| // Copyright (c) 2019 The Chromium Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style license that can be |
| // found in the LICENSE file. |
| |
| #ifndef QUICHE_QUIC_CORE_QUIC_INTERVAL_SET_H_ |
| #define QUICHE_QUIC_CORE_QUIC_INTERVAL_SET_H_ |
| |
| // QuicIntervalSet<T> is a data structure used to represent a sorted set of |
| // non-empty, non-adjacent, and mutually disjoint intervals. Mutations to an |
| // interval set preserve these properties, altering the set as needed. For |
| // example, adding [2, 3) to a set containing only [1, 2) would result in the |
| // set containing the single interval [1, 3). |
| // |
| // Supported operations include testing whether an Interval is contained in the |
| // QuicIntervalSet, comparing two QuicIntervalSets, and performing |
| // QuicIntervalSet union, intersection, and difference. |
| // |
| // QuicIntervalSet maintains the minimum number of entries needed to represent |
| // the set of underlying intervals. When the QuicIntervalSet is modified (e.g. |
| // due to an Add operation), other interval entries may be coalesced, removed, |
| // or otherwise modified in order to maintain this invariant. The intervals are |
| // maintained in sorted order, by ascending min() value. |
| // |
| // The reader is cautioned to beware of the terminology used here: this library |
| // uses the terms "min" and "max" rather than "begin" and "end" as is |
| // conventional for the STL. The terminology [min, max) refers to the half-open |
| // interval which (if the interval is not empty) contains min but does not |
| // contain max. An interval is considered empty if min >= max. |
| // |
| // T is required to be default- and copy-constructible, to have an assignment |
| // operator, a difference operator (operator-()), and the full complement of |
| // comparison operators (<, <=, ==, !=, >=, >). These requirements are inherited |
| // from value_type. |
| // |
| // QuicIntervalSet has constant-time move operations. |
| // |
| // |
| // Examples: |
| // QuicIntervalSet<int> intervals; |
| // intervals.Add(Interval<int>(10, 20)); |
| // intervals.Add(Interval<int>(30, 40)); |
| // // intervals contains [10,20) and [30,40). |
| // intervals.Add(Interval<int>(15, 35)); |
| // // intervals has been coalesced. It now contains the single range [10,40). |
| // EXPECT_EQ(1, intervals.Size()); |
| // EXPECT_TRUE(intervals.Contains(Interval<int>(10, 40))); |
| // |
| // intervals.Difference(Interval<int>(10, 20)); |
| // // intervals should now contain the single range [20, 40). |
| // EXPECT_EQ(1, intervals.Size()); |
| // EXPECT_TRUE(intervals.Contains(Interval<int>(20, 40))); |
| |
| #include <stddef.h> |
| #include <algorithm> |
| #include <initializer_list> |
| #include <set> |
| #include <utility> |
| #include <vector> |
| |
| #include <string> |
| |
| #include "quic/core/quic_interval.h" |
| #include "quic/platform/api/quic_containers.h" |
| #include "quic/platform/api/quic_logging.h" |
| |
| namespace quic { |
| |
| template <typename T> |
| class QUIC_NO_EXPORT QuicIntervalSet { |
| public: |
| using value_type = QuicInterval<T>; |
| |
| private: |
| struct QUIC_NO_EXPORT IntervalLess { |
| using is_transparent = void; |
| bool operator()(const value_type& a, const value_type& b) const; |
| // These transparent overloads are used when we do all of our searches (via |
| // Set::lower_bound() and Set::upper_bound()), which avoids the need to |
| // construct an interval when we are looking for a point and also avoids |
| // needing to worry about comparing overlapping intervals in the overload |
| // that takes two value_types (the one just above this comment). |
| bool operator()(const value_type& a, const T& point) const; |
| bool operator()(const value_type& a, T&& point) const; |
| bool operator()(const T& point, const value_type& a) const; |
| bool operator()(T&& point, const value_type& a) const; |
| }; |
| |
| using Set = QuicSmallOrderedSet<value_type, IntervalLess>; |
| |
| public: |
| using const_iterator = typename Set::const_iterator; |
| using const_reverse_iterator = typename Set::const_reverse_iterator; |
| |
| // Instantiates an empty QuicIntervalSet. |
| QuicIntervalSet() = default; |
| |
| // Instantiates a QuicIntervalSet containing exactly one initial half-open |
| // interval [min, max), unless the given interval is empty, in which case the |
| // QuicIntervalSet will be empty. |
