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test/2_library_checker/data_structure/set_xor_min.test.cpp
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- Last update: 2024-12-13 13:55:16+09:00
- Problem: https://judge.yosupo.jp/problem/set_xor_min
Depends on
ds/binary_trie.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/set_xor_min"
#include "my_template.hpp"
#include "other/io.hpp"
#include "ds/binary_trie.hpp"
#include "ds/hashmap.hpp"
void solve() {
INT(Q);
HashMap<char> MP(Q);
Binary_Trie<30, false, 1'000'000, int, int> X;
using np = decltype(X)::np;
np root = nullptr;
FOR(Q) {
INT(t, x);
if (t == 0) {
if (MP[x] == 0) {
MP[x] = 1;
root = X.add(root, x, 1);
}
}
if (t == 1) {
if (MP[x] == 1) {
MP[x] = 0;
root = X.add(root, x, -1);
}
}
if (t == 2) { print(X.min(root, x)); }
}
}
signed main() {
solve();
return 0;
}#line 1 "test/2_library_checker/data_structure/set_xor_min.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/set_xor_min"
#line 1 "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 u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
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_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (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 kth_bit(int k) {
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
return x >> k & 1;
}
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;
}
template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
vc<T> &res = first;
(res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 1 "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::read;
using fastio::print;
using fastio::flush;
#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, 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()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), 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); }
void YA(bool t = 1) { print(t ? "YA" : "TIDAK"); }
void TIDAK(bool t = 1) { YES(!t); }
#line 1 "ds/binary_trie.hpp"
// 非永続ならば、2 * 要素数 のノード数
template <int LOG, bool PERSISTENT, int NODES, typename UINT = u64,
typename SIZE_TYPE = int>
struct Binary_Trie {
using T = SIZE_TYPE;
struct Node {
int width;
UINT val;
T cnt;
Node *l, *r;
};
Node *pool;
int pid;
using np = Node *;
Binary_Trie() : pid(0) { pool = new Node[NODES]; }
void reset() { pid = 0; }
np new_root() { return nullptr; }
np add(np root, UINT val, T cnt = 1) {
if (!root) root = new_node(0, 0);
assert(0 <= val && val < (1LL << LOG));
return add_rec(root, LOG, val, cnt);
}
// f(val, cnt)
template <typename F>
void enumerate(np root, F f) {
auto dfs = [&](auto &dfs, np root, UINT val, int ht) -> void {
if (ht == 0) {
f(val, root->cnt);
return;
}
np c = root->l;
if (c) { dfs(dfs, c, val << (c->width) | (c->val), ht - (c->width)); }
c = root->r;
if (c) { dfs(dfs, c, val << (c->width) | (c->val), ht - (c->width)); }
};
if (root) dfs(dfs, root, 0, LOG);
}
// xor_val したあとの値で昇順 k 番目
UINT kth(np root, T k, UINT xor_val) {
assert(root && 0 <= k && k < root->cnt);
return kth_rec(root, 0, k, LOG, xor_val) ^ xor_val;
}
// xor_val したあとの値で最小値
UINT min(np root, UINT xor_val) {
assert(root && root->cnt);
return kth(root, 0, xor_val);
}
// xor_val したあとの値で最大値
UINT max(np root, UINT xor_val) {
assert(root && root->cnt);
return kth(root, (root->cnt) - 1, xor_val);
}
// xor_val したあとの値で [0, upper) 内に入るものの個数
T prefix_count(np root, UINT upper, UINT xor_val) {
if (!root) return 0;
return prefix_count_rec(root, LOG, upper, xor_val, 0);
}
// xor_val したあとの値で [lo, hi) 内に入るものの個数
T count(np root, UINT lo, UINT hi, UINT xor_val) {
return prefix_count(root, hi, xor_val) - prefix_count(root, lo, xor_val);
}
private:
inline UINT mask(int k) { return (UINT(1) << k) - 1; }
np new_node(int width, UINT val) {
pool[pid].l = pool[pid].r = nullptr;
pool[pid].width = width;
pool[pid].val = val;
