STL的二分查找

binary_search

二分查找，复杂度时$O(\log N)$O(logN)，如果存在返回true，否则返回false。

template <class ForwardIterator, class T>
  bool binary_search (ForwardIterator first, ForwardIterator last,
                      const T& val);
                      
template <class ForwardIterator, class T, class Compare>
  bool binary_search (ForwardIterator first, ForwardIterator last,
                      const T& val, Compare comp);

comp是自定义的二元谓词，相当于下面的算法：

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));
}

lower_bound

寻找元素下界，时间复杂度是：$O(\log N)$O(logN)，本质上是二分查找。如果元素存在，返回第一个位置，否则返回区间的end()。

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

算法实现：

template <class ForwardIterator, class T>
  ForwardIterator lower_bound (ForwardIterator first, ForwardIterator last, const T& val)
{
  ForwardIterator it;
  iterator_traits<ForwardIterator>::difference_type count, step;
  count = distance(first,last);
  while (count>0)
  {
    it = first; step=count/2; advance (it,step);
    if (*it<val) {                 // or: if (comp(*it,val)), for version (2)
      first=++it;
      count-=step+1;
    }
    else count=step;
  }
  return first;
}

upper_bound

寻找元素上界,时间复杂度是：$O(\log N)$O(logN)，本质上是二分查找。返回第一个大于目标元素的位置，否则返回end()

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

实现代码：

template <class ForwardIterator, class T>
  ForwardIterator upper_bound (ForwardIterator first, ForwardIterator last, const T& val)
{
  ForwardIterator it;
  iterator_traits<ForwardIterator>::difference_type count, step;
  count = std::distance(first,last);
  while (count>0)
  {
    it = first; step=count/2; std::advance (it,step);
    if (!(val<*it))                 // or: if (!comp(val,*it)), for version (2)
      { first=++it; count-=step+1;  }
    else count=step;
  }
  return first;
}

equal_range

default (1)	

template <class ForwardIterator, class T>
  pair<ForwardIterator,ForwardIterator>
    equal_range (ForwardIterator first, ForwardIterator last, const T& val);

custom (2)	

template <class ForwardIterator, class T, class Compare>
  pair<ForwardIterator,ForwardIterator>
    equal_range (ForwardIterator first, ForwardIterator last, const T& val,
                  Compare comp);

返回等于制定元素的区间，区间是左闭右开的。时间复杂度是$O(\log N)$O(logN)。

template <class ForwardIterator, class T>
  pair<ForwardIterator,ForwardIterator>
    equal_range (ForwardIterator first, ForwardIterator last, const T& val)
{
  ForwardIterator it = std::lower_bound (first,last,val);
  return std::make_pair ( it, std::upper_bound(it,last,val) );
}