| explicit QuicIntervalSet(const value_type& interval) { Add(interval); } |
| |
| // Instantiates a QuicIntervalSet containing the half-open interval [min, |
| // max). |
| QuicIntervalSet(const T& min, const T& max) { Add(min, max); } |
| |
| QuicIntervalSet(std::initializer_list<value_type> il) { assign(il); } |
| |
| // Clears this QuicIntervalSet. |
| void Clear() { intervals_.clear(); } |
| |
| // Returns the number of disjoint intervals contained in this QuicIntervalSet. |
| size_t Size() const { return intervals_.size(); } |
| |
| // Returns the smallest interval that contains all intervals in this |
| // QuicIntervalSet, or the empty interval if the set is empty. |
| value_type SpanningInterval() const; |
| |
| // Adds "interval" to this QuicIntervalSet. Adding the empty interval has no |
| // effect. |
| void Add(const value_type& interval); |
| |
| // Adds the interval [min, max) to this QuicIntervalSet. Adding the empty |
| // interval has no effect. |
| void Add(const T& min, const T& max) { Add(value_type(min, max)); } |
| |
| // Same semantics as Add(const value_type&), but optimized for the case where |
| // rbegin()->min() <= |interval|.min() <= rbegin()->max(). |
| void AddOptimizedForAppend(const value_type& interval) { |
| if (Empty()) { |
| Add(interval); |
| return; |
| } |
| |
| const_reverse_iterator last_interval = intervals_.rbegin(); |
| |
| // If interval.min() is outside of [last_interval->min, last_interval->max], |
| // we can not simply extend last_interval->max. |
| if (interval.min() < last_interval->min() || |
| interval.min() > last_interval->max()) { |
| Add(interval); |
| return; |
| } |
| |
| if (interval.max() <= last_interval->max()) { |
| // interval is fully contained by last_interval. |
| return; |
| } |
| |
| // Extend last_interval.max to interval.max, in place. |
| // |
| // Set does not allow in-place updates due to the potential of violating its |
| // ordering requirements. But we know setting the max of the last interval |
| // is safe w.r.t set ordering and other invariants of QuicIntervalSet, so we |
| // force an in-place update for performance. |
| const_cast<value_type*>(&(*last_interval))->SetMax(interval.max()); |
| } |
| |
| // Same semantics as Add(const T&, const T&), but optimized for the case where |
| // rbegin()->max() == |min|. |
| void AddOptimizedForAppend(const T& min, const T& max) { |
| AddOptimizedForAppend(value_type(min, max)); |
| } |
| |
| // TODO(wub): Similar to AddOptimizedForAppend, we can also have a |
| // AddOptimizedForPrepend if there is a use case. |
| |
| // Remove the first interval. |
| // REQUIRES: !Empty() |
| void PopFront() { |
| QUICHE_DCHECK(!Empty()); |
| intervals_.erase(intervals_.begin()); |
| } |
| |
| // Trim all values that are smaller than |value|. Which means |
| // a) If all values in an interval is smaller than |value|, the entire |
| // interval is removed. |
| // b) If some but not all values in an interval is smaller than |value|, the |
| // min of that interval is raised to |value|. |
| // Returns true if some intervals are trimmed. |
| bool TrimLessThan(const T& value) { |
| // Number of intervals that are fully or partially trimmed. |
| size_t num_intervals_trimmed = 0; |
| |
| while (!intervals_.empty()) { |
| const_iterator first_interval = intervals_.begin(); |
| if (first_interval->min() >= value) { |
| break; |
| } |
| |
| ++num_intervals_trimmed; |
| |
| if (first_interval->max() <= value) { |
| // a) Trim the entire interval. |
| intervals_.erase(first_interval); |
| continue; |
| } |
| |
| // b) Trim a prefix of the interval. |
| // |
| // Set does not allow in-place updates due to the potential of violating |
| // its ordering requirements. But increasing the min of the first interval |
| // will not break the ordering, hence the const_cast. |
| const_cast<value_type*>(&(*first_interval))->SetMin(value); |
| break; |
| } |
| |
| return num_intervals_trimmed != 0; |
| } |
| |
| // Returns true if this QuicIntervalSet is empty. |
| bool Empty() const { return intervals_.empty(); } |
| |
| // Returns true if any interval in this QuicIntervalSet contains the indicated |
| // value. |
| bool Contains(const T& value) const; |
| |
| // Returns true if there is some interval in this QuicIntervalSet that wholly |
| // contains the given interval. An interval O "wholly contains" a non-empty |
