std::upper_bound(3)

NAME
std::upper_bound - std::upper_bound

Synopsis
   Defined in header <algorithm>
   template< class ForwardIt, class T >
                        (constexpr since
   ForwardIt upper_bound( ForwardIt first, C++20)
   ForwardIt last, (until C++26)
                        const T& value );
   template< class ForwardIt, class T =
   typename std::iterator_traits
    <ForwardIt>::value_type > (since C++26)
   constexpr ForwardIt upper_bound( ForwardIt
   first, ForwardIt last,
                        const T&
   value );
   template< class ForwardIt, class T, class
   Compare > (1)
                        (constexpr since
   ForwardIt upper_bound( ForwardIt first, C++20)
   ForwardIt last, (until C++26)
                        const T& value,
   Compare comp );
   template< class ForwardIt, class T =
   typename std::iterator_traits (2)
    <ForwardIt>::value_type,
             class Compare > (since C++26)
   constexpr ForwardIt upper_bound( ForwardIt
   first, ForwardIt last,
                        const T&
   value, Compare comp );
   Searches for the first element in the partitioned range [first, last) which is
   ordered after value.
   1) The order is determined by operator<:
   Returns the first iterator iter in [first, last) where bool(value <
   *iter) is true, or last if no such iter exists.
                        (until C++20)
   If the elements elem of [first, last) are not partitioned with respect
   to the expression bool(value < elem), the behavior is undefined.
   Equivalent to std::upper_bound(first, last, value, std::less{}). (since C++20)
   2) The order is determined by comp:
   Returns the first iterator iter in [first, last) where bool(comp(value, *iter)) is
   true, or last if no such iter exists.
   If the elements elem of [first, last) are not partitioned with respect to the
   expression bool(comp(value, elem)), the behavior is undefined.

Parameters
   first, last - the partitioned range of elements to examine
   value - value to compare the elements to
                 binary predicate which returns true if the first argument is ordered
                 before the second.
                 The signature of the predicate function should be equivalent to the
                 following:
                  bool pred(const Type1 &a, const Type2 &b);
   comp - While the signature does not need to have const &, the function must
                 not modify the objects passed to it and must be able to accept all
                 values of type (possibly const) Type1 and Type2 regardless of value
                 category (thus, Type1 & is not allowed
                 , nor is Type1 unless for Type1 a move is equivalent to a copy
                 (since C++11)).
                 The type Type1 must be such that an object of type T can be implicitly
                 converted to Type1. The type Type2 must be such that an object of type
                 ForwardIt can be dereferenced and then implicitly converted to Type2.

Type requirements
   -
   ForwardIt must meet the requirements of LegacyForwardIterator.
   -
   Compare must meet the requirements of BinaryPredicate. It is not required to satisfy
   Compare.

Return value
   Iterator to the first element of the range [first, last) ordered after value, or
   last if no such element is found.

Complexity
   Given \(\scriptsize N\)N as std::distance(first, last):
   1) At most \(\scriptsize \log_{2}(N)+O(1)\)log
   2(N)+O(1) comparisons with value using
   operator<
   (until C++20)
   std::less{}
   (since C++20).
   2) At most \(\scriptsize \log_{2}(N)+O(1)\)log
   2(N)+O(1) applications of the comparator comp.
   However, if ForwardIt is not a LegacyRandomAccessIterator, the number of iterator
   increments is linear in \(\scriptsize N\)N. Notably, std::map, std::multimap,
   std::set, and std::multiset iterators are not random access, and so their member
   upper_bound functions should be preferred.

Possible implementation
   See also the implementations in libstdc++ and libc++.
                        upper_bound (1)
 template<class ForwardIt, class T = typename std::iterator_traits<ForwardIt>::value_type>
 ForwardIt upper_bound(ForwardIt first, ForwardIt last, const T& value)
 {
     return std::upper_bound(first, last, value, std::less{});
 }
                        upper_bound (2)
 template<class ForwardIt, class T = typename std::iterator_traits<ForwardIt>::value_type,
          class Compare>
 ForwardIt upper_bound(ForwardIt first, ForwardIt last, const T& value, Compare comp)
 {
     ForwardIt it;
     typename std::iterator_traits<ForwardIt>::difference_type count, step;
     count = std::distance(first, last);
     while (count > 0)
     {
         it = first;
         step = count / 2;
         std::advance(it, step);
         if (!comp(value, *it))
         {
             first = ++it;
             count -= step + 1;
         }
         else
             count = step;
     }
     return first;
 }

