ds/bit.hpp
| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | #pragma once | ||
| 2 | |||
| 3 | #include <vector> | ||
| 4 | #include <cassert> | ||
| 5 | |||
| 6 | namespace wala { | ||
| 7 | |||
| 8 | /** Binary-indexed tree | ||
| 9 | * | ||
| 10 | * A binary indexed tree with N nodes of type T provides the | ||
| 11 | * following two functions for 0 <= i <= N: | ||
| 12 | * | ||
| 13 | * prefix(int i) -> prefix_iterator<T> | ||
| 14 | * suffix(int i) -> suffix_iterator<T> | ||
| 15 | * | ||
| 16 | * such that size(suffix(i) intersect prefix(j)) = (1 if i < j else 0). | ||
| 17 | * Furthermore, the resulting lists always have size at most log_2(N). | ||
| 18 | * | ||
| 19 | * This can be used to implement either point-update/(prefix|suffix)-query or | ||
| 20 | * (prefix|suffix)-update/point-query over a virtual array of size N of a | ||
| 21 | * commutative monoid. This can be generalized to implement | ||
| 22 | * point-update/range-query or range-update/point-query over a virtual array | ||
| 23 | * of size N of a commutative group. | ||
| 24 | * | ||
| 25 | * With 0-indexed data, prefixes are more natural: | ||
| 26 | * * For range update/query, use for_prefix for the ranges and for_suffix for the points. | ||
| 27 | * * For prefix update/query, no change. | ||
| 28 | * * For suffix update/query, use for_prefix(point + 1); 1-index the data. | ||
| 29 | */ | ||
| 30 | template <typename T> class binary_indexed_tree { | ||
| 31 | private: | ||
| 32 | std::vector<T> dat; | ||
| 33 | |||
| 34 | public: | ||
| 35 | ✗ | binary_indexed_tree() {} | |
| 36 | ✗ | explicit binary_indexed_tree(size_t N) : dat(N) {} | |
| 37 | ✗ | binary_indexed_tree(size_t N, const T& t) : dat(N, t) {} | |
| 38 | |||
| 39 | ✗ | size_t size() const { return dat.size(); } | |
| 40 | ✗ | const std::vector<T>& data() const { return dat; } | |
| 41 | ✗ | std::vector<T>& data() { return dat; } | |
| 42 | |||
| 43 | private: | ||
| 44 | template <typename I, typename S = I> struct iterator_range { | ||
| 45 | private: | ||
| 46 | I begin_; | ||
| 47 | S end_; | ||
| 48 | |||
| 49 | public: | ||
| 50 | ✗ | iterator_range() : begin_(), end_() {} | |
| 51 | ✗ | iterator_range(const I& begin__, const S& end__) : begin_(begin__), end_(end__) {} | |
| 52 | ✗ | iterator_range(I&& begin__, S&& end__) : begin_(begin__), end_(end__) {} | |
| 53 | ✗ | I begin() const { return begin_; } | |
| 54 | ✗ | S end() const { return end_; } | |
| 55 | }; | ||
| 56 | |||
| 57 | public: | ||
| 58 | class const_suffix_iterator { | ||
| 59 | private: | ||
| 60 | const T* dat; | ||
| 61 | int a; | ||
| 62 | ✗ | const_suffix_iterator(const T* dat_, int a_) : dat(dat_), a(a_) {} | |
| 63 | friend class binary_indexed_tree; | ||
| 64 | |||
| 65 | public: | ||
| 66 | ✗ | friend bool operator != (const const_suffix_iterator& i, const const_suffix_iterator& j) { | |
| 67 | ✗ | assert(j.dat == nullptr); | |
| 68 | ✗ | return i.a < j.a; | |
| 69 | } | ||
| 70 | ✗ | const_suffix_iterator& operator ++ () { | |
| 71 | ✗ | a |= a+1; | |
| 72 | ✗ | return *this; | |
| 73 | } | ||
| 74 | ✗ | const T& operator * () const { | |
| 75 | ✗ | return dat[a]; | |
| 76 | } | ||
| 77 | }; | ||
