This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub suisen-cp/cp-library-cpp
#include "library/range_query/range_set_range_composite.hpp"
#ifndef SUISEN_RANGE_SET_RANGE_COMPOSITE #define SUISEN_RANGE_SET_RANGE_COMPOSITE #include "library/datastructure/fenwick_tree/fenwick_tree_set.hpp" #include <atcoder/segtree> namespace suisen { template <typename T, T(*op)(T, T), T(*e)()> struct RangeSetRangeComposite { RangeSetRangeComposite() : RangeSetRangeComposite(0) {} explicit RangeSetRangeComposite(int n, T val = e()) : _n(n), _seg(std::vector(_n, e())), _vs(n, e()) { _pos.insert(0), _vs[0] = val; _seg.set(0, _pow(0, n)); _pos.insert(_n); } explicit RangeSetRangeComposite(const std::vector<T>& a) : _n(a.size()), _seg(a), _vs(a), _pos(_n + 1, true) {} void set(int l, int r, const T& f) { assert(0 <= l and l <= r and r <= _n); if (l == r) return; if (const int ml = _pos.min_geq(l); ml != l) { const int pl = _pos.max_lt(ml); _pos.insert(l); _vs[l] = _vs[pl]; _seg.set(pl, _pow(pl, l - pl)); } if (const int mr = _pos.min_geq(r); mr != r) { const int pr = _pos.max_lt(mr); _pos.insert(r); _vs[r] = _vs[pr]; _seg.set(r, _pow(r, mr - r)); } _vs[l] = f; _seg.set(l, _pow(l, r - l)); for (int i = l; (i = _pos.min_gt(i)) != r;) _pos.erase(i), _seg.set(i, e()); } T prod(int l, int r) { assert(0 <= l and l <= r and r <= _n); if (l == r) return e(); const auto ml = _pos.min_geq(l); if (ml >= r) return _pow(_pos.max_lt(ml), r - l); const int mr = _pos.max_leq(r); T fl = ml == l ? e() : _pow(_pos.max_lt(ml), ml - l); T fm = _seg.prod(ml, mr); T fr = mr == r ? e() : _pow(mr, r - mr); return op(op(fl, fm), fr); } private: int _n; atcoder::segtree<T, op, e> _seg; std::vector<T> _vs; suisen::fenwick_tree_set _pos; T _pow(int i, int n) const { T res = e(); for (T v = _vs[i]; n; n >>= 1) { if (n & 1) res = op(res, v); v = op(v, v); } return res; } }; } // namespace suisen #endif // SUISEN_RANGE_SET_RANGE_COMPOSITE
#line 1 "library/range_query/range_set_range_composite.hpp" #line 1 "library/datastructure/fenwick_tree/fenwick_tree_set.hpp" #include <array> #include <cassert> #include <cstdint> #include <numeric> #include <vector> #ifdef _MSC_VER # include <intrin.h> #else # include <x86intrin.h> #endif namespace suisen { struct fenwick_tree_set { private: template <typename T> struct is_container { template <typename T2> static auto test(T2 t) -> decltype(++t.begin() != t.end(), *t.begin(), std::true_type{}); static std::false_type test(...); public: static constexpr bool value = decltype(test(std::declval<T>()))::value; }; static constexpr int WORD = 64, MASK_WORD = 63, LOG_WORD = 6; static constexpr int SEARCH_WIDTH = 1; public: fenwick_tree_set() : fenwick_tree_set(0) {} // Construct (an empty / a full) set and set the universe as {0,1,...,n-1} explicit fenwick_tree_set(int n, bool fullset = false): _n(n), _wn(std::max((_n + (WORD - 1)) >> LOG_WORD, 1)), _lg(top_setbit(_wn)), _siz(0), _d(_wn + 1), _bs(_wn) { if (fullset) { std::vector<int> values(n); std::iota(values.begin(), values.end(), 0); construct_from_values(values); } } // Construct a set containing the values in `values`. template <typename Container, std::enable_if_t<is_container<Container>::value, std::nullptr_t> = nullptr> fenwick_tree_set(int n, const Container &values): fenwick_tree_set(n) { construct_from_values(values); } // Construct a set containing the values `i` such that `seq01[i] == 1` (or `one` you give). template <typename Container, std::enable_if_t<is_container<Container>::value, std::nullptr_t> = nullptr> fenwick_tree_set(const Container &seq01, typename Container::value_type one = 1): fenwick_tree_set(seq01.size()) { std::vector<int> values; for (int i = 0; i < _n; ++i) if (seq01[i] == one) values.push_back(i); construct_from_values(values); } // O(1). // Number of elements. int size() const { return _siz; } // O(1). // Check if `v` is contained. `v` may be out of range. bool contains(int v) const { if (not (0 <= v and v < _n)) return false; const auto [t, u] = index(v); return (_bs[t] >> u) & 1; } // O(log n) if `v` is not a member, O(1) otherwise. // Insert `v` if not contained. Raise an assertion error if `v` is out of range. // Return `true` if `v` is inserted, `false` otherwise. bool insert(int