Notes
   Although std::upper_bound only requires [first, last) to be partitioned, this
   algorithm is usually used in the case where [first, last) is sorted, so that the
   binary search is valid for any value.
   For any iterator iter in [first, last), std::upper_bound requires value < *iter and
   comp(value, *iter) to be well-formed, while std::lower_bound requires *iter < value
   and comp(*iter, value) to be well-formed instead.
             Feature-test macro Value Std Feature
   __cpp_lib_algorithm_default_value_type 202403 (C++26) List-initialization for
                        algorithms (1,2)

Example
// Run this code
 #include <algorithm>
 #include <cassert>
 #include <complex>
 #include <iostream>
 #include <vector>
 struct PriceInfo { double price; };
 int main()
 {
     const std::vector<int> data{1, 2, 4, 5, 5, 6};
     for (int i = 0; i < 7; ++i)
     {
         // Search first element that is greater than i
         auto upper = std::upper_bound(data.begin(), data.end(), i);
         std::cout << i << " < ";
         upper != data.end()
             ? std::cout << *upper << " at index " << std::distance(data.begin(), upper)
             : std::cout << "not found";
         std::cout << '\n';
     }
     std::vector<PriceInfo> prices{{100.0}, {101.5}, {102.5}, {102.5}, {107.3}};
     for (double to_find : {102.5, 110.2})
     {
         auto prc_info = std::upper_bound(prices.begin(), prices.end(), to_find,
             [](double value, const PriceInfo& info)
             {
                 return value < info.price;
             });
         prc_info != prices.end()
             ? std::cout << prc_info->price << " at index " << prc_info - prices.begin()
             : std::cout << to_find << " not found";
         std::cout << '\n';
     }
     using CD = std::complex<double>;
     std::vector<CD> nums{{1, 0}, {2, 2}, {2, 1}, {3, 0}, {3, 1}};
     auto cmpz = [](CD x, CD y) { return x.real() < y.real(); };
     #ifdef __cpp_lib_algorithm_default_value_type
         auto it = std::upper_bound(nums.cbegin(), nums.cend(), {2, 0}, cmpz);
     #else
         auto it = std::upper_bound(nums.cbegin(), nums.cend(), CD{2, 0}, cmpz);
     #endif
     assert((*it == CD{3, 0}));
 }

Output:
 0 < 1 at index 0
 1 < 2 at index 1
 2 < 4 at index 2
 3 < 4 at index 2
 4 < 5 at index 3
 5 < 6 at index 5
 6 < not found
 107.3 at index 4
 110.2 not found
   Defect reports
   The following behavior-changing defect reports were applied retroactively to
   previously published C++ standards.
      DR Applied to Behavior as published Correct behavior
                       Compare was required to satisfy only a partitioning is required;
   LWG 270 C++98 Compare and T was required heterogeneous comparisons
                       to be LessThanComparable permitted
                       (strict weak ordering required)
                       at most \(\scriptsize corrected to \(\scriptsize
   LWG 384 C++98 \log(N)+1\)log \log_{2}(N)+O(1)\)log
                       2(N)+1 comparisons were allowed 2(N)+O(1)
   LWG 577 C++98 last could not be returned allowed
                       if any iterator iter exists in
                       [first, last) such that
   LWG 2150 C++98 bool(comp(value, *iter)) is no iterator after
                       true, std::lower_bound iter can be returned
                       could return any iterator in
                       [iter, last)

See also
   equal_range returns range of elements matching a specific key
                       (function template)
                       returns an iterator to the first element not less than the given
   lower_bound value
                       (function template)
   partition divides a range of elements into two groups
                       (function template)
   partition_point locates the partition point of a partitioned range
   (C++11) (function template)
   ranges::upper_bound returns an iterator to the first element greater than a certain
   (C++20) value
                       (niebloid)
                       returns an iterator to the first element greater than the given
   upper_bound key
                       (public member function of std::set<Key,Compare,Allocator>)
                       returns an iterator to the first element greater than the given
   upper_bound key
                       (public member function of std::multiset<Key,Compare,Allocator>)