STL之Binary search

STL之Binary search

    STL中对于有序序列（vector,list等）提供了相当相当强大的二分搜索Binary search算法。对于可以随机访问容器（如vector等），binary search负载度为对数级别（LogN)，对于非随机访问容器（如list），则算法复杂度为线性。现在简要介绍一下几种常用的binary search算法：

ForwardIterator lower_bound (ForwardIterator first,ForwardIterator last, const T& value)
ForwardIterator lower_bound (ForwardIterator first,ForwardIterator last, const T& value, Compare comp)
//查找最远的一个iterator i， 使得[first,i)里面的任意一个iterator j，有 *j < value or comp(*j,value)==true.

ForwardIterator upper_bound (ForwardIterator first,ForwardIterator last, const T& value)
ForwardIterator upper_bound (ForwardIterator first,ForwardIterator last, const T& value, Compare comp)
//查找最远的一个iterator i， 使得[first,i)里面的任意一个iterator j，有 !(*j < value) or comp(*j,value)==false.

pair equal_range(ForwardIterator first, ForwardIterator last, const T& value)
pair equal_range(ForwardIterator first, ForwardIterator last, const T& value, Compare comp)
//查找最大的subrange[i,j)，使得任意一个iterator in [i,j)满足!(*k<value) && !(value<*k) or comp(*k,value)==false && comp(value,*k)==false.

bool binary_search (ForwardIterator first, ForwardIterator last, const T& value)
bool binary_search (ForwardIterator first, ForwardIterator last, const T& value, Compare comp)
// 查找是否在[first,last)中存在iterator i,满足 !(*i<value) && !(value<*i) or comp(*i,value)==false && comp(value,*i)==false
// 存在则返回true,否则返回false. 

#include < algorithm >
#include < iostream >
#include < vector >
#include < iterator >
using   namespace  std;
int  main()
{
    vector < int > v;
    vector < int > ::iterator itr;
    pair <  vector < int > ::iterator, vector < int > ::iterator  > vecpair;
    
     for ( int  i  =   1 ; i  <=   20 ; i ++ ){
        v.push_back(i % 6 );
    }
    sort(v.begin(),v.end());
    cout  <<   " array:  "   <<  endl  <<   "      " ;
    copy(v.begin(),v.end(),ostream_iterator < int > (cout, "   " ));
    cout  <<  endl;
    
     // lower_bound
    cout  <<   " lower_bound function, value = 3: "   <<  endl; 
    itr  =  lower_bound(v.begin(),v.end(), 3 );
    cout  <<   "     [first, itr) =  " ;
    copy(v.begin(),itr,ostream_iterator < int > (cout, "   " ));
    cout  <<  endl;
    cout  <<   "     [itr, last) =  " ;
    copy(itr,v.end(),ostream_iterator < int > (cout, "   " ));
    cout  <<  endl  <<  endl;
    
     //  upper_bound
    cout  <<   " upper_bound function, value = 3: "   <<  endl; 
    itr  =  upper_bound(v.begin(),v.end(), 3 );
    cout  <<   "     [first, itr) =  " ;
    copy(v.begin(),itr,ostream_iterator < int > (cout, "   " ));
    cout  <<  endl;
    cout  <<   "     [itr, last) =  " ;
    copy(itr,v.end(),ostream_iterator < int > (cout, "   " ));
    cout  <<  endl  <<  endl;
    
     //  equal_range
    cout  <<   " equal_range function, value = 3: "   <<  endl; 
    vecpair  =  equal_range(v.begin(),v.end(), 3 );
    
    cout  <<   "     [vecpair->first, vecpair->second) =  " ;
    copy(vecpair.first, vecpair.second, ostream_iterator < int > (cout, "   " ));
    cout  <<  endl  <<  endl;
    
     // binary_search, value = 3
    cout  <<   " binary_search function, value = 3: "   <<  endl;
    cout  <<   " 3 is  "   <<  (binary_search(v.begin(),v.end(), 3 )  ?   "" : " not  " )  <<   " in array. "   <<  endl;
    cout  <<  endl;
    
     // binary_search, value = 6
    cout  <<   " binary_search function, value = 6: "   <<  endl;
    cout  <<   " 6 is  "   <<  (binary_search(v.begin(),v.end(), 6 )  ?   "" : " not  " )  <<   " in array. "   <<  endl;
    cout  <<  endl;
    
     return   0 ;    
}
 

array:
     0   0   0   1   1   1   1   2   2   2   2   3   3   3   4   4   4   5   5   5
lower_bound function, value  =   3 :
    [first, itr)  =   0   0   0   1   1   1   1   2   2   2   2
    [itr, last)  =   3   3   3   4   4   4   5   5   5

upper_bound function, value  =   3 :
    [first, itr)  =   0   0   0   1   1   1   1   2   2   2   2   3   3   3
    [itr, last)  =   4   4   4   5   5   5

equal_range function, value  =   3 :
    [vecpair -> first, vecpair -> second)  =   3   3   3

binary_search function, value  =   3 :
3   is   in  array.

binary_search function, value  =   6 :
6   is  not  in  array.