| // interval I if O.Contains(p) is true for every p in I. This is the same |
| // definition used by value_type::Contains(). This method returns false on |
| // the empty interval, due to a (perhaps unintuitive) convention inherited |
| // from value_type. |
| // Example: |
| // Assume an QuicIntervalSet containing the entries { [10,20), [30,40) }. |
| // Contains(Interval(15, 16)) returns true, because [10,20) contains |
| // [15,16). However, Contains(Interval(15, 35)) returns false. |
| bool Contains(const value_type& interval) const; |
| |
| // Returns true if for each interval in "other", there is some (possibly |
| // different) interval in this QuicIntervalSet which wholly contains it. See |
| // Contains(const value_type& interval) for the meaning of "wholly contains". |
| // Perhaps unintuitively, this method returns false if "other" is the empty |
| // set. The algorithmic complexity of this method is O(other.Size() * |
| // log(this->Size())). The method could be rewritten to run in O(other.Size() |
| // + this->Size()), and this alternative could be implemented as a free |
| // function using the public API. |
| bool Contains(const QuicIntervalSet<T>& other) const; |
| |
| // Returns true if there is some interval in this QuicIntervalSet that wholly |
| // contains the interval [min, max). See Contains(const value_type&). |
| bool Contains(const T& min, const T& max) const { |
| return Contains(value_type(min, max)); |
| } |
| |
| // Returns true if for some interval in "other", there is some interval in |
| // this QuicIntervalSet that intersects with it. See value_type::Intersects() |
| // for the definition of interval intersection. Runs in time O(n+m) where n |
| // is the number of intervals in this and m is the number of intervals in |
| // other. |
| bool Intersects(const QuicIntervalSet& other) const; |
| |
| // Returns an iterator to the value_type in the QuicIntervalSet that contains |
| // the given value. In other words, returns an iterator to the unique interval |
| // [min, max) in the QuicIntervalSet that has the property min <= value < max. |
| // If there is no such interval, this method returns end(). |
| const_iterator Find(const T& value) const; |
| |
| // Returns an iterator to the value_type in the QuicIntervalSet that wholly |
| // contains the given interval. In other words, returns an iterator to the |
| // unique interval outer in the QuicIntervalSet that has the property that |
| // outer.Contains(interval). If there is no such interval, or if interval is |
| // empty, returns end(). |
| const_iterator Find(const value_type& interval) const; |
| |
| // Returns an iterator to the value_type in the QuicIntervalSet that wholly |
| // contains [min, max). In other words, returns an iterator to the unique |
| // interval outer in the QuicIntervalSet that has the property that |
| // outer.Contains(Interval<T>(min, max)). If there is no such interval, or if |
| // interval is empty, returns end(). |
| const_iterator Find(const T& min, const T& max) const { |
| return Find(value_type(min, max)); |
| } |
| |
| // Returns an iterator pointing to the first value_type which contains or |
| // goes after the given value. |
| // |
| // Example: |
| // [10, 20) [30, 40) |
| // ^ LowerBound(10) |
| // ^ LowerBound(15) |
| // ^ LowerBound(20) |
| // ^ LowerBound(25) |
| const_iterator LowerBound(const T& value) const; |
| |
| // Returns an iterator pointing to the first value_type which goes after |
| // the given value. |
| // |
| // Example: |
| // [10, 20) [30, 40) |
| // ^ UpperBound(10) |
| // ^ UpperBound(15) |
| // ^ UpperBound(20) |
| // ^ UpperBound(25) |
| const_iterator UpperBound(const T& value) const; |
| |
| // Returns true if every value within the passed interval is not Contained |
| // within the QuicIntervalSet. |
| // Note that empty intervals are always considered disjoint from the |
| // QuicIntervalSet (even though the QuicIntervalSet doesn't `Contain` them). |
| bool IsDisjoint(const value_type& interval) const; |
| |
| // Merges all the values contained in "other" into this QuicIntervalSet. |
| // |
| // Performance: Let n == Size() and m = other.Size(). Union() runs in O(m) |
| // Set operations, so that if Set is a tree, it runs in time O(m log(n+m)) and |
| // if Set is a flat_set it runs in time O(m(n+m)). In principle, for the |
| // flat_set, we should be able to make this run in time O(n+m). |
