#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #include "../../template/template.hpp" #include "../../data-structure-2d/wavelet-matrix.hpp" uint64_t rng() { static uint64_t x_ = chrono::duration_cast<chrono::nanoseconds>( chrono::high_resolution_clock::now().time_since_epoch()) .count(); return x_ ^= (x_ << 7), x_ ^= (x_ >> 9); } int randint(int l, int r) { assert(l < r); return rng() % (r - l) + l; } void test(int n, int q, bool all_zero = false, bool large = false) { assert(n > 0); WaveletMatrix<int> wm(n); vector<int> v(n, 0); vector<int> buffer; if (large) { for (int i = 0; i < n; ++i) v[i] = randint(0, 1 << 30); } else if (!all_zero) { iota(begin(v), end(v), 0); } mt19937_64 mt; shuffle(begin(v), end(v), mt); for (int i = n; i--;) wm.set(i, v[i]); wm.build(); // access for (int Q = q; Q--;) { int i = randint(0, n); assert(wm.access(i) == v[i]); } // kth-smallest / kth-largest for (int Q = q; Q--;) { int len = randint(1, n + 1); int l = randint(0, n - len + 1); int r = l + len; int k = randint(0, len); buffer.clear(); copy(begin(v) + l, begin(v) + r, back_inserter(buffer)); sort(begin(buffer), end(buffer)); assert(wm.kth_smallest(l, r, k) == buffer[k]); assert(wm.kth_largest(l, r, k) == buffer[len - k - 1]); } // range-freq for (int Q = q; Q--;) { int len = randint(1, n + 1); int l = randint(0, n - len + 1); int r = l + len; int lower, upper; do { lower = randint(0, n + 5); upper = randint(0, n + 5); if (lower > upper) swap(lower, upper); } while (lower != upper); buffer.clear(); copy(begin(v) + l, begin(v) + r, back_inserter(buffer)); sort(begin(buffer), end(buffer)); int up = lower_bound(begin(buffer), end(buffer), upper) - begin(buffer); assert(wm.range_freq(l, r, upper) == up); int lo = lower_bound(begin(buffer), end(buffer), lower) - begin(buffer); assert(wm.range_freq(l, r, lower, upper) == up - lo); int pv = len - 1; while (pv != -1 and buffer[pv] >= upper) --pv; assert(wm.prev_value(l, r, upper) == (pv == -1 ? -1 : buffer[pv])); int nv = 0; while (nv != len and buffer[nv] < lower) ++nv; assert(wm.next_value(l, r, lower) == (nv == len ? -1 : buffer[nv])); } } void Nyaan::solve() { test(63, 1000); test(64, 1000); test(65, 1000); test(63, 1000, true); test(64, 1000, true); test(65, 1000, true); test(63, 1000, false, true); test(64, 1000, false, true); test(65, 1000, false, true); for (int i = 100; i--;) { test(1, 1); test(1, 1, true); test(1, 1, false, true); test(2, 10); test(2, 10, true); test(2, 10, false, true); } test(65535, 10); test(65536, 10); test(65537, 10); test(65535, 10, false, true); test(65536, 10, false, true); test(65537, 10, false, true); int a, b; cin >> a >> b; cout << (a + b) << endl; }
#line 1 "verify/verify-unit-test/wavelet-matrix.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #line 2 "template/template.hpp" using namespace std; // intrinstic #include <immintrin.h> #include <algorithm> #include <array> #include <bitset> #include <cassert> #include <cctype> #include <cfenv> #include <cfloat> #include <chrono> #include <cinttypes> #include <climits> #include <cmath> #include <complex> #include <cstdarg> #include <cstddef> #include <cstdint> #include <cstdio> #include <cstdlib> #include <cstring> #include <deque> #include <fstream> #include <functional> #include <initializer_list> #include <iomanip> #include <ios> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <map> #include <memory> #include <new> #include <numeric> #include <ostream> #include <queue> #include <random> #include <set> #include <sstream> #include <stack> #include <streambuf> #include <string> #include <tuple> #include <type_traits> #include <typeinfo> #include <unordered_map> #include <unordered_set> #include <utility> #include <vector> // utility #line 1 "template/util.hpp" namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template <typename T> using V = vector<T>; template <typename T> using VV = vector<vector<T>>; using vi = vector<int>; using vl = vector<long long>; using vd = V<double>; using vs = V<string>; using vvi = vector<vector<int>>; using vvl = vector<vector<long long>>; template <typename T> using minpq = priority_queue<T, vector<T>, greater<T>>; template <typename T, typename U> struct P : pair<T, U> { template <typename... Args> P(Args... args) : pair<T, U>(args...) {} using pair<T, U>::first; using pair<T, U>::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template <typename S> P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template <typename S> P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P<ll, ll>; using pi = P<int, int>; using vp = V<pl>; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template <typename T> int sz(const T &t) { return t.size(); } template <typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template <typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template <typename T> inline T Max(const vector<T> &v) { return *max_element(begin(v), end(v)); } template <typename T> inline T Min(const vector<T> &v) { return *min_element(begin(v), end(v)); } template <typename T> inline long long Sum(const vector<T> &v) { return accumulate(begin(v), end(v), 0LL); } template <typename T> int lb(const vector<T> &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template <typename T> int ub(const vector<T> &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template <typename T, typename U> pair<T, U> mkp(const T &t, const U &u) { return make_pair(t, u); } template <typename T> vector<T> mkrui(const vector<T> &v, bool rev = false) { vector<T> ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template <typename T> vector<T> mkuni(const vector<T> &v) { vector<T> ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template <typename F> vector<int> mkord(int N, F f) { vector<int> ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template <typename T> vector<int> mkinv(vector<T> &v) { int max_val = *max_element(begin(v), end(v)); vector<int> inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector<int> mkiota(int n) { vector<int> ret(n); iota(begin(ret), end(ret), 0); return ret; } template <typename T> T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template <typename T> bool nxp(vector<T> &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template <typename T> vector<vector<T>> product(const vector<T> &a) { vector<vector<T>> ret; vector<T> v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I, const function<void(T &)> &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I) { return Power(a, n, I, function<void(T &)>{[](T &) -> void {}}); } } // namespace Nyaan #line 58 "template/template.hpp" // bit operation #line 1 "template/bitop.hpp" namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template <typename T> inline int gbit(const T &a, int i) { return (a >> i) & 1; } template <typename T> inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan #line 61 "template/template.hpp" // inout #line 1 "template/inout.hpp" namespace Nyaan { template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; } template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; } 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> istream &operator>>(istream &is, vector<T> &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } 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...