【C++】C++11 STL算法(五)：设置操作(Set operations)、堆操作(Heap operations)

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发布时间：2019-05-26

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设置操作(Set operations)

一、includes

1、原型：

template< class InputIt1, class InputIt2 >bool includes( InputIt1 first1, InputIt1 last1,           InputIt2 first2, InputIt2 last2 );		   template< class InputIt1, class InputIt2, class Compare >bool includes( InputIt1 first1, InputIt1 last1,           InputIt2 first2, InputIt2 last2, Compare comp );

2、说明：

如果一个集合是另一个集合的子集，则返回true

3、官方demo

#include 
   
    #include 
    
     #include 
     
      #include 
      
        int main(){
     std::vector
       
         v1 {
   'a', 'b', 'c', 'f', 'h', 'x'};  std::vector
        
          v2 { 'a', 'b', 'c'}; std::vector
         
           v3 { 'a', 'c'}; std::vector
          
            v4 { 'g'}; std::vector
           
             v5 { 'a', 'c', 'g'}; for (auto i : v1) std::cout << i << ' '; std::cout << "\nincludes:\n" << std::boolalpha; for (auto i : v2) std::cout << i << ' '; std::cout << ": " << std::includes(v1.begin(), v1.end(), v2.begin(), v2.end()) << '\n'; for (auto i : v3) std::cout << i << ' '; std::cout << ": " << std::includes(v1.begin(), v1.end(), v3.begin(), v3.end()) << '\n'; for (auto i : v4) std::cout << i << ' '; std::cout << ": " << std::includes(v1.begin(), v1.end(), v4.begin(), v4.end()) << '\n'; for (auto i : v5) std::cout << i << ' '; std::cout << ": " << std::includes(v1.begin(), v1.end(), v5.begin(), v5.end()) << '\n'; auto cmp_nocase = [](char a, char b) { return std::tolower(a) < std::tolower(b); }; std::vector
            
              v6 { 'A', 'B', 'C'}; for (auto i : v6) std::cout << i << ' '; std::cout << ": (case-insensitive) " << std::includes(v1.begin(), v1.end(), v6.begin(), v6.end(), cmp_nocase) << '\n';}

Output:

a b c f h xincludes:a b c : truea c : trueg : falsea c g : falseA B C : (case-insensitive) true

二、set_difference

1、原型：

template< class InputIt1, class InputIt2, class OutputIt >OutputIt set_difference( InputIt1 first1, InputIt1 last1,                     InputIt2 first2, InputIt2 last2,                     OutputIt d_first );					 template< class InputIt1, class InputIt2, class OutputIt, class Compare >OutputIt set_difference( InputIt1 first1, InputIt1 last1,                     InputIt2 first2, InputIt2 last2,                     OutputIt d_first, Compare comp );

2、说明：

计算两个集合的差：将[first1,last1)中剔除[first1，last2)的元素，输出到d_first中

3、官方demo

#include 
   
    #include 
    
     #include 
     
      #include 
      
        int main() {
       std::vector
       
         v1 {
   1, 2, 5, 5, 5, 9};    std::vector
        
          v2 { 2, 5, 7}; std::vector
         
           diff; std::set_difference(v1.begin(), v1.end(), v2.begin(), v2.end(), std::inserter(diff, diff.begin())); for (auto i : v1) std::cout << i << ' '; std::cout << "minus "; for (auto i : v2) std::cout << i << ' '; std::cout << "is: "; for (auto i : diff) std::cout << i << ' '; std::cout << '\n';}

Output:

1 2 5 5 5 9 minus 2 5 7 is: 1 5 5 9

三、set_intersection

1、原型：

template< class InputIt1, class InputIt2, class OutputIt >OutputIt set_intersection( InputIt1 first1, InputIt1 last1,                       InputIt2 first2, InputIt2 last2,                       OutputIt d_first );					   template< class InputIt1, class InputIt2, class OutputIt, class Compare >OutputIt set_intersection( InputIt1 first1, InputIt1 last1,                       InputIt2 first2, InputIt2 last2,                       OutputIt d_first, Compare comp );

2、说明：

计算两个集合从交集

3、官方demo

#include 
   
    #include 
    
     #include 
     
      #include 
      
       int main(){
       std::vector
       
         v1{
   1,2,3,4,5,6,7,8};    std::vector
        
          v2{ 5,7,9,10}; std::sort(v1.begin(), v1.end()); std::sort(v2.begin(), v2.end()); std::vector
         
           v_intersection; std::set_intersection(v1.begin(), v1.end(), v2.begin(), v2.end(), std::back_inserter(v_intersection)); for(int n : v_intersection) std::cout << n << ' ';}

Output:

