【C++】upper_bound和lower_bound

资料来源于：https://en.cppreference.com/w/cpp/algorithm/upper_bound

upper_bound()和lower_bound()利用二分查找的方法在有序数组里面进行查找。

upper_bound()

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

返回一个迭代器，该迭代器指向范围[first，last]中大于value的第一个元素，如果找不到此元素，则返回last。

给定comp函数或lambda表达式，前面的元素满足!comp(value, element)为true，返回第一个!comp(value, element)为false，即comp(value, element)为true的元素迭代器。

comp默认为<，即前面的元素满足!(value<element)，直到遇到第一个value<element的元素，返回指向element的迭代器。

源码：

template<class ForwardIt, class T, 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;
}

使用举例：

#include <algorithm>
#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';
    }
}

 

lower_bound() 

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

  返回一个迭代器，该迭代器指向范围[first，last]中不小于（大于等于）value的第一个元素，如果找不到此元素，则返回last。

给定comp函数或lambda表达式，前面的元素满足comp(element, value)为true，返回第一个comp(element, value)为false的元素迭代器。

comp默认为<，即前面的元素都满足element<value，直到element≥value，返回指向element的迭代器。

源码：

template<class ForwardIt, class T, class Compare>
ForwardIt lower_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(*it, value)) {
            first = ++it;
            count -= step + 1;
        }
        else
            count = step;
    }
    return first;
}

使用举例：

#include <algorithm>
#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 < 8; ++i) {
        // Search for first element x such that i ≤ x
        auto lower = std::lower_bound(data.begin(), data.end(), i);
 
        std::cout << i << " ≤ ";
        lower != data.end()
            ? std::cout << *lower << " at index " << std::distance(data.begin(), lower)
            : 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::lower_bound(prices.begin(), prices.end(), to_find,
          [](const PriceInfo& info, double value){
              return info.price < value;
          });
 
      prc_info != prices.end()
          ? std::cout << prc_info->price << " at index " << prc_info - prices.begin()
          : std::cout << to_find << " not found";
      std::cout << '\n';
    }
}