| 78 | using const_suffix_range = iterator_range<const_suffix_iterator>; | ||
| 79 | ✗ | const_suffix_range suffix(int a) const { | |
| 80 | ✗ | assert(0 <= a && a <= int(dat.size())); | |
| 81 | ✗ | return const_suffix_range{const_suffix_iterator{dat.data(), a}, const_suffix_iterator{nullptr, int(dat.size())}}; | |
| 82 | } | ||
| 83 | |||
| 84 | class suffix_iterator { | ||
| 85 | private: | ||
| 86 | T* dat; | ||
| 87 | int a; | ||
| 88 | ✗ | suffix_iterator(T* dat_, int a_) : dat(dat_), a(a_) {} | |
| 89 | friend class binary_indexed_tree; | ||
| 90 | |||
| 91 | public: | ||
| 92 | ✗ | friend bool operator != (const suffix_iterator& i, const suffix_iterator& j) { | |
| 93 | ✗ | assert(j.dat == nullptr); | |
| 94 | ✗ | return i.a < j.a; | |
| 95 | } | ||
| 96 | ✗ | suffix_iterator& operator ++ () { | |
| 97 | ✗ | a |= a+1; | |
| 98 | ✗ | return *this; | |
| 99 | } | ||
| 100 | ✗ | T& operator * () const { | |
| 101 | ✗ | return dat[a]; | |
| 102 | } | ||
| 103 | }; | ||
| 104 | using suffix_range = iterator_range<suffix_iterator>; | ||
| 105 | ✗ | suffix_range suffix(int a) { | |
| 106 | ✗ | assert(0 <= a && a <= int(dat.size())); | |
| 107 | ✗ | return suffix_range{suffix_iterator{dat.data(), a}, suffix_iterator{nullptr, int(dat.size())}}; | |
| 108 | } | ||
| 109 | |||
| 110 | class const_prefix_iterator { | ||
| 111 | private: | ||
| 112 | const T* dat; | ||
| 113 | int a; | ||
| 114 | ✗ | const_prefix_iterator(const T* dat_, int a_) : dat(dat_), a(a_) {} | |
| 115 | friend class binary_indexed_tree; | ||
| 116 | |||
| 117 | public: | ||
| 118 | ✗ | friend bool operator != (const const_prefix_iterator& i, const const_prefix_iterator& j) { | |
| 119 | ✗ | assert(j.dat == nullptr); | |
| 120 | ✗ | return i.a > 0; | |
| 121 | } | ||
| 122 | ✗ | const_prefix_iterator& operator ++ () { | |
| 123 | ✗ | a &= a-1; | |
| 124 | ✗ | return *this; | |
| 125 | } | ||
| 126 | ✗ | const T& operator * () const { | |
| 127 | ✗ | return dat[a-1]; | |
| 128 | } | ||
| 129 | }; | ||
| 130 | using const_prefix_range = iterator_range<const_prefix_iterator>; | ||
| 131 | ✗ | const_prefix_range prefix(int a) const { | |
| 132 | ✗ | return const_prefix_range{const_prefix_iterator{dat.data(), a}, const_prefix_iterator{nullptr, 0}}; | |
| 133 | } | ||
| 134 | |||
| 135 | class prefix_iterator { | ||
| 136 | private: | ||
| 137 | T* dat; | ||
| 138 | int a; | ||
| 139 | ✗ | prefix_iterator(T* dat_, int a_) : dat(dat_), a(a_) {} | |
| 140 | friend class binary_indexed_tree; | ||
| 141 | |||
| 142 | public: | ||
| 143 | ✗ | friend bool operator != (const prefix_iterator& i, const prefix_iterator& j) { | |
| 144 | ✗ | assert(j.dat == nullptr); | |
| 145 | ✗ | return i.a > 0; | |
| 146 | } | ||
| 147 | ✗ | prefix_iterator& operator ++ () { | |
| 148 | ✗ | a &= a-1; | |
| 149 | ✗ | return *this; | |
| 150 | } | ||
| 151 | ✗ | T& operator * () const { | |
| 152 | ✗ | return dat[a-1]; | |
| 153 | } | ||
| 154 | }; | ||
| 155 | using prefix_range = iterator_range<prefix_iterator>; | ||
| 156 | ✗ | prefix_range prefix(int a) { | |
| 157 | ✗ | return prefix_range{prefix_iterator{dat.data(), a}, prefix_iterator{nullptr, 0}}; | |
| 158 | } | ||
| 159 | }; | ||
| 160 | |||
| 161 | } // namespace wala | ||
| 162 |