pool[pid].cnt = 0;
return &(pool[pid++]);
}
np copy_node(np c) {
if (!c || !PERSISTENT) return c;
np res = &(pool[pid++]);
res->width = c->width, res->val = c->val;
res->cnt = c->cnt, res->l = c->l, res->r = c->r;
return res;
}
np add_rec(np root, int ht, UINT val, T cnt) {
root = copy_node(root);
root->cnt += cnt;
if (ht == 0) return root;
bool go_r = (val >> (ht - 1)) & 1;
np c = (go_r ? root->r : root->l);
if (!c) {
c = new_node(ht, val);
c->cnt = cnt;
if (!go_r) root->l = c;
if (go_r) root->r = c;
return root;
}
int w = c->width;
if ((val >> (ht - w)) == c->val) {
c = add_rec(c, ht - w, val & mask(ht - w), cnt);
if (!go_r) root->l = c;
if (go_r) root->r = c;
return root;
}
int same = w - 1 - topbit((val >> (ht - w)) ^ (c->val));
np n = new_node(same, (c->val) >> (w - same));
n->cnt = c->cnt + cnt;
c = copy_node(c);
c->width = w - same;
c->val = c->val & mask(w - same);
if ((val >> (ht - same - 1)) & 1) {
n->l = c;
n->r = new_node(ht - same, val & mask(ht - same));
n->r->cnt = cnt;
} else {
n->r = c;
n->l = new_node(ht - same, val & mask(ht - same));
n->l->cnt = cnt;
}
if (!go_r) root->l = n;
if (go_r) root->r = n;
return root;
}
UINT kth_rec(np root, UINT val, T k, int ht, UINT xor_val) {
if (ht == 0) return val;
np left = root->l, right = root->r;
if ((xor_val >> (ht - 1)) & 1) swap(left, right);
T sl = (left ? left->cnt : 0);
np c;
if (k < sl) { c = left; }
if (k >= sl) { c = right, k -= sl; }
int w = c->width;
return kth_rec(c, val << w | (c->val), k, ht - w, xor_val);
}
T prefix_count_rec(np root, int ht, UINT LIM, UINT xor_val, UINT val) {
UINT now = (val << ht) ^ (xor_val);
if ((LIM >> ht) > (now >> ht)) return root->cnt;
if (ht == 0 || (LIM >> ht) < (now >> ht)) return 0;
T res = 0;
FOR(k, 2) {
np c = (k == 0 ? root->l : root->r);
if (c) {
int w = c->width;
res += prefix_count_rec(c, ht - w, LIM, xor_val, val << w | c->val);
}
}
return res;
}
};
#line 2 "ds/hashmap.hpp"
// u64 -> Val
template <typename Val>
struct HashMap {
// n は入れたいものの個数で ok
HashMap(u32 n = 0) { build(n); }
void build(u32 n) {
u32 k = 8;
while (k < n * 2) k *= 2;
cap = k / 2, mask = k - 1;
key.resize(k), val.resize(k), used.assign(k, 0);
}
// size を保ったまま. size=0 にするときは build すること.
void clear() {
used.assign(len(used), 0);
cap = (mask + 1) / 2;
}
int size() { return len(used) / 2 - cap; }
int index(const u64& k) {
int i = 0;
for (i = hash(k); used[i] && key[i] != k; i = (i + 1) & mask) {}
return i;
}
Val& operator[](const u64& k) {
if (cap == 0) extend();
int i = index(k);
if (!used[i]) { used[i] = 1, key[i] = k, val[i] = Val{}, --cap; }
return val[i];
}
Val get(const u64& k, Val default_value) {
int i = index(k);
return (used[i] ? val[i] : default_value);
}
bool count(const u64& k) {
int i = index(k);
return used[i] && key[i] == k;
}
// f(key, val)
template <typename F>
void enumerate_all(F f) {
FOR(i, len(used)) if (used[i]) f(key[i], val[i]);
}
private:
u32 cap, mask;
vc<u64> key;
vc<Val> val;
vc<bool> used;
u64 hash(u64 x) {
static const u64 FIXED_RANDOM = std::chrono::steady_clock::now().time_since_epoch().count();
x += FIXED_RANDOM;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return (x ^ (x >> 31)) & mask;
}
void extend() {
vc<pair<u64, Val>> dat;
dat.reserve(len(used) / 2 - cap);
FOR(i, len(used)) {
if (used[i]) dat.eb(key[i], val[i]);
}
build(2 * len(dat));
for (auto& [a, b]: dat) (*this)[a] = b;
}
};
#line 6 "test/2_library_checker/data_structure/set_xor_min.test.cpp"
void solve() {
INT(Q);
HashMap<char> MP(Q);
Binary_Trie<30, false, 1'000'000, int, int> X;
using np = decltype(X)::np;
np root = nullptr;
FOR(Q) {
INT(t, x);
if (t == 0) {
if (MP[x] == 0) {
MP[x] = 1;
root = X.add(root, x, 1);
}
}
if (t == 1) {
if (MP[x] == 1) {
MP[x] = 0;
root = X.add(root, x, -1);
}
}
if (t == 2) { print(X.min(root, x)); }
}
}
signed main() {
solve();
return 0;
}