5 7

四、set_symmetric_difference

1、原型：

template< class InputIt1, class InputIt2, class OutputIt >OutputIt set_symmetric_difference( InputIt1 first1, InputIt1 last1,                               InputIt2 first2, InputIt2 last2,                               OutputIt d_first );							   template< class InputIt1, class InputIt2, class OutputIt, class Compare >OutputIt set_symmetric_difference( InputIt1 first1, InputIt1 last1,                               InputIt2 first2, InputIt2 last2,                               OutputIt d_first, Compare comp );

2、说明：

计算两个集合之间的对称差：两个集合的并集减去它们的交集

3、官方demo

#include 
   
    #include 
    
     #include 
     
      #include 
      
       int main(){
       std::vector
       
         v1{
   1,2,3,4,5,6,7,8     };    std::vector
        
          v2{ 5, 7, 9,10}; std::sort(v1.begin(), v1.end()); std::sort(v2.begin(), v2.end()); std::vector
         
           v_symDifference; std::set_symmetric_difference( v1.begin(), v1.end(), v2.begin(), v2.end(), std::back_inserter(v_symDifference)); for(int n : v_symDifference) std::cout << n << ' ';}

Output:

1 2 3 4 6 8 9 10

五、set_union

1、原型：

template< class InputIt1, class InputIt2, class OutputIt >OutputIt set_union( InputIt1 first1, InputIt1 last1,                InputIt2 first2, InputIt2 last2,                OutputIt d_first );				template< class InputIt1, class InputIt2, class OutputIt, class Compare >OutputIt set_union( InputIt1 first1, InputIt1 last1,                InputIt2 first2, InputIt2 last2,                OutputIt d_first, Compare comp );

2、说明：

计算两个集合的并集

3、官方demo

#include 
   
    #include 
    
     #include 
     
      #include 
      
        int main(){
       {
           std::vector
       
         v1 = {
   1, 2, 3, 4, 5};         std::vector
        
          v2 = { 3, 4, 5, 6, 7}; std::vector
         
           dest1; std::set_union(v1.begin(), v1.end(), v2.begin(), v2.end(), std::back_inserter(dest1)); for (const auto &i : dest1) { std::cout << i << ' '; } std::cout << '\n'; } { std::vector
          
            v1 = { 1, 2, 3, 4, 5, 5, 5}; std::vector
           
             v2 = { 3, 4, 5, 6, 7}; std::vector
            
              dest1; std::set_union(v1.begin(), v1.end(), v2.begin(), v2.end(), std::back_inserter(dest1)); for (const auto &i : dest1) { std::cout << i << ' '; } std::cout << '\n'; }}

Output:

1 2 3 4 5 6 7 1 2 3 4 5 5 5 6 7

堆操作（Heap operations）

一、is_heap

1、原型：

template< class RandomIt >bool is_heap( RandomIt first, RandomIt last );template< class RandomIt, class Compare >bool is_heap( RandomIt first, RandomIt last, Compare comp );

2、说明：

判断是否为最大堆：父结点的键值总是大于或等于任何一个子结点的键值时为最大堆

3、官方demo

#include 
   
    #include 
    
     #include 
     
       int main(){
       std::vector
      
        v {
    3, 1, 4, 1, 5, 9 };     std::cout << "initially, v: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n';     if (!std::is_heap(v.begin(), v.end())) {
           std::cout << "making heap...\n";        std::make_heap(v.begin(), v.end());    }     std::cout << "after make_heap, v: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n';}

Output:

initially, v: 3 1 4 1 5 9 making heap...after make_heap, v: 9 5 4 1 1 3

二、is_heap_until

1、原型：

template< class RandomIt >RandomIt is_heap_until( RandomIt first, RandomIt last );template< class RandomIt, class Compare >RandomIt is_heap_until( RandomIt first, RandomIt last, Compare comp );

2、说明：

找到从first开始最大范围的最大堆

3、官方demo

#include 
   
    #include 
    
     #include 
     
       int main(){
       std::vector
      
        v {
    3, 1, 4, 1, 5, 9 };     std::make_heap(v.begin(), v.end());     // 可能把堆搞乱了    v.push_back(2);    v.push_back(6);     auto heap_end = std::is_heap_until(v.begin(), v.end());     std::cout << "all of v: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n';     std::cout << "only heap: ";    for (auto i = v.begin(); i != heap_end; ++i) std::cout << *i << ' ';    std::cout << '\n';}

Output:

all of v:  9 5 4 1 1 3 2 6 only heap: 9 5 4 1 1 3 2

三、make_heap

1、原型：

template< class RandomIt >void make_heap( RandomIt first, RandomIt last );