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan #line 64 "template/template.hpp" // debug #line 1 "template/debug.hpp" namespace DebugImpl { template <typename U, typename = void> struct is_specialize : false_type {}; template <typename U> struct is_specialize< U, typename conditional<false, typename U::iterator, void>::type> : true_type {}; template <typename U> struct is_specialize< U, typename conditional<false, decltype(U::first), void>::type> : true_type {}; template <typename U> struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } void dump(__int128_t t) { if (t == 0) cerr << 0; if (t < 0) cerr << '-', t = -t; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } void dump(__uint128_t t) { if (t == 0) cerr << 0; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } template <typename U, enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template <typename T> void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template <typename T, typename U> void dump(const pair<T, U>&); template <typename T> void dump(const pair<T*, int>&); template <typename T> void dump(const T& t, enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template <typename T, typename U> void dump(const pair<T, U>& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template <typename T> void dump(const pair<T*, int>& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template <typename Head, typename... Tail> void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward<Tail>(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc2(...) (void(0)) #endif #line 67 "template/template.hpp" // macro #line 1 "template/macro.hpp" #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) #line 70 "template/template.hpp" namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } #line 2 "data-structure-2d/wavelet-matrix.hpp" #line 4 "data-structure-2d/wavelet-matrix.hpp" struct bit_vector { using u32 = uint32_t; using i64 = int64_t; using u64 = uint64_t; static constexpr u32 w = 64; vector<u64> block; vector<u32> count; u32 n, zeros; inline u32 get(u32 i) const { return u32(block[i / w] >> (i % w)) & 1u; } inline void set(u32 i) { block[i / w] |= 1LL << (i % w); } bit_vector() {} bit_vector(int _n) { init(_n); } __attribute__((optimize("O3", "unroll-loops"))) void init(int _n) { n = zeros = _n; block.resize(n / w + 1, 0); count.resize(block.size(), 0); } __attribute__((target("popcnt"))) void build() { for (u32 i = 1; i < block.size(); ++i) count[i] = count[i - 1] + _mm_popcnt_u64(block[i - 1]); zeros = rank0(n); } inline u32 rank0(u32 i) const { return i - rank1(i); } __attribute__((target("bmi2,popcnt"))) inline u32 rank1(u32 i) const { return count[i / w] + _mm_popcnt_u64(_bzhi_u64(block[i / w], i % w)); } }; template <typename T> struct WaveletMatrix { using u32 = uint32_t; using i64 = int64_t; using u64 = uint64_t; int n, lg; vector<T> a; vector<bit_vector> bv; WaveletMatrix(u32 _n) : n(max<u32>(_n, 1)), a(n) {} WaveletMatrix(const vector<T>& _a) : n(_a.size()), a(_a) { build(); } __attribute__((optimize("O3"))) void build() { lg = __lg(max<T>(*max_element(begin(a), end(a)), 1)) + 1; bv.assign(lg, n); vector<T> cur = a, nxt(n); for (int h = lg - 1; h >= 0; --h) { for (int i = 0; i < n; ++i) if ((cur[i] >> h) & 1) bv[h].set(i); bv[h].build(); array<decltype(begin(nxt)), 2> it{begin(nxt), begin(nxt) + bv[h].zeros}; for (int i = 0; i < n; ++i) *it[bv[h].get(i)]++ = cur[i]; swap(cur, nxt); } return; } void set(u32 i, const T& x) { assert(x >= 0); a[i] = x; } inline pair<u32, u32> succ0(int l, int r, int h) const { return make_pair(bv[h].rank0(l), bv[h].rank0(r)); } inline pair<u32, u32> succ1(int l, int r, int h) const { u32 l0 = bv[h].rank0(l); u32 r0 = bv[h].rank0(r); u32 zeros = bv[h].zeros; return make_pair(l + zeros - l0, r + zeros - r0); } // return a[k] T access(u32 k) const { T ret = 0; for (int h = lg - 1; h >= 0; --h) { u32 f = bv[h].get(k); ret |= f ? T(1) << h : 0; k = f ? bv[h].rank1(k) + bv[h].zeros : bv[h].rank0(k); } return ret; } // k-th (0-indexed) smallest number in a[l, r) T kth_smallest(u32 l, u32 r, u32 k) const { T res = 0; for (int h = lg - 1; h >= 0; --h) { u32 l0 = bv[h].rank0(l), r0 = bv[h].rank0(r); if (k < r0 - l0) l = l0, r = r0; else { k -= r0 - l0; res |= (T)1 << h; l += bv[h].zeros - l0; r += bv[h].zeros - r0; } } return res; } // k-th (0-indexed) largest number in a[l, r) T kth_largest(int l, int r, int k) { return kth_smallest(l, r, r - l - k - 1); } // count i s.t. (l <= i < r) && (v[i] < upper) int range_freq(int l, int r, T upper) { if (upper >= (T(1) << lg)) return r - l; int ret = 0; for (int h = lg - 1; h >= 0; --h) { bool f = (upper >> h) & 1; u32 l0 = bv[h].rank0(l), r0 = bv[h].rank0(r); if (f) { ret += r0 - l0; l += bv[h].zeros - l0; r += bv[h].zeros - r0; } else { l = l0; r = r0; } } return ret; } int range_freq(int l, int r, T lower, T upper) { return range_freq(l, r, upper) - range_freq(l, r, lower); } // max v[i] s.t. (l <= i < r) && (v[i] < upper) T prev_value(int l, int r, T upper) { int cnt = range_freq(l, r, upper); return cnt == 0 ? T(-1) : kth_smallest(l, r, cnt - 1); } // min v[i] s.t. (l <= i < r) && (lower <= v[i]) T next_value(int l, int r, T lower) { int cnt = range_freq(l, r, lower); return cnt == r - l ? T(-1) : kth_smallest(l, r, cnt); } }; /* * @brief Wavelet Matrix * @docs docs/data-structure-2d/wavelet-matrix.md */ #line 5 "verify/verify-unit-test/wavelet-matrix.test.cpp" uint64_t rng() { static uint64_t x_ = chrono::duration_cast<chrono::nanoseconds>( chrono::high_resolution_clock::now().time_since_epoch()) .count(); return x_ ^= (x_ << 7), x_ ^= (x_ >> 9); } int randint(int l, int r) { assert(l < r); return rng() % (r - l) + l; } void test(int n, int q, bool all_zero = false, bool large = false) { assert(n > 0); WaveletMatrix<int> wm(n); vector<int> v(n, 0); vector<int> buffer; if (large) { for (int i = 0; i < n; ++i) v[i] = randint(0, 1 << 30); } else if (!all_zero) { iota(begin(v), end(v), 0); } mt19937_64 mt; shuffle(begin(v), end(v), mt); for (int i = n; i--;) wm.set(i, v[i]); wm.build(); // access for (int Q = q; Q--;) { int i = randint(0, n); assert(wm.access(i) == v[i]); } // kth-smallest / kth-largest for (int Q = q; Q--;) { int len = randint(1, n + 1); int l = randint(0, n - len + 1); int r = l + len; int k = randint(0, len); buffer.clear(); copy(begin(v) + l, begin(v) + r, back_inserter(buffer)); sort(begin(buffer), end(buffer)); assert(wm.kth_smallest(l, r, k) == buffer[k]); assert(wm.kth_largest(l, r, k) == buffer[len - k - 1]); } // range-freq for (int Q = q; Q--;) { int len = randint(1, n + 1); int l = randint(0, n - len + 1); int r = l + len; int lower, upper; do { lower = randint(0, n + 5); upper = randint(0, n + 5); if (lower > upper) swap(lower, upper); } while (lower != upper); buffer.clear(); copy(begin(v) + l, begin(v) + r, back_inserter(buffer)); sort(begin(buffer), end(buffer)); int up = lower_bound(begin(buffer), end(buffer), upper) - begin(buffer); assert(wm.range_freq(l, r, upper) == up); int lo = lower_bound(begin(buffer), end(buffer), lower) - begin(buffer); assert(wm.range_freq(l, r, lower, upper) == up - lo); int pv = len - 1; while (pv != -1 and buffer[pv] >= upper) --pv; assert(wm.prev_value(l, r, upper) == (pv == -1 ? -1 : buffer[pv])); int nv = 0; while (nv != len and buffer[nv] < lower) ++nv; assert(wm.next_value(l, r, lower) == (nv == len ? -1 : buffer[nv])); } } void Nyaan::solve() { test(63, 1000); test(64, 1000); test(65, 1000); test(63, 1000, true); test(64, 1000, true); test(65, 1000, true); test(63, 1000, false, true); test(64, 1000, false, true); test(65, 1000, false, true); for (int i = 100; i--;) { test(1, 1); test(1, 1, true); test(1, 1, false, true); test(2, 10); test(2, 10, true); test(2, 10, false, true); } test(65535, 10); test(65536, 10); test(65537, 10); test(65535, 10, false, true); test(65536, 10, false, true); test(65537, 10, false, true); int a, b; cin >> a >> b; cout << (a + b) << endl; }