| // |
| // TODO(bradleybear): Make Union() run in time O(n+m) for flat_set. This may |
| // require an additional template parameter to indicate that the Set is a |
| // linear-time data structure instead of a log-time data structure. |
| void Union(const QuicIntervalSet& other); |
| |
| // Modifies this QuicIntervalSet so that it contains only those values that |
| // are currently present both in *this and in the QuicIntervalSet "other". |
| void Intersection(const QuicIntervalSet& other); |
| |
| // Mutates this QuicIntervalSet so that it contains only those values that are |
| // currently in *this but not in "interval". |
| void Difference(const value_type& interval); |
| |
| // Mutates this QuicIntervalSet so that it contains only those values that are |
| // currently in *this but not in the interval [min, max). |
| void Difference(const T& min, const T& max); |
| |
| // Mutates this QuicIntervalSet so that it contains only those values that are |
| // currently in *this but not in the QuicIntervalSet "other". Runs in time |
| // O(n+m) where n is this->Size(), m is other.Size(), regardless of whether |
| // the Set is a flat_set or a std::set. |
| void Difference(const QuicIntervalSet& other); |
| |
| // Mutates this QuicIntervalSet so that it contains only those values that are |
| // in [min, max) but not currently in *this. |
| void Complement(const T& min, const T& max); |
| |
| // QuicIntervalSet's begin() iterator. The invariants of QuicIntervalSet |
| // guarantee that for each entry e in the set, e.min() < e.max() (because the |
| // entries are non-empty) and for each entry f that appears later in the set, |
| // e.max() < f.min() (because the entries are ordered, pairwise-disjoint, and |
| // non-adjacent). Modifications to this QuicIntervalSet invalidate these |
| // iterators. |
| const_iterator begin() const { return intervals_.begin(); } |
| |
| // QuicIntervalSet's end() iterator. |
| const_iterator end() const { return intervals_.end(); } |
| |
| // QuicIntervalSet's rbegin() and rend() iterators. Iterator invalidation |
| // semantics are the same as those for begin() / end(). |
| const_reverse_iterator rbegin() const { return intervals_.rbegin(); } |
| |
| const_reverse_iterator rend() const { return intervals_.rend(); } |
| |
| template <typename Iter> |
| void assign(Iter first, Iter last) { |
| Clear(); |
| for (; first != last; ++first) |
| Add(*first); |
| } |
| |
| void assign(std::initializer_list<value_type> il) { |
| assign(il.begin(), il.end()); |
| } |
| |
| // Returns a human-readable representation of this set. This will typically be |
| // (though is not guaranteed to be) of the form |
| // "[a1, b1) [a2, b2) ... [an, bn)" |
| // where the intervals are in the same order as given by traversal from |
| // begin() to end(). This representation is intended for human consumption; |
| // computer programs should not rely on the output being in exactly this form. |
| std::string ToString() const; |
| |
| QuicIntervalSet& operator=(std::initializer_list<value_type> il) { |
| assign(il.begin(), il.end()); |
| return *this; |
| } |
| |
| friend bool operator==(const QuicIntervalSet& a, const QuicIntervalSet& b) { |
| return a.Size() == b.Size() && |
| std::equal(a.begin(), a.end(), b.begin(), NonemptyIntervalEq()); |
| } |
| |
| friend bool operator!=(const QuicIntervalSet& a, const QuicIntervalSet& b) { |
| return !(a == b); |
| } |
| |
| private: |
| // Simple member-wise equality, since all intervals are non-empty. |
| struct QUIC_NO_EXPORT NonemptyIntervalEq { |
| bool operator()(const value_type& a, const value_type& b) const { |
| return a.min() == b.min() && a.max() == b.max(); |
| } |
| }; |
| |
| // Returns true if this set is valid (i.e. all intervals in it are non-empty, |
| // non-adjacent, and mutually disjoint). Currently this is used as an |
| // integrity check by the Intersection() and Difference() methods, but is only |
| // invoked for debug builds (via QUICHE_DCHECK). |
| bool Valid() const; |
| |
| // Finds the first interval that potentially intersects 'other'. |
| const_iterator FindIntersectionCandidate(const QuicIntervalSet& other) const; |
| |
| // Finds the first interval that potentially intersects 'interval'. More |
| // precisely, return an interator it pointing at the last interval J such that |
| // interval <= J. If all the intervals are > J then return begin(). |
