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rotate
--------------------------------------------------------------

描写叙述：将[first, middle) 内的元素和[middle, last) 内的元素互换。

/*------------------------------------------------------------
*分派函数(dispatch function)
*/
template <class ForwardIterator>
inline void rotate(ForwardIterator first, ForwardIterator middle, ForwardIterator last){
	if(first == middle || middle == last) return ;
	__rotate(first, middle, last, distance_type(first), iterator_category(first));
}

以下依据不同的迭代器类型完毕三个旋转操作

rotate 的 forward iterator 版
思路：
1.以短段为根据。相应元素逐一对调
2.调整，对新的前、后段再作交换
3.当两段都结束时，循环结束

复杂度：O(n)

template<class ForwardIterator, class Distance>
void __rotate(ForwardIterator first, ForwardIterator middle, 
			ForwardIterator last, Distance*, forward_iterator_tag){
	for(ForwardIterator i = middle ; ; ){
		iter_swap(first, i); //前段，后段的元素一一交换
		++first; ++i;  // 双双前进 1
		// 下面推断是前段[first, middle)先结束还是后段 [middle, last) 后结束
		if(first == middle){ //前段结束了
			if(i == last) return; //假设后段同一时候也结束，整个就结束了
			middle = i;
		}
		else if(i == last){ //后段先结束
			i = middle; // 调整。准备对新的的前、后段再作交换
		}
	}
}

rotate 的 bidirectional iterator 版
思路：
1.对前段逆转
2.对后段逆转
3.对总体逆转
复杂度：O(n)

template<class BidirectionalIterator, class Distance>
void __rotate(BidirectionalIterator first, BidirectionalIterator middle, 
		BidirectionalIterator last, Distance *,
		bidirectional_iterator_tag){
	reverse(first, middle);
	reverse(middle,last);
	reverse(first, last);
}

rotate 的 random access iterator 版 --> ?? 看不太懂。。。

template<class RandomAccessIterator, class Distance>
void __rotate(RandomAccessIterator first, RandomAccessIterator middle，
		RandomAccessIterator last, Distance *,
		random_access_iterator_tag){
	//取全长和前段长度的最大公因子
	Distance n = __gcd(last - first, middle - first);
	while(n--){
		__rotate_cycle(first, last, first + n, middle - first, value_type(first));
	}
}

template <class EuclideanRingElement>
EuclideanRingElement __gcd(EuclideanRingElement m, EuclideanRingElement n)
{
  while (n != 0) {
    EuclideanRingElement t = m % n;
    m = n;
    n = t;
  }
  return m;
}

template <class RandomAccessIterator, class Distance, class T>
void __rotate_cycle(RandomAccessIterator first, RandomAccessIterator last,
                    RandomAccessIterator initial, Distance shift, T*) {
  T value = http://www.mamicode.com/*initial;>

演示样例：

char alpha[] = "abcdefghijklmnopqrstuvwxyz";
rotate(alpha, alpha + 13, alpha + 26);
printf("%s\n", alpha);
// The output is nopqrstuvwxyzabcdefghijklm