【C++】C++11 STL算法(四):二分查找法(Binary search operations)、合并操作

目录

        • 一、lower_bound
          • 1、原型:
          • 2、说明:
          • 3、官方demo
        • 二、upper_bound
          • 1、原型:
          • 2、说明:
          • 3、官方demo
        • 三、binary_search
          • 1、原型:
          • 2、说明:
          • 3、官方demo
        • 四、equal_range
          • 1、原型:
          • 2、说明:
          • 3、官方demo
        • 五、merge
          • 1、原型:
          • 2、说明:
          • 3、官方demo
        • 六、inplace_merge
          • 1、原型:
          • 2、说明:
          • 2、官方demo

头文件:#include

一、lower_bound

1、原型:
template< class ForwardIt, class T >
ForwardIt lower_bound( ForwardIt first, ForwardIt last, const T& value );

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

返回不小于给定值的第一个元素的位置(迭代器)。

3、官方demo
#include 
#include 
#include 
#include 
 
template<class ForwardIt, class T, class Compare=std::less<>>
ForwardIt binary_find(ForwardIt first, ForwardIt last, const T& value, Compare comp={})
{
    // Note: BOTH type T and the type after ForwardIt is dereferenced  must be implicitly convertible to BOTH Type1 and Type2, used in Compare. 
    // This is stricter than lower_bound requirement (see above)
 
    first = std::lower_bound(first, last, value, comp);
    return first != last && !comp(value, *first) ? first : last;
}
 
int main()
{
    std::vector<int> data = { 1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6 };
    auto lower = std::lower_bound(data.begin(), data.end(), 4);
    auto upper = std::upper_bound(data.begin(), data.end(), 4);
    std::copy(lower, upper, std::ostream_iterator<int>(std::cout, " "));
    std::cout << '\n';
    
    // :经典的二分查找,只有在存在值时才返回值
    data = { 1, 2, 4, 6, 9, 10 }; 
    auto it = binary_find(data.cbegin(), data.cend(), 4); //使用 '5' 将返回 end()
    if(it != data.cend())
      std::cout << *it << " found at index "<< std::distance(data.cbegin(), it);
    return 0;
}

Output:

4 4 4 
4 found at index 2

二、upper_bound

1、原型:
template< class ForwardIt, class T >
ForwardIt upper_bound( ForwardIt first, ForwardIt last, const T& value );

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

返回大于给定值的第一个元素的位置(迭代器),如果没有返回last

3、官方demo
#include 
#include 
#include 
#include 
 
int main()
{
    std::vector<int> data = { 1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6 };
 
    auto lower = std::lower_bound(data.begin(), data.end(), 4);
    auto upper = std::upper_bound(data.begin(), data.end(), 4);
 
    std::copy(lower, upper, std::ostream_iterator<int>(std::cout, " "));
}

Output:

4 4 4

三、binary_search

1、原型:
template< class ForwardIt, class T >
bool binary_search( ForwardIt first, ForwardIt last, const T& value );

template< class ForwardIt, class T, class Compare >
bool binary_search( ForwardIt first, ForwardIt last, const T& value, Compare comp );
2、说明:

确定某个元素是否存于[first, last)范围中。

3、官方demo
#include 
#include 
#include 
 
int main()
{
    std::vector<int> haystack {1, 3, 4, 5, 9};
    std::vector<int> needles {1, 2, 3};
 
    for (auto needle : needles) {
        std::cout << "Searching for " << needle << '\n';
        if (std::binary_search(haystack.begin(), haystack.end(), needle)) {
            std::cout << "Found " << needle << '\n';
        } else {
            std::cout << "no dice!\n";
        }
    }
}

Output:

Searching for 1
Found 1
Searching for 2
no dice!
Searching for 3
Found 3

四、equal_range

1、原型:
template< class ForwardIt, class T >
std::pair
	equal_range( ForwardIt first, ForwardIt last, const T& value );
	
template< class ForwardIt, class T, class Compare >
std::pair
	equal_range( ForwardIt first, ForwardIt last, const T& value, Compare comp );
2、说明:

