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lower_bound(应用于有序区间)
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描写叙述：二分查找，返回一个迭代器指向每个"不小于 value "的元素，
或 value 应该存在的位置
思路：
1.循环直到区间长度为 0
2.假设 *middle < value，在后半段继续查找
3.假设 *middle >= value，在前半段继续查找 (等于的时候也会继续在前半段查找，所以能保证找到的是 lower bound)
源代码：
template <class ForwardIterator, class T>
inline ForwardIterator lower_bound(ForwardIterator first, ForwardIterator last,
const T& value) {
return __lower_bound(first, last, value, distance_type(first),
iterator_category(first));
} // forward_iterator_tag 版本号
template <class ForwardIterator, class T, class Distance>
ForwardIterator __lower_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); // 由于仅仅是 ForwardIterator，不能採用 middle = middle + half 的方式
if (*middle < value) {
first = middle;
++first;
len = len - half - 1;
} // 由于 *middle >= value 时，会在前半段继续查找。所以终于找到的是 lower bound
else
len = half;
}
return first;
} // random_access_iterator_tag 版本号
template <class RandomAccessIterator, class T, class Distance>
RandomAccessIterator __lower_bound(RandomAccessIterator first,
RandomAccessIterator last, const T& value,
Distance*, random_access_iterator_tag) {
Distance len = last - first; // 整个区间长度
Distance half;
RandomAccessIterator middle; while (len > 0) {
half = len >> 1; //除以2
middle = first + half;
if (*middle < value) {
first = middle + 1;
len = len - half - 1; // -half-1 是由于前面那段有first指向的元素和half指向的区间
}
else //为什么这种代码能保证找到的是 lower bound ？--> 由于小于等于都是到前面一段区间查找，所以最后找到的一定是 lower bound
len = half;
}
return first;
}
演示样例：
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 = lower_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 = 0, A[0] == 1
Searching for 2. Result: index = 1, A[1] == 2
Searching for 3. Result: index = 2, A[2] == 3
Searching for 4. Result: index = 5, A[5] == 5
Searching for 5. Result: index = 5, A[5] == 5
Searching for 6. Result: index = 6, A[6] == 8
Searching for 7. Result: index = 6, A[6] == 8
Searching for 8. Result: index = 6, A[6] == 8
Searching for 9. Result: index = 7, which is off-the-end.
Searching for 10. Result: index = 7, which is off-the-end.
*/