std::upper_bound

 

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Defined in header <algorithm>
	(1)
template< class ForwardIt, class T > ForwardIt upper_bound( ForwardIt first, ForwardIt last,                        const T& value );			(constexpr since C++20) (until C++26)
template< class ForwardIt, class T = typename std::iterator_traits                                          <ForwardIt>::value_type > constexpr ForwardIt upper_bound( ForwardIt first, ForwardIt last,                                  const T& value );			(since C++26)
		(2)
template< class ForwardIt, class T, class Compare > ForwardIt upper_bound( ForwardIt first, ForwardIt last,                        const T& value, Compare comp );				(constexpr since C++20) (until C++26)
template< class ForwardIt, class T = typename std::iterator_traits                                          <ForwardIt>::value_type,           class Compare > constexpr ForwardIt upper_bound( ForwardIt first, ForwardIt last,                                  const T& value, Compare comp );				(since C++26)

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. If the elements elem of [first, last) are not partitioned with respect to the expression bool(value < elem), the behavior is undefined.	(until C++20)
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
comp	-	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); 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 \(\scriptsize \log_{2}(N)+O(1)\)log2(N)+O(1) comparisons with value using operator<(until C++20)std::less{}(since C++20).

2) At most \(\scriptsize \log_{2}(N)+O(1)\)log2(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
LWG 270	C++98	Compare was required to satisfy Compare and T was required to be LessThanComparable (strict weak ordering required)	only a partitioning is required; heterogeneous comparisons permitted
LWG 384	C++98	at most \(\scriptsize \log(N)+1\)log2(N)+1 comparisons were allowed	corrected to \(\scriptsize \log_{2}(N)+O(1)\)log2(N)+O(1)
LWG 577	C++98	last could not be returned	allowed
LWG 2150	C++98	if any iterator iter exists in [first, last) such that bool(comp(value, *iter)) is true, std::lower_bound could return any iterator in [iter, last)	no iterator after iter can be returned

See also

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