返回[first, last)范围内等于value的子范围

3、官方demo
#include 
#include 
#include 
 
struct S
{
    int number;
    char name;
    // note: name is ignored by this comparison operator
    bool operator< ( const S& s ) const { return number < s.number; }
};
 
int main()
{
    // note: not ordered, only partitioned w.r.t. S defined below
    std::vector<S> vec = { {1,'A'}, {2,'B'}, {2,'C'}, {2,'D'}, {4,'G'}, {3,'F'} };
    S value = {2, '?'};
    auto p = std::equal_range(vec.begin(), vec.end(), value);
    for ( auto i = p.first; i != p.second; ++i )
        std::cout << i->name << ' ';
 
    // heterogeneous comparison:
    struct Comp   {
        bool operator() ( const S& s, int i ) const { return s.number < i; }
        bool operator() ( int i, const S& s ) const { return i < s.number; }
    };
    auto p2 = std::equal_range(vec.begin(),vec.end(), 2, Comp{});
    for ( auto i = p2.first; i != p2.second; ++i )
        std::cout << i->name << ' ';
}

Output:

B C D B C D

五、merge

1、原型:
template< class InputIt1, class InputIt2, class OutputIt >
OutputIt merge( InputIt1 first1, InputIt1 last1,
            InputIt2 first2, InputIt2 last2,
            OutputIt d_first );
			
template< class InputIt1, class InputIt2, class OutputIt, class Compare>
OutputIt merge( InputIt1 first1, InputIt1 last1,
            InputIt2 first2, InputIt2 last2,
            OutputIt d_first, Compare comp );
2、说明:

合并两个已经排序好的序列

3、官方demo
#include 
#include 
#include 
#include 
#include 
#include 
 
int main()
{
    // 用随机数填充向量
    std::random_device rd;
    std::mt19937 mt(rd());
    std::uniform_int_distribution<> dis(0, 9);
 
    std::vector<int> v1(10), v2(10);
    std::generate(v1.begin(), v1.end(), std::bind(dis, std::ref(mt)));
    std::generate(v2.begin(), v2.end(), std::bind(dis, std::ref(mt)));
 
    // 排序
    std::sort(v1.begin(), v1.end());
    std::sort(v2.begin(), v2.end());
 
    // output v1
    std::cout << "v1 : ";
    std::copy(v1.begin(), v1.end(), std::ostream_iterator<int>(std::cout, " "));
    std::cout << '\n';
 
    // output v2
    std::cout << "v2 : ";
    std::copy(v2.begin(), v2.end(), std::ostream_iterator<int>(std::cout, " "));
    std::cout << '\n';
 
    // 合并
    std::vector<int> dst;
    std::merge(v1.begin(), v1.end(), v2.begin(), v2.end(), std::back_inserter(dst));
 
    // output
    std::cout << "dst: ";
    std::copy(dst.begin(), dst.end(), std::ostream_iterator<int>(std::cout, " "));
    std::cout << '\n';
}

Possible output:

v1 : 0 1 3 4 4 5 5 8 8 9 
v2 : 0 2 2 3 6 6 8 8 8 9 
dst: 0 0 1 2 2 3 3 4 4 5 5 6 6 8 8 8 8 8 9 9

六、inplace_merge

1、原型:
template< class BidirIt >
void inplace_merge( BidirIt first, BidirIt middle, BidirIt last );
2、说明:

将已经排序好的两段序列[first, middle)、[middle,last)合并并且配序成[first, last)

2、官方demo
#include 
#include 
#include 
 
template<class Iter>
void merge_sort(Iter first, Iter last)	//归并排序,参见https://www.runoob.com/w3cnote/merge-sort.html,有动图演示
{
    if (last - first > 1) {
        Iter middle = first + (last - first) / 2;
        merge_sort(first, middle);
        merge_sort(middle, last);
        std::inplace_merge(first, middle, last);
    }
}
 
int main()
{
    std::vector<int> v{8, 2, -2, 0, 11, 11, 1, 7, 3};
    merge_sort(v.begin(), v.end());
    for(auto n : v) {
        std::cout << n << ' ';
    }
    std::cout << '\n';
}

Output:

-2 0 1 2 3 7 8 11 11

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