v) { if (contains(v)) return false; add<+1>(v); const auto [t, u] = index(v); _bs[t] |= uint64_t(1) << u; return true; } // O(log n) if `v` is a member, O(1) otherwise. // Erase `v` if contained. Raise an assertion error if `v` is out of range. // Return `true` if `v` is erased, `false` otherwise. bool erase(int v) { if (not contains(v)) return false; add<-1>(v); const auto [t, u] = index(v); _bs[t] &= ~(uint64_t(1) << u); return true; } // O(log n). // Count elements < `v`. `v` may be out of range. int count_lt(int v) const { if (v <= 0) return 0; if (v >= _n) return _siz; auto [t, u] = index(v); int res = __builtin_popcountll(_bs[t] & ((uint64_t(1) << u) - 1)); for (; t; t &= t - 1) res += _d[t]; return res; } // O(log n). // Count elements <= `v`. `v` may be out of range. int count_leq(int v) const { return count_lt(v + 1); } // O(log n). // Count elements > `v`. `v` may be out of range. int count_gt(int v) const { return _siz - count_leq(v); } // O(log n). // Count elements >= `v`. `v` may be out of range. int count_geq(int v) const { return _siz - count_lt(v); } // O(log n). // `k`-th smallest element or `-1` if `k` is out of range. int kth_element(int k) const { // Out of range if (not (0 <= k and k < _siz)) return -1; // Binary search int t = 1 << _lg; // (I) non-leaf node // [ t ] // [t-p] [t+p] for (int p = 1 << _lg >> 1; p; p >>= 1) { if (int nk = t <= _wn ? k - _d[t] : -1; nk >= 0) k = nk, t += p; else t -= p; } // (II) leaf node if (int nk = t <= _wn ? k - _d[t] : -1; nk >= 0) k = nk, ++t; --t; return (t << LOG_WORD) | kth_setbit(_bs[t], k); } // O(log n). // `k`-th smallest element or `-1` if `k` is out of range. int operator[](int k) const { return kth_element(k); } // O(log n). // Max element <= `v` or `-1` if not exists int max_leq(int v) const { if (v < 0) return -1; v = std::min(v, _n - 1); const auto [t, u] = index(v); const int lz = (WORD - 1) - u; if (const uint64_t bits = _bs[t] << lz >> lz) { return (t << LOG_WORD) | top_setbit(bits); } for (int i = 1; i <= SEARCH_WIDTH; ++i) { if (t - i < 0) return -1; if (_bs[t - i]) return ((t - i) << LOG_WORD) | top_setbit(_bs[t - i]); } return *--upper_bound(v); } // O(log n). // Max element < `v` or `-1` if not exists int max_lt(int v) const { return max_leq(v - 1); } // O(log n). // Min element >= `v` or `-1` if not exists int min_geq(int v) const { if (v >= _n) return -1; v = std::max(v, 0); const auto [t, u] = index(v); if (const uint64_t bits = _bs[t] >> u << u) { return (t << LOG_WORD) | __builtin_ctzll(bits); } for (int i = 1; i <= SEARCH_WIDTH; ++i) { if (t + i >= _wn) return -1; if (_bs[t + i]) return ((t + i) << LOG_WORD) | __builtin_ctzll(_bs[t + i]); } return *lower_bound(v); } // O(log n). // Min element > `v` or `-1` if not exists int min_gt(int v) const { return min_geq(v + 1); } private: struct IndexHolder { friend fenwick_tree_set; using difference_type = int; using value_type = int; using pointer = value_type*; using reference = value_type&; using iterator_category = std::random_access_iterator_tag; // O(1). Index of the element pointed to by the iterator. Negative values or values greater than or equal to `n` (= size of the set) means that the iterator doesn't point to any element. int index() const { return i; } // O(1). Check if the iterator points to some element. bool has_value() const { return 0 <= i and i < ptr->size(); } // O(1) IndexHolder& operator++() { return ++i, *this; } // O(1) IndexHolder operator++(int) { IndexHolder ret = *this; ++(*this); return ret; } // O(1) IndexHolder& operator--() { return --i, *this; } // O(1) IndexHolder operator--(int) { IndexHolder ret = *this; --(*this); return ret; } // O(1) IndexHolder& operator+=(difference_type dif) { return i += dif, *this; } // O(1) friend IndexHolder operator+(IndexHolder it, difference_type dif) { it += dif; return it; } // O(1) friend IndexHolder operator+(difference_type dif, IndexHolder it) { it += dif; return it; } // O(1) IndexHolder& operator-=(difference_type dif) { return i -= dif, *this; } // O(1) friend IndexHolder operator-(IndexHolder it, difference_type dif) { it -= dif; return it; } // O(1) difference_type operator-(const IndexHolder &rhs) const { return i - rhs.i; } // O(log n) value_type operator[](difference_type i) const { return *((*this) + i); } // O(log n) value_type operator*() const { return ptr->kth_element(i); } // O(1) bool operator!