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add doc: Binary search algorithms
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Bolero-MURAKAMI
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21 changed files with 1204 additions and 78 deletions
53
source/libs/sprout/algorithm/binary_search.rst
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53
source/libs/sprout/algorithm/binary_search.rst
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.. _sprout-algorithm-binary_search:
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###############################################################################
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binary_search
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###############################################################################
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Interface
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========================================
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.. sourcecode:: c++
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template<typename ForwardIterator, typename T>
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inline SPROUT_CONSTEXPR bool
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binary_search(ForwardIterator first, ForwardIterator last, T const& value);
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template<typename ForwardIterator, typename T, typename Compare>
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inline SPROUT_CONSTEXPR bool
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binary_search(ForwardIterator first, ForwardIterator last, T const& value, Compare comp);
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Requires
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========================================
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| The elements e of [first,last) are partitioned with respect to the expressions ``e < value`` and ``!(value < e)`` or ``comp(e, value)`` and ``!comp(value, e)``.
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| Also, for all elements e of [first,last), ``e < value`` implies ``!(value < e)`` or ``comp(e, value)`` implies ``!comp(value, e)``.
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Returns
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========================================
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| true if there is an iterator i in the range [first,last) that satisfies the corresponding conditions: ``!(*i < value) && !(value < *i)`` or ``comp(*i, value) && comp(value, *i)``.
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Examples
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========================================
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.. sourcecode:: c++
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#include <sprout/algorithm/binary_search.hpp>
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#include <sprout/array.hpp>
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#include <sprout/container.hpp>
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using namespace sprout;
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SPROUT_STATIC_CONSTEXPR auto input = array<int, 10>{{1, 2, 3, 5, 5, 5, 5, 8, 9, 10}};
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SPROUT_STATIC_CONSTEXPR auto result = sprout::binary_search(begin(input), end(input), 5);
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static_assert(result, "found 5 by binary search.");
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Complexity
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========================================
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| At most ``log2(last - first) + O(1)`` comparisons.
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| Recursive function invocations in *O(logN)* (logarithmic) depth.
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Header
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========================================
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| ``sprout/algorithm/binary_search.hpp``
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| Convenience header: ``sprout/algorithm.hpp``
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58
source/libs/sprout/algorithm/equal_range.rst
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58
source/libs/sprout/algorithm/equal_range.rst
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.. _sprout-algorithm-equal_range:
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###############################################################################
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equal_range
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###############################################################################
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Interface
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========================================
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.. sourcecode:: c++
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template<typename ForwardIterator, typename T>
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inline SPROUT_CONSTEXPR sprout::pair<ForwardIterator, ForwardIterator>
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equal_range(ForwardIterator first, ForwardIterator last, T const& value);
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template<typename ForwardIterator, typename T, typename Compare>
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inline SPROUT_CONSTEXPR sprout::pair<ForwardIterator, ForwardIterator>
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equal_range(ForwardIterator first, ForwardIterator last, T const& value, Compare comp);
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Requires
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========================================
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| The elements e of [first,last) shall be partitioned with respect to the expressions ``e < value`` and ``!(value < e)`` or ``comp(e, value)`` and ``!comp(value, e)``.
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| Also, for all elements e of [first, last), ``e < value`` shall imply ``!(value < e)`` or ``comp(e, value)`` shall imply ``!comp(value, e)``.
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Returns
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========================================
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| ``make_pair(lower_bound(first, last, value), upper_bound(first, last, value))``
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| or
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| ``make_pair(lower_bound(first, last, value, comp), upper_bound(first, last, value, comp))``
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Examples
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========================================
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.. sourcecode:: c++
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#include <sprout/algorithm/equal_range.hpp>
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#include <sprout/algorithm/all_of_equal.hpp>
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#include <sprout/array.hpp>
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#include <sprout/container.hpp>
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using namespace sprout;
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SPROUT_STATIC_CONSTEXPR auto input = array<int, 10>{{1, 2, 3, 5, 5, 5, 5, 8, 9, 10}};
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SPROUT_STATIC_CONSTEXPR auto result = sprout::equal_range(begin(input), end(input), 5);
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static_assert(result.first - begin(input) == 3, "a lower bound position is 3.");
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static_assert(result.second - begin(input) == 7, "a upper bound position is 7.");
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static_assert(sprout::all_of_equal(result.first, result.second. 5), "all of result range is equal to 5.");
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Complexity
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========================================
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| At most ``2 * log2(last - first) + O(1)`` comparisons.