| const_iterator FindIntersectionCandidate(const value_type& interval) const; |
| |
| // Helper for Intersection() and Difference(): Finds the next pair of |
| // intervals from 'x' and 'y' that intersect. 'mine' is an iterator |
| // over x->intervals_. 'theirs' is an iterator over y.intervals_. 'mine' |
| // and 'theirs' are advanced until an intersecting pair is found. |
| // Non-intersecting intervals (aka "holes") from x->intervals_ can be |
| // optionally erased by "on_hole". "on_hole" must return an iterator to the |
| // first element in 'x' after the hole, or x->intervals_.end() if no elements |
| // exist after the hole. |
| template <typename X, typename Func> |
| static bool FindNextIntersectingPairImpl(X* x, |
| const QuicIntervalSet& y, |
| const_iterator* mine, |
| const_iterator* theirs, |
| Func on_hole); |
| |
| // The variant of the above method that doesn't mutate this QuicIntervalSet. |
| bool FindNextIntersectingPair(const QuicIntervalSet& other, |
| const_iterator* mine, |
| const_iterator* theirs) const { |
| return FindNextIntersectingPairImpl( |
| this, other, mine, theirs, |
| [](const QuicIntervalSet*, const_iterator, const_iterator end) { |
| return end; |
| }); |
| } |
| |
| // The variant of the above method that mutates this QuicIntervalSet by |
| // erasing holes. |
| bool FindNextIntersectingPairAndEraseHoles(const QuicIntervalSet& other, |
| const_iterator* mine, |
| const_iterator* theirs) { |
| return FindNextIntersectingPairImpl( |
| this, other, mine, theirs, |
| [](QuicIntervalSet* x, const_iterator from, const_iterator to) { |
| return x->intervals_.erase(from, to); |
| }); |
| } |
| |
| // The representation for the intervals. The intervals in this set are |
| // non-empty, pairwise-disjoint, non-adjacent and ordered in ascending order |
| // by min(). |
| Set intervals_; |
| }; |
| |
| template <typename T> |
| auto operator<<(std::ostream& out, const QuicIntervalSet<T>& seq) |
| -> decltype(out << *seq.begin()) { |
| out << "{"; |
| for (const auto& interval : seq) { |
| out << " " << interval; |
| } |
| out << " }"; |
| |
| return out; |
| } |
| |
| //============================================================================== |
| // Implementation details: Clients can stop reading here. |
| |
| template <typename T> |
| typename QuicIntervalSet<T>::value_type QuicIntervalSet<T>::SpanningInterval() |
| const { |
| value_type result; |
| if (!intervals_.empty()) { |
| result.SetMin(intervals_.begin()->min()); |
| result.SetMax(intervals_.rbegin()->max()); |
| } |
| return result; |
| } |
| |
| template <typename T> |
| void QuicIntervalSet<T>::Add(const value_type& interval) { |
| if (interval.Empty()) |
| return; |
| const_iterator it = intervals_.lower_bound(interval.min()); |
| value_type the_union = interval; |
| if (it != intervals_.begin()) { |
| --it; |
| if (it->Separated(the_union)) { |
| ++it; |
| } |
| } |
| // Don't erase the elements one at a time, since that will produce quadratic |
| // work on a flat_set, and apparently an extra log-factor of work for a |
| // tree-based set. Instead identify the first and last intervals that need to |
| // be erased, and call erase only once. |
| const_iterator start = it; |
| while (it != intervals_.end() && !it->Separated(the_union)) { |
| the_union.SpanningUnion(*it); |
| ++it; |
| } |
| intervals_.erase(start, it); |
| intervals_.insert(the_union); |
| } |
| |
| template <typename T> |
| bool QuicIntervalSet<T>::Contains(const T& value) const { |
| // Find the first interval with min() > value, then move back one step |
| const_iterator it = intervals_.upper_bound(value); |
| if (it == intervals_.begin()) |
| return false; |
| --it; |
| return it->Contains(value); |
| } |
| |
| template <typename T> |
| bool QuicIntervalSet<T>::Contains(const value_type& interval) const { |
| // Find the first interval with min() > value, then move back one step. |
| const_iterator it = intervals_.upper_bound(interval.min()); |
| if (it == intervals_.begin()) |
| return false; |
| --it; |
| return it->Contains(interval); |
| } |
| |
| template <typename T> |
| bool QuicIntervalSet<T>::Contains(const QuicIntervalSet<T>& other) const { |
| if (!SpanningInterval().Contains(other.SpanningInterval())) { |
| return false; |
| } |
| |
| for (const_iterator i = other.begin(); i != other.end(); ++i) { |