=(const IndexHolder &rhs) const { return i != rhs.i; } // O(1) bool operator==(const IndexHolder &rhs) const { return i == rhs.i; } // O(1) bool operator<(const IndexHolder &rhs) const { return i < rhs.i; } // O(1) bool operator<=(const IndexHolder &rhs) const { return i <= rhs.i; } // O(1) bool operator>(const IndexHolder &rhs) const { return i > rhs.i; } // O(1) bool operator>=(const IndexHolder &rhs) const { return i >= rhs.i; } private: IndexHolder(const fenwick_tree_set* ptr, int i) : ptr(ptr), i(i) {} const fenwick_tree_set* ptr; int i; }; public: using iterator = IndexHolder; using difference_type = iterator::difference_type; using value_type = iterator::value_type; using pointer = iterator::pointer; using reference = iterator::reference; // O(1). iterator begin() const { return iterator(this, 0); } // O(1). iterator end() const { return iterator(this, _siz); } // O(log n). iterator lower_bound(int v) const { return iterator(this, count_lt(v)); } // O(log n). iterator upper_bound(int v) const { return iterator(this, count_leq(v)); } // O(log n) if `v` is a member, O(1) otherwise. iterator find(int v) const { return contains(v) ? lower_bound(v) : end(); } // O(log n). iterator erase(iterator it) { return erase(*it), it; } private: int _n, _wn, _lg, _siz; std::vector<int> _d; // Fenwick Tree std::vector<uint64_t> _bs; // Bitset template <typename Container, std::enable_if_t<is_container<Container>::value, std::nullptr_t> = nullptr> void construct_from_values(const Container &values) { for (int v : values) { assert(0 <= v and v < _n); const auto [t, u] = index(v); if ((_bs[t] >> u) & 1) continue; ++_siz; ++_d[t + 1]; _bs[t] |= uint64_t(1) << u; } for (int i = 1; i <= _wn; ++i) { const int p = i + (-i & i); if (p <= _wn) _d[p] += _d[i]; } } static constexpr int _large(int i) { return i >> LOG_WORD; } static constexpr int _small(int i) { return i & MASK_WORD; } static constexpr std::array<int, 2> index(int i) { return { _large(i), _small(i) }; } // Position of highest set bit static constexpr int top_setbit(uint64_t x) { return (WORD - 1) - __builtin_clzll(x); } // Position of k-th set bit __attribute__((target("bmi2"))) static int kth_setbit(uint64_t x, int k) { return __builtin_ctzll(_pdep_u64(uint64_t(1) << k, x)); } template <int k> void add(int v) { assert(0 <= v and v < _n); _siz += k; for (int t = _large(v) + 1; t <= _wn; t += -t & t) _d[t] += k; } }; } // namespace suisen #line 5 "library/range_query/range_set_range_composite.hpp" #include <atcoder/segtree> namespace suisen { template <typename T, T(*op)(T, T), T(*e)()> struct RangeSetRangeComposite { RangeSetRangeComposite() : RangeSetRangeComposite(0) {} explicit RangeSetRangeComposite(int n, T val = e()) : _n(n), _seg(std::vector(_n, e())), _vs(n, e()) { _pos.insert(0), _vs[0] = val; _seg.set(0, _pow(0, n)); _pos.insert(_n); } explicit RangeSetRangeComposite(const std::vector<T>& a) : _n(a.size()), _seg(a), _vs(a), _pos(_n + 1, true) {} void set(int l, int r, const T& f) { assert(0 <= l and l <= r and r <= _n); if (l == r) return; if (const int ml = _pos.min_geq(l); ml != l) { const int pl = _pos.max_lt(ml); _pos.insert(l); _vs[l] = _vs[pl]; _seg.set(pl, _pow(pl, l - pl)); } if (const int mr = _pos.min_geq(r); mr != r) { const int pr = _pos.max_lt(mr); _pos.insert(r); _vs[r] = _vs[pr]; _seg.set(r, _pow(r, mr - r)); } _vs[l] = f; _seg.set(l, _pow(l, r - l)); for (int i = l; (i = _pos.min_gt(i)) != r;) _pos.erase(i), _seg.set(i, e()); } T prod(int l, int r) { assert(0 <= l and l <= r and r <= _n); if (l == r) return e(); const auto ml = _pos.min_geq(l); if (ml >= r) return _pow(_pos.max_lt(ml), r - l); const int mr = _pos.max_leq(r); T fl = ml == l ? e() : _pow(_pos.max_lt(ml), ml - l); T fm = _seg.prod(ml, mr); T fr = mr == r ? e() : _pow(mr, r - mr); return op(op(fl, fm), fr); } private: int _n; atcoder::segtree<T, op, e> _seg; std::vector<T> _vs; suisen::fenwick_tree_set _pos; T _pow(int i, int n) const { T res = e(); for (T v = _vs[i]; n; n >>= 1) { if (n & 1) res = op(res, v); v = op(v, v); } return res; } }; } // namespace suisen