2、说明：

生成堆

3、官方demo

#include 
   
    #include 
    
     #include 
     
      #include 
      
        int main(){    std::cout << "Max heap:\n";     std::vector
       
         v { 3, 2, 4, 1, 5, 9 };	// 最初序列     std::cout << "initially, v: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n';     std::make_heap(v.begin(), v.end());	// 产生最大堆     std::cout << "after make_heap, v: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n';     std::pop_heap(v.begin(), v.end());	// 将最大元素移至尾部（待删除）     std::cout << "after pop_heap, v: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n';     auto top = v.back();    v.pop_back();	// 删除尾部元素    std::cout << "former top element: " << top << '\n';     std::cout << "after removing the former top element, v: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n' << '\n';     std::cout << "Min heap:\n";     std::vector
        
          v1 { 3, 2, 4, 1, 5, 9 }; std::cout << "initially, v1: "; for (auto i : v1) std::cout << i << ' '; std::cout << '\n'; std::make_heap(v1.begin(), v1.end(), std::greater<>{}); // 产生最小堆 std::cout << "after make_heap, v1: "; for (auto i : v1) std::cout << i << ' '; std::cout << '\n'; std::pop_heap(v1.begin(), v1.end(), std::greater<>{}); // 将最小元素移至尾部（待删除） std::cout << "after pop_heap, v1: "; for (auto i : v1) std::cout << i << ' '; std::cout << '\n'; auto top1 = v1.back(); v1.pop_back(); // 删除尾部数据 std::cout << "former top element: " << top1 << '\n'; std::cout << "after removing the former top element, v1: "; for (auto i : v1) std::cout << i << ' '; std::cout << '\n';}

Output:

Max heap:initially, v: 3 2 4 1 5 9 after make_heap, v: 9 5 4 1 2 3 after pop_heap, v: 5 3 4 1 2 9 former top element: 9after removing the former top element, v: 5 3 4 1 2 Min heap:initially, v1: 3 2 4 1 5 9 after make_heap, v1: 1 2 4 3 5 9 after pop_heap, v1: 2 3 4 9 5 1 former top element: 1after removing the former top element, v1: 2 3 4 9 5

四、push_heap

1、原型：

template< class RandomIt >void push_heap( RandomIt first, RandomIt last );template< class RandomIt, class Compare >void push_heap( RandomIt first, RandomIt last, Compare comp );

2、说明：

将位于last-1的元素插入到[first, last-1)中，并保持最大堆。在此之前需要执行push_back将新元素添加到尾部。

3、官方demo

#include 
   
    #include 
    
     #include 
     
       int main(){
       std::vector
      
        v {
    3, 1, 4, 1, 5, 9 };     std::make_heap(v.begin(), v.end());     std::cout << "v: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n';     v.push_back(6);     std::cout << "before push_heap: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n';     std::push_heap(v.begin(), v.end());     std::cout << "after push_heap: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n';}

Output:

v: 9 5 4 1 1 3 before push_heap: 9 5 4 1 1 3 6 after push_heap:  9 5 6 1 1 3 4

五、pop_heap

1、原型：

template< class RandomIt >void pop_heap( RandomIt first, RandomIt last );template< class RandomIt, class Compare >void pop_heap( RandomIt first, RandomIt last, Compare comp );

2、说明：

交换位于first和last-1的值，然后使子范围[first, last-1)成为堆。

等于把最大堆中第一个元素即最大的值“删除”，这里的删除是加引号，因为没有真正删除。紧接着使用pop_back才能真正删除最大的元素。

3、官方demo

#include 
   
    #include 
    
     #include 
     
       int main(){
       std::vector
      
        v {
    3, 1, 4, 1, 5, 9 };     std::make_heap(v.begin(), v.end());     std::cout << "v: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n';     std::pop_heap(v.begin(), v.end()); // 把最大的元素移到最后，此时还没有删除     std::cout << "after pop_heap: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n';     int largest = v.back();    v.pop_back();  // 在这里会真正删除最大元素。    std::cout << "largest element: " << largest << '\n';     std::cout << "heap without largest: ";    for (auto i : v) std::cout << i << ' ';    std::cout << '\n';}

Output:

v: 9 5 4 1 1 3 after pop_heap: 5 3 4 1 1 9 largest element: 9heap without largest: 5 3 4 1 1

六、sort_heap

1、原型：

template< class RandomIt >void sort_heap( RandomIt first, RandomIt last );template< class RandomIt, class Compare >void sort_heap( RandomIt first, RandomIt last, Compare comp );

2、说明：

将最大堆转换成升序排列

3、官方demo

#include 
   
    #include 
    
     #include 
     
       int main(){
       std::vector
      
        v = {
   3, 1, 4, 1, 5, 9};      std::make_heap(v.begin(), v.end());     std::cout << "heap:\t";    for (const auto &i : v) {
           std::cout << i << ' ';    }        std::sort_heap(v.begin(), v.end());     std::cout << "\nsorted:\t";    for (const auto &i : v) {
                                                              std::cout << i << ' ';    }       std::cout << '\n';}