std::upper_bound(3)

🌸 std::upper_bound(3) — C++ Standard Libary, bestie edition 🌸

💖 NAME 💖

std::upper_bound - std::upper_bound

✨ Synopsis ✨

Defined in header <algorithm>

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)

template< class ForwardIt, class T, class Compare >
ForwardIt upper_bound( ForwardIt first, ForwardIt last, const T& value, Compare comp );

(1) (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 );

(2) (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.

(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.
• 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 N — written in the original as \(\scriptsize N\)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) or 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

• __cpp_lib_algorithm_default_value_type
• Value: 202403
• Std: (C++26)
• Feature: 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.

• LWG 270, applied to C++98 — behavior as published: Compare was required to satisfy only a and Compare and T was required to be LessThanComparable (strict weak ordering required); correct behavior: partitioning is required; heterogeneous comparisons permitted.
• LWG 384, applied to C++98 — behavior as published: at most \(\scriptsize \log(N)+1\)log₂(N)+1 comparisons were allowed; correct behavior: corrected to \(\scriptsize \log_{2}(N)+O(1)\)log₂(N)+O(1).
• LWG 577, applied to C++98 — behavior as published: last could not be returned; correct behavior: allowed.
• LWG 2150, applied to C++98 — behavior as published: 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); correct behavior: 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>).

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mwah 💋 this glow-up is based on http://cppreference.com, dated 2024.06.10, for the manual page std::upper_bound(3).