| // If we don't contain the interval, can return false now. |
| if (!Contains(*i)) { |
| return false; |
| } |
| } |
| return true; |
| } |
| |
| // This method finds the interval that Contains() "value", if such an interval |
| // exists in the QuicIntervalSet. The way this is done is to locate the |
| // "candidate interval", the only interval that could *possibly* contain value, |
| // and test it using Contains(). The candidate interval is the interval with the |
| // largest min() having min() <= value. |
| // |
| // Another detail involves the choice of which Set method to use to try to find |
| // the candidate interval. The most appropriate entry point is |
| // Set::upper_bound(), which finds the least interval with a min > the |
| // value. The semantics of upper_bound() are slightly different from what we |
| // want (namely, to find the greatest interval which is <= the probe interval) |
| // but they are close enough; the interval found by upper_bound() will always be |
| // one step past the interval we are looking for (if it exists) or at begin() |
| // (if it does not). Getting to the proper interval is a simple matter of |
| // decrementing the iterator. |
| template <typename T> |
| typename QuicIntervalSet<T>::const_iterator QuicIntervalSet<T>::Find( |
| const T& value) const { |
| const_iterator it = intervals_.upper_bound(value); |
| if (it == intervals_.begin()) |
| return intervals_.end(); |
| --it; |
| if (it->Contains(value)) |
| return it; |
| else |
| return intervals_.end(); |
| } |
| |
| // This method finds the interval that Contains() the interval "probe", if such |
| // an interval exists in the QuicIntervalSet. The way this is done is to locate |
| // the "candidate interval", the only interval that could *possibly* contain |
| // "probe", and test it using Contains(). We use the same algorithm as for |
| // Find(value), except that instead of checking that the value is contained, we |
| // check that the probe is contained. |
| template <typename T> |
| typename QuicIntervalSet<T>::const_iterator QuicIntervalSet<T>::Find( |
| const value_type& probe) const { |
| const_iterator it = intervals_.upper_bound(probe.min()); |
| if (it == intervals_.begin()) |
| return intervals_.end(); |
| --it; |
| if (it->Contains(probe)) |
| return it; |
| else |
| return intervals_.end(); |
| } |
| |
| template <typename T> |
| typename QuicIntervalSet<T>::const_iterator QuicIntervalSet<T>::LowerBound( |
| const T& value) const { |
| const_iterator it = intervals_.lower_bound(value); |
| if (it == intervals_.begin()) { |
| return it; |
| } |
| |
| // The previous intervals_.lower_bound() checking is essentially based on |
| // interval.min(), so we need to check whether the `value` is contained in |
| // the previous interval. |
| --it; |
| if (it->Contains(value)) { |
| return it; |
| } else { |
| return ++it; |
| } |
| } |
| |
| template <typename T> |
| typename QuicIntervalSet<T>::const_iterator QuicIntervalSet<T>::UpperBound( |
| const T& value) const { |
| return intervals_.upper_bound(value); |
| } |
| |
| template <typename T> |
| bool QuicIntervalSet<T>::IsDisjoint(const value_type& interval) const { |
| if (interval.Empty()) |
| return true; |
| // Find the first interval with min() > interval.min() |
| const_iterator it = intervals_.upper_bound(interval.min()); |
| if (it != intervals_.end() && interval.max() > it->min()) |
| return false; |
| if (it == intervals_.begin()) |
| return true; |
| --it; |
| return it->max() <= interval.min(); |
| } |
| |
| template <typename T> |
| void QuicIntervalSet<T>::Union(const QuicIntervalSet& other) { |
| for (const value_type& interval : other.intervals_) { |
| Add(interval); |
| } |
| } |
| |
| template <typename T> |
| typename QuicIntervalSet<T>::const_iterator |
| QuicIntervalSet<T>::FindIntersectionCandidate( |
| const QuicIntervalSet& other) const { |
| return FindIntersectionCandidate(*other.intervals_.begin()); |
| } |
| |
| template <typename T> |
| typename QuicIntervalSet<T>::const_iterator |
| QuicIntervalSet<T>::FindIntersectionCandidate( |
| const value_type& interval) const { |
| // Use upper_bound to efficiently find the first interval in intervals_ |
| // where min() is greater than interval.min(). If the result |
| // isn't the beginning of intervals_ then move backwards one interval since |
| // the interval before it is the first candidate where max() may be |