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| Recursive function invocations in *O(logN)* (logarithmic) depth.
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Header
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========================================
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| ``sprout/algorithm/equal_range.hpp``
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| Convenience header: ``sprout/algorithm.hpp``
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@ -33,6 +33,10 @@ Sprout.Algorithm
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is_decreasing
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is_strictly_increasing
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is_strictly_decreasing
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lower_bound
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upper_bound
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equal_range
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binary_search
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.. _sprout-algorithm-non_modifying:
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*******************************************************************************
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52
source/libs/sprout/algorithm/lower_bound.rst
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52
source/libs/sprout/algorithm/lower_bound.rst
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.. _sprout-algorithm-lower_bound:
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###############################################################################
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lower_bound
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###############################################################################
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Interface
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========================================
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.. sourcecode:: c++
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template<typename ForwardIterator, typename T>
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inline SPROUT_CONSTEXPR ForwardIterator
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lower_bound(ForwardIterator first, ForwardIterator last, T const& value);
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template<typename ForwardIterator, typename T, typename Compare>
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inline SPROUT_CONSTEXPR ForwardIterator
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lower_bound(ForwardIterator first, ForwardIterator last, T const& value, Compare comp);
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Requires
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========================================
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| The elements e of [first,last) shall be partitioned with respect to the expression ``e < value`` or ``comp(e, value)``.
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Returns
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========================================
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| The furthermost iterator i in the range [first,last] such that for any iterator j in the range [first,i) the following corresponding conditions hold: ``*j < value`` or ``comp(*j, value)``.
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Examples
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========================================
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.. sourcecode:: c++
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#include <sprout/algorithm/lower_bound.hpp>
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#include <sprout/array.hpp>
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#include <sprout/container.hpp>
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using namespace sprout;
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SPROUT_STATIC_CONSTEXPR auto input = array<int, 10>{{1, 2, 3, 5, 5, 5, 5, 8, 9, 10}};
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SPROUT_STATIC_CONSTEXPR auto result = sprout::lower_bound(begin(input), end(input), 5);
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static_assert(result - begin(input) == 3, "a lower bound position is 3.");
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Complexity
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========================================
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| At most ``log2(last - first) + O(1)`` comparisons.
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| Recursive function invocations in *O(logN)* (logarithmic) depth.
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Header
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========================================
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| ``sprout/algorithm/lower_bound.hpp``
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| Convenience header: ``sprout/algorithm.hpp``
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52
source/libs/sprout/algorithm/upper_bound.rst
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52
source/libs/sprout/algorithm/upper_bound.rst
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.. _sprout-algorithm-upper_bound:
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###############################################################################
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upper_bound
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###############################################################################
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Interface
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========================================
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.. sourcecode:: c++
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template<typename ForwardIterator, typename T>
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inline SPROUT_CONSTEXPR ForwardIterator
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upper_bound(ForwardIterator first, ForwardIterator last, T const& value);
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template<typename ForwardIterator, typename T, typename Compare>
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inline SPROUT_CONSTEXPR ForwardIterator
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upper_bound(ForwardIterator first, ForwardIterator last, T const& value, Compare comp);
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Requires
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========================================
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| The elements e of [first,last) shall be partitioned with respect to the expression ``!(value < e)`` or ``!comp(value, e)``.
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Returns
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========================================
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| The furthermost iterator i in the range [first,last] such that for any iterator j in the range [first,i) the following corresponding conditions hold: ``!(value < *j)`` or ``!comp(value, *j)``.
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Examples
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========================================
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.. sourcecode:: c++
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#include <sprout/algorithm/upper_bound.hpp>
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#include <sprout/array.hpp>
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#include <sprout/container.hpp>
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using namespace sprout;
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SPROUT_STATIC_CONSTEXPR auto input = array<int, 10>{{1, 2, 3, 5, 5, 5, 5, 8, 9, 10}};
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SPROUT_STATIC_CONSTEXPR auto result = sprout::upper_bound(begin(input), end(input), 5);
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static_assert(result - begin(input) == 7, "a upper bound position is 7.");
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Complexity
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========================================
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| At most ``log2(last - first) + O(1)`` comparisons.
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| Recursive function invocations in *O(logN)* (logarithmic) depth.
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Header
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========================================
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| ``sprout/algorithm/upper_bound.hpp``
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| Convenience header: ``sprout/algorithm.hpp``
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