v[i]) cnt++;else {res.emplace_back(cur, cnt);cnt = 1; cur = v[i];}}res.emplace_back(cur, cnt);return res;}template<class T, class S>inline bool chmax(T &a, const S &b) { return (a < b ? a = b, true : false); }template<class T, class S>inline bool chmin(T &a, const S &b) { return (a > b ? a = b, true : false); }void YESNO(bool flag) { out(flag ? "YES" : "NO"); }void yesno(bool flag) { out(flag ? "Yes" : "No"); }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_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); }int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }int popcnt_sgn(ll x) { return (__builtin_parity(x) & 1 ? -1 : 1); }int popcnt_sgn(u64 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }int highbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int highbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int highbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }int highbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }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 get_bit(T x, int k) { return x >> k & 1; }template <typename T>T set_bit(T x, int k) { return x | T(1) << k; }template <typename T>T reset_bit(T x, int k) { return x & ~(T(1) << k); }template <typename T>T flip_bit(T x, int k) { return x ^ T(1) << k; }template <typename T>T popf(deque<T> &que) { T a = que.front(); que.pop_front(); return a; }template <typename T>T popb(deque<T> &que) { T a = que.back(); que.pop_back(); return a; }template <typename T>T pop(queue<T> &que) { T a = que.front(); que.pop(); return a; }template <typename T>T pop(stack<T> &que) { T a = que.top(); que.pop(); return a; }template <typename T>T pop(PQ<T> &que) { T a = que.top(); que.pop(); return a; }template <typename T>T pop(minPQ<T> &que) { T a = que.top(); que.pop(); 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) {ll mid = (ok + ng) / 2;(check(mid) ? ok : ng) = mid;}return ok;}template <typename F>ll binary_search_real(F check, double ok, double ng, int iter = 60) {for (int _ = 0; _ < iter; _++) {double mid = (ok + ng) / 2;(check(mid) ? ok : ng) = mid;}return (ok + ng) / 2;}// max x s.t. b*x <= all div_floor(ll a, ll b) {assert(b != 0);if (b < 0) a = -a, b = -b;return a / b - (a % b < 0);}// max x s.t. b*x < all div_under(ll a, ll b) {assert(b != 0);if (b < 0) a = -a, b = -b;return a / b - (a % b <= 0);}// min x s.t. b*x >= all div_ceil(ll a, ll b) {assert(b != 0);if (b < 0) a = -a, b = -b;return a / b + (a % b > 0);}// min x s.t. b*x > all div_over(ll a, ll b) {assert(b != 0);if (b < 0) a = -a, b = -b;return a / b + (a % b >= 0);}// x = a mod b (b > 0), 0 <= x < bll modulo(ll a, ll b) {assert(b > 0);ll c = a % b;return c < 0 ? c + b : c;}// (q,r) s.t. a = b*q + r, 0 <= r < b (b > 0)// div_floor(a,b), modulo(a,b)pair<ll,ll> divmod(ll a, ll b) {ll q = div_floor(a,b);return {q, a - b*q};}template <typename T, int MAX_LOG>struct BinaryTrie {public:struct Node {Node *nxt[2];int exist;vector<int> accept;Node(): nxt{nullptr, nullptr}, exist(0) {}};Node *root;T lazy;explicit BinaryTrie(): root(new Node()), lazy(T(0)) {}void insert(const T &x, int idx = -1) {insert(root, x, MAX_LOG, 1, idx);}void erase(const T &x) {insert(root, x, MAX_LOG, -1, -1);}Node *find(const T &x) {return find(root, x, MAX_LOG);}int count(const T &x) {Node *nx = find(x);return nx == nullptr ? 0 : nx->exist;}pair<T, Node *> min_element() {assert(root->exist > 0);return kth_element(0);}pair<T, Node *> max_element() {assert(root->exist > 0);return kth_element(root->exist - 1);}pair<T, Node *> kth_element(int k) {assert(0 <= k and k < root->exist);return kth_element(root, k, MAX_LOG);}int count_less(const T &x) {return count_less(root, x, MAX_LOG);}int count_leq(const T &x) {return count_less(root, x+1, MAX_LOG);}int count_greater(const T &x) {return root->exist - count_less(root, x+1, MAX_LOG);}int count_geq(const T &x) {return root->exist - count_less(root, x, MAX_LOG);}void operate_xor(const T &x) {lazy ^= x;}private:void insert(Node *n_cur, const T &x, int depth, int delta, int idx) {if (depth == -1) {n_cur->exist += delta;if (idx != -1) n_cur->accept.emplace_back(idx);}else {bool nxt_01 = (lazy >> depth & 1) ^ (x >> depth & 1);if(!n_cur->nxt[nxt_01]) n_cur->nxt[nxt_01] = new Node();insert(n_cur->nxt[nxt_01], x, depth - 1, delta, idx);n_cur->exist += delta;}}Node *find(Node *n_cur, const T &x, int depth) {if (depth == -1) {return n_cur;}else {bool nxt_01 = (lazy >> depth & 1) ^ (x >> depth & 1);Node *n_nxt = n_cur->nxt[nxt_01];return n_nxt == nullptr ? n_nxt : find(n_nxt, x, depth - 1);}}pair<T, Node *> kth_element(Node *n_cur, int k, int depth) {if (depth == -1) {return make_pair(0, n_cur);}else {bool nxt_01 = lazy >> depth & 1;int comp = n_cur->nxt[nxt_01] == nullptr ?0 : n_cur->nxt[nxt_01]->exist;if (comp <= k) {pair<T, Node*> ret = kth_element(n_cur->nxt[nxt_01 ^ 1], k - comp, depth - 1);ret.first |= T(1) << depth;return ret;}else{return kth_element(n_cur->nxt[nxt_01], k, depth - 1);}}}int count_less(Node *n_cur, const T &x, int depth) {if (depth == -1) return 0;int ret = 0;bool nxt_01 = lazy >> depth & 1;bool xi = x >> depth & 1;if (xi and n_cur->nxt[nxt_01] != nullptr)ret += n_cur->nxt[nxt_01]->exist;if (n_cur->nxt[nxt_01 ^ xi] != nullptr)ret += count_less(n_cur->nxt[nxt_01 ^ xi], x, depth - 1);return ret;}};template<typename T, int MAX_LOG>struct BinaryTrie_Pool {struct Node {int nxt[2];int exist;vector<int> accept;Node(): nxt{-1, -1}, exist(0) {}};vector<Node> nodes;int root;T lazy;explicit BinaryTrie_Pool(): root(0), lazy(T(0)) {nodes.emplace_back(Node());}void insert(const T &x, int delta, int idx = -1) {int n_cur = root;for (int depth = MAX_LOG - 1; depth >= 0; depth--) {bool nxt_01 = (x >> depth & 1) ^ (lazy >> depth & 1);if (nodes[n_cur].nxt[nxt_01] == -1) {nodes[n_cur].nxt[nxt_01] = (int)nodes.size();nodes.emplace_back(Node());}nodes[n_cur].exist += delta;n_cur = nodes[n_cur].nxt[nxt_01];}nodes[n_cur].exist += delta;if(idx != -1) nodes[n_cur].accept.emplace_back(idx);}void insert(const T &x, int idx = -1) {insert(x, 1, idx);}void erase(const T &x) {insert(x, -1, -1);}int find(const T &x) const {int n_cur = root;for (int depth = MAX_LOG - 1; depth >= 0; depth--) {bool nxt_01 = (x >> depth & 1) ^ (lazy >> depth & 1);int n_nxt = nodes[n_cur].nxt[nxt_01];if (n_nxt == -1) return -1;n_cur = n_nxt;}return n_cur;}int count(const T &x) const {int nx = find(x);return nx == -1 ? 0 : nodes[nx].exist;}pair<int, int> kth_element(int n_cur, int k, int depth) const {if (depth == -1) return make_pair(0, n_cur);bool nxt_01 = (lazy >> depth) & 1;int comp = nodes[n_cur].nxt[nxt_01] == -1 ?0 : nodes[n_cur].nxt[nxt_01].exist;if (comp <= k) {pair<int, int> ret = kth_element(nodes[n_cur].nxt[nxt_01 ^ 1], k - comp, depth - 1);ret.first |= T(1) << depth;return ret;}else{return kth_element(nodes[n_cur].nxt[nxt_01], k, depth-1);}}pair<int, int> kth_element(int k) const {assert(0 <= k and k < nodes[root].exist);int n_cur = root;T ret = 0;for (int depth = MAX_LOG - 1; depth >= 0; depth--) {bool nxt_01 = (lazy >> depth) & 1;int comp = nodes[n_cur].nxt[nxt_01] == -1 ?0 : nodes[n_cur].nxt[nxt_01].exist;if (comp <= k) {k -= comp;n_cur = nodes[n_cur].nxt[nxt_01 ^ 1];ret |= T(1) << depth;}else{n_cur = nodes[n_cur].nxt[nxt_01];}}// return make_pair(ret, n_cur);return kth_element(root, k, MAX_LOG - 1);}pair<int, int> min_element() const {assert(nodes[root].exist > 0);return kth_element(0);}pair<int, int> max_element() const {assert(nodes[root].exist > 0);return kth_element(nodes[root].exist - 1);}int count_less(int n_cur, const T &x, int depth) const {if (depth == -1) return 0;int ret = 0;bool nxt_01 = (lazy >> depth) & 1;bool xi = (x >> depth) & 1;if (xi and nodes[n_cur].nxt[nxt_01] != -1)ret += nodes[nodes[n_cur].nxt[nxt_01]].exist;if (nodes[n_cur].nxt[nxt_01 ^ xi] != -1)ret += count_less(nodes[n_cur].nxt[nxt_01 ^ xi], x, depth - 1);return ret;}int count_less(const T &x) const {/*int ret = 0;int n_cur = root;for (int depth = MAX_LOG - 1; depth >= 0; depth--) {bool nxt_01 = (lazy >> depth) & 1;bool xi = (x >> depth) & 1;if (xi and nodes[n_cur].nxt[nxt_01] != -1) {ret += nodes[nodes[n_cur].nxt[nxt_01]].exist;}if (nodes[n_cur].nxt[nxt_01 ^ xi] != -1) {n_cur = nodes[n_cur].nxt[nxt_01 ^ xi];}else break;}return ret;*/return count_less(root, x, MAX_LOG - 1);}int count_leq(const T &x) const {return count_less(root, x+1, MAX_LOG - 1);}int count_greater(const T &x) const {return nodes[root].exist - count_less(x+1);}int count_geq(const T &x) const {return nodes[root].exist - count_less(x);}void operate_xor(const T &x) {lazy ^= x;}};int main() {ll n,k; in(n,k);k = k*2 + n;vector<int> a(n); in(a);BinaryTrie_Pool<int, 30> bt;rep(i,n) bt.insert(a[i]);int ans = binary_search([&](int m){ll cleq = 0;rep(i,n) {bt.operate_xor(a[i]);cleq += bt.count_leq(m);bt.operate_xor(a[i]);}return cleq >= k;}, (1<<30)-1, -1, false);out(ans);}