| // greater than interval.min(). |
| // In other words, no interval before that can possibly intersect with any |
| // of other.intervals_. |
| const_iterator mine = intervals_.upper_bound(interval.min()); |
| if (mine != intervals_.begin()) { |
| --mine; |
| } |
| return mine; |
| } |
| |
| template <typename T> |
| template <typename X, typename Func> |
| bool QuicIntervalSet<T>::FindNextIntersectingPairImpl(X* x, |
| const QuicIntervalSet& y, |
| const_iterator* mine, |
| const_iterator* theirs, |
| Func on_hole) { |
| QUICHE_CHECK(x != nullptr); |
| if ((*mine == x->intervals_.end()) || (*theirs == y.intervals_.end())) { |
| return false; |
| } |
| while (!(**mine).Intersects(**theirs)) { |
| const_iterator erase_first = *mine; |
| // Skip over intervals in 'mine' that don't reach 'theirs'. |
| while (*mine != x->intervals_.end() && (**mine).max() <= (**theirs).min()) { |
| ++(*mine); |
| } |
| *mine = on_hole(x, erase_first, *mine); |
| // We're done if the end of intervals_ is reached. |
| if (*mine == x->intervals_.end()) { |
| return false; |
| } |
| // Skip over intervals 'theirs' that don't reach 'mine'. |
| while (*theirs != y.intervals_.end() && |
| (**theirs).max() <= (**mine).min()) { |
| ++(*theirs); |
| } |
| // If the end of other.intervals_ is reached, we're done. |
| if (*theirs == y.intervals_.end()) { |
| on_hole(x, *mine, x->intervals_.end()); |
| return false; |
| } |
| } |
| return true; |
| } |
| |
| template <typename T> |
| void QuicIntervalSet<T>::Intersection(const QuicIntervalSet& other) { |
| if (!SpanningInterval().Intersects(other.SpanningInterval())) { |
| intervals_.clear(); |
| return; |
| } |
| |
| const_iterator mine = FindIntersectionCandidate(other); |
| // Remove any intervals that cannot possibly intersect with other.intervals_. |
| mine = intervals_.erase(intervals_.begin(), mine); |
| const_iterator theirs = other.FindIntersectionCandidate(*this); |
| |
| while (FindNextIntersectingPairAndEraseHoles(other, &mine, &theirs)) { |
| // OK, *mine and *theirs intersect. Now, we find the largest |
| // span of intervals in other (starting at theirs) - say [a..b] |
| // - that intersect *mine, and we replace *mine with (*mine |
| // intersect x) for all x in [a..b] Note that subsequent |
| // intervals in this can't intersect any intervals in [a..b) -- |
| // they may only intersect b or subsequent intervals in other. |
| value_type i(*mine); |
| intervals_.erase(mine); |
| mine = intervals_.end(); |
| value_type intersection; |
| while (theirs != other.intervals_.end() && |
| i.Intersects(*theirs, &intersection)) { |
| std::pair<const_iterator, bool> ins = intervals_.insert(intersection); |
| QUICHE_DCHECK(ins.second); |
| mine = ins.first; |
| ++theirs; |
| } |
| QUICHE_DCHECK(mine != intervals_.end()); |
| --theirs; |
| ++mine; |
| } |
| QUICHE_DCHECK(Valid()); |
| } |
| |
| template <typename T> |
| bool QuicIntervalSet<T>::Intersects(const QuicIntervalSet& other) const { |
| // Don't bother to handle nonoverlapping spanning intervals as a special case. |
| // This code runs in time O(n+m), as guaranteed, even for that case . |
| // Handling the nonoverlapping spanning intervals as a special case doesn't |
| // improve the asymptotics but does make the code more complex. |
| auto mine = intervals_.begin(); |
| auto theirs = other.intervals_.begin(); |
| while (mine != intervals_.end() && theirs != other.intervals_.end()) { |
| if (mine->Intersects(*theirs)) |
| return true; |
| else if (*mine < *theirs) |
| ++mine; |
| else |
| ++theirs; |
| } |
| return false; |
| } |
| |
| template <typename T> |
| void QuicIntervalSet<T>::Difference(const value_type& interval) { |
| if (!SpanningInterval().Intersects(interval)) { |
| return; |
| } |
| Difference(QuicIntervalSet<T>(interval)); |
| } |
| |
| template <typename T> |
| void QuicIntervalSet<T>::Difference(const T& min, const T& max) { |
| Difference(value_type(min, max)); |
| } |
| |
| template <typename T> |
| void QuicIntervalSet<T>::Difference(const QuicIntervalSet& other) { |
| // In order to avoid quadratic-time when using a flat set, we don't try to |
| // update intervals_ in place. Instead we build up a new result_, always |
| // inserting at the end which is O(1) time per insertion. Since the number of |
| // elements in the result is O(Size() + other.Size()), the cost for all the |
| // insertions is also O(Size() + other.Size()). |
