C++的二分查找函数

一、背景

lower_bound()和upper_bound()，binary_search()都是利用二分查找的方法在一个排好序的数组中进行查找的。

lower_bound()：返回大于或等于目标值的第一个位置
upper_bound()：返回大于目标值的第一个位置
binary_search()：若目标值存在则返回true，否则返回false

二、lower_bound( )

lower_bound 的作用是在已经排好序的数组中返回第一个大于等于（不小于）你所给定的值。

源码版本一

template<class ForwardIt, class T>
ForwardIt lower_bound(ForwardIt first, ForwardIt last, const T& value)
{ForwardIt it;typename std::iterator_traits<ForwardIt>::difference_type count, step;count = std::distance(first, last); // 首项与尾项的距离while (count > 0) {it = first; step = count / 2; std::advance(it, step); // 将 it 迭代器右移 n 个位置。if (*it < value) {first = ++it; count -= step + 1; }elsecount = step;}return first;
}

源码版本二

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;}elsecount = step;}return first;
}

三、upper_bound( )

upper_bound( begin,end,num)：从数组的begin位置到end-1位置二分查找第一个大于num的数字，找到返回该数字的地址，不存在则返回end。

源码版本一

template<class ForwardIt, class T>
ForwardIt upper_bound(ForwardIt first, ForwardIt last, const T& value)
{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 (!(value < *it)) {first = ++it;count -= step + 1;} elsecount = step;}return first;
}

源码版本二

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;} elsecount = step;}return first;
}

四、 binary_search()

在数组中以二分法检索的方式查找，若在数组中查找到indx元素则真，若查找不到则返回值是假

源码版本

template <class ForwardIterator, class T>bool binary_search (ForwardIterator first, ForwardIterator last, const T& val)
{first = std::lower_bound(first,last,val);return (first!=last && !(val<*first));
}

五、实例

#include <algorithm>
#include <iostream>
#include <vector>int main()
{const std::vector<int> data = { 1, 2, 4, 5, 5, 6 };for (int i = 0; i < 8; ++i) {// 返回数组中第一个大于或等于i的值 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::cout << '\n';// 返回数组中第一个大于5的值 auto upper = std::upper_bound(data.begin(), data.end(), 5);upper != data.end()? std::cout << *upper << " at index " << std::distance(data.begin(), upper): std::cout << "not found";std::cout << '\n';int a[100] = { 5,9,11,30,69,70,96,100 };bool ans = binary_search(a, a + 9, 5);//查找成功，返回truecout << "在数组中查找元素5，结果为：" << std::boolalpha << ans << endl;bool res = binary_search(a, a + 9, 99);//查找失败，返回falsecout << "在数组中查找元素99，结果为：" << std::boolalpha << res << endl;system("pause");return 0;
}

打印

参考：

std::lower_bound - cppreference.com

std::upper_bound - cppreference.com

upper_bound和lower_bound的区别_zifengningyu的博客-CSDN博客_upper_bound