本文为senlie原创，转载请保留此地址：http://blog.csdn.net/zhengsenlie

upper_bound(应用于有序区间)

-------------------------------------------------------------------------------------------------------------------------------------------------
描述：受STL区间前闭后开习惯的影响，upper_bound成功找到某个值时，
返回一个迭代器指向每一个"不大于 value "的元素的下一个位置，而不是指向 value 的迭代器，
或找不到，返回value 应该存在的位置
思路：
1.循环直到区间长度为 0 
2.如果 value < *middle，在前半段继续查找
3.如果 value >= *middle，在后半段继续查找 (等于的时候也会继续在后半段查找，所以能保证找到的是 upper bound)

源码：

template <class ForwardIterator, class T>
inline ForwardIterator upper_bound(ForwardIterator first, ForwardIterator last,
                                   const T& value) {
  return __upper_bound(first, last, value, distance_type(first),
                       iterator_category(first));
}


// forward_iterator_tag 版本
template <class ForwardIterator, class T, class Distance>
ForwardIterator __upper_bound(ForwardIterator first, ForwardIterator last,
                              const T& value, Distance*,
                              forward_iterator_tag) {
  Distance len = 0;
  distance(first, last, len);
  Distance half;
  ForwardIterator middle;


  while (len > 0) {
    half = len >> 1;
    middle = first;
    advance(middle, half);
    if (value < *middle)
      len = half;
    else { 
      first = middle;
      ++first;
      len = len - half - 1;
    }
  }
  return first;
}


// random_access_iterator_tag 版本
template <class RandomAccessIterator, class T, class Distance>
RandomAccessIterator __upper_bound(RandomAccessIterator first,
                                   RandomAccessIterator last, const T& value,
                                   Distance*, random_access_iterator_tag) {
  Distance len = last - first;
  Distance half;
  RandomAccessIterator middle;


  while (len > 0) {
    half = len >> 1;
    middle = first + half;
    if (value < *middle)
      len = half;
    else { //因为大于等都是在后半段区间查找，所以最后找到的一定是 upper bound，而且存在 value 的话， first 最后指示的就是 value 的下一个位置
      first = middle + 1;
      len = len - half - 1;
    }
  }
  return first;
}

int main()
{
  int A[] = { 1, 2, 3, 3, 3, 5, 8 };
  const int N = sizeof(A) / sizeof(int);


  for (int i = 1; i <= 10; ++i) {
    int* p = upper_bound(A, A + N, i);
    cout << "Searching for " << i << ".  ";
    cout << "Result: index = " << p - A << ", ";
    if (p != A + N)
      cout << "A[" << p - A << "] == " << *p << endl;
    else
      cout << "which is off-the-end." << endl;
  }
}
/*
The output is:
Searching for 1.  Result: index = 1, A[1] == 2
Searching for 2.  Result: index = 2, A[2] == 3
Searching for 3.  Result: index = 5, A[5] == 5
Searching for 4.  Result: index = 5, A[5] == 5
Searching for 5.  Result: index = 6, A[6] == 8
Searching for 6.  Result: index = 6, A[6] == 8
Searching for 7.  Result: index = 6, A[6] == 8
Searching for 8.  Result: index = 7, which is off-the-end.
Searching for 9.  Result: index = 7, which is off-the-end.
Searching for 10.  Result: index = 7, which is off-the-end.
*/