| // |
| // We look at all the elements of intervals_, so that's O(Size()). |
| // |
| // We also look at all the elements of other.intervals_, for O(other.Size()). |
| if (Empty()) |
| return; |
| Set result; |
| const_iterator mine = intervals_.begin(); |
| value_type myinterval = *mine; |
| const_iterator theirs = other.intervals_.begin(); |
| while (mine != intervals_.end()) { |
| // Loop invariants: |
| // myinterval is nonempty. |
| // mine points at a range that is a suffix of myinterval. |
| QUICHE_DCHECK(!myinterval.Empty()); |
| QUICHE_DCHECK(myinterval.max() == mine->max()); |
| |
| // There are 3 cases. |
| // myinterval is completely before theirs (treat theirs==end() as if it is |
| // infinity). |
| // --> consume myinterval into result. |
| // myinterval is completely after theirs |
| // --> theirs can no longer affect us, so ++theirs. |
| // myinterval touches theirs with a prefix of myinterval not touching |
| // *theirs. |
| // --> consume the prefix of myinterval into the result. |
| // myinterval touches theirs, with the first element of myinterval in |
| // *theirs. |
| // -> reduce myinterval |
| if (theirs == other.intervals_.end() || myinterval.max() <= theirs->min()) { |
| // Keep all of my_interval. |
| result.insert(result.end(), myinterval); |
| myinterval.Clear(); |
| } else if (theirs->max() <= myinterval.min()) { |
| ++theirs; |
| } else if (myinterval.min() < theirs->min()) { |
| // Keep a nonempty prefix of my interval. |
| result.insert(result.end(), value_type(myinterval.min(), theirs->min())); |
| myinterval.SetMin(theirs->max()); |
| } else { |
| // myinterval starts at or after *theirs, chop down myinterval. |
| myinterval.SetMin(theirs->max()); |
| } |
| // if myinterval became empty, find the next interval |
| if (myinterval.Empty()) { |
| ++mine; |
| if (mine != intervals_.end()) { |
| myinterval = *mine; |
| } |
| } |
| } |
| std::swap(result, intervals_); |
| QUICHE_DCHECK(Valid()); |
| } |
| |
| template <typename T> |
| void QuicIntervalSet<T>::Complement(const T& min, const T& max) { |
| QuicIntervalSet<T> span(min, max); |
| span.Difference(*this); |
| intervals_.swap(span.intervals_); |
| } |
| |
| template <typename T> |
| std::string QuicIntervalSet<T>::ToString() const { |
| std::ostringstream os; |
| os << *this; |
| return os.str(); |
| } |
| |
| template <typename T> |
| bool QuicIntervalSet<T>::Valid() const { |
| const_iterator prev = end(); |
| for (const_iterator it = begin(); it != end(); ++it) { |
| // invalid or empty interval. |
| if (it->min() >= it->max()) |
| return false; |
| // Not sorted, not disjoint, or adjacent. |
| if (prev != end() && prev->max() >= it->min()) |
| return false; |
| prev = it; |
| } |
| return true; |
| } |
| |
| // This comparator orders intervals first by ascending min(). The Set never |
| // contains overlapping intervals, so that suffices. |
| template <typename T> |
| bool QuicIntervalSet<T>::IntervalLess::operator()(const value_type& a, |
| const value_type& b) const { |
| // This overload is probably used only by Set::insert(). |
| return a.min() < b.min(); |
| } |
| |
| // It appears that the Set::lower_bound(T) method uses only two overloads of the |
| // comparison operator that take a T as the second argument.. In contrast |
| // Set::upper_bound(T) uses the two overloads that take T as the first argument. |
| template <typename T> |
| bool QuicIntervalSet<T>::IntervalLess::operator()(const value_type& a, |
| const T& point) const { |
| // Compare an interval to a point. |
| return a.min() < point; |
| } |
| |
| template <typename T> |
| bool QuicIntervalSet<T>::IntervalLess::operator()(const value_type& a, |
| T&& point) const { |
| // Compare an interval to a point |
| return a.min() < point; |
| } |
| |
| // It appears that the Set::upper_bound(T) method uses only the next two |
| // overloads of the comparison operator. |
| template <typename T> |
| bool QuicIntervalSet<T>::IntervalLess::operator()(const T& point, |
| const value_type& a) const { |
| // Compare an interval to a point. |
| return point < a.min(); |
| } |
| |
| template <typename T> |
| bool QuicIntervalSet<T>::IntervalLess::operator()(T&& point, |
| const value_type& a) const { |
| // Compare an interval to a point. |
| return point < a.min(); |
| } |
| |
| } // namespace quic |
| |
| #endif // QUICHE_QUIC_CORE_QUIC_INTERVAL_SET_H_ |