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#pragma once
#include "std/algorithm.hpp"
#include "std/set.hpp"
#include "std/utility.hpp"
#include "std/vector.hpp"
namespace my
{
// This class represents a set of disjoint intervals in the form
// [begin, end). Note that neighbour intervals are always coalesced,
// so while [0, 1), [1, 2) and [2, 3) are disjoint, after addition to
// the set they will be stored as a single [0, 3).
template <typename TElem>
class IntervalSet
{
public:
using TInterval = pair<TElem, TElem>;
// Adds an |interval| to the set, coalescing adjacent intervals if needed.
//
// Complexity: O(num of intervals intersecting with |interval| +
// log(total number of intervals)).
void Add(TInterval const & interval);
// Subtracts set from an |interval| and appends result to
// |difference|.
//
// Complexity: O(num of intervals intersecting with |interval| +
// log(total number of intervals)).
void SubtractFrom(TInterval const & interval, vector<TInterval> & difference) const;
// Returns all elements of the set as a set of intervals.
//
// Complexity: O(1).
inline set<TInterval> const & Elems() const { return m_intervals; }
private:
using TIterator = typename set<TInterval>::iterator;
// Calculates range of intervals that have non-empty intersection with a given |interval|.
void Cover(TInterval const & interval, TIterator & begin, TIterator & end) const;
// This is a set of disjoint intervals.
set<TInterval> m_intervals;
};
template <typename TElem>
void IntervalSet<TElem>::Add(TInterval const & interval)
{
// Skips empty intervals.
if (interval.first == interval.second)
return;
TIterator begin;
TIterator end;
Cover(interval, begin, end);
TElem from = interval.first;
TElem to = interval.second;
// Updates |from| and |to| in accordance with corner intervals (if any).
if (begin != end)
{
if (begin->first < from)
from = begin->first;
auto last = end;
--last;
if (last->second > to)
to = last->second;
}
// Now all elements [from, to) can be added to the set as a single
// interval which will replace all intervals in [begin, end). But
// note that it can be possible to merge new interval with its
// neighbors, so following code checks it.
if (begin != m_intervals.begin())
{
auto prevBegin = begin;
--prevBegin;
if (prevBegin->second == from)
{
begin = prevBegin;
from = prevBegin->first;
}
}
if (end != m_intervals.end() && end->first == to)
{
to = end->second;
++end;
}
m_intervals.erase(begin, end);
m_intervals.emplace(from, to);
}
template <typename TElem>
void IntervalSet<TElem>::SubtractFrom(TInterval const & interval,
vector<TInterval> & difference) const
{
TIterator begin;
TIterator end;
Cover(interval, begin, end);
TElem from = interval.first;
TElem const to = interval.second;
for (auto it = begin; it != end && from < to; ++it)
{
if (it->first > from)
{
difference.emplace_back(from, it->first);
from = it->second;
}
else
{
from = max(from, it->second);
}
}
if (from < to)
difference.emplace_back(from, to);
}
template <typename TElem>
void IntervalSet<TElem>::Cover(TInterval const & interval, TIterator & begin, TIterator & end) const
{
TElem const & from = interval.first;
TElem const & to = interval.second;
begin = m_intervals.lower_bound(make_pair(from, from));
if (begin != m_intervals.begin())
{
auto prev = begin;
--prev;
if (prev->second > from)
begin = prev;
}
end = m_intervals.lower_bound(make_pair(to, to));
}
} // namespace my
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