STL 源代码剖析 算法 stl_algo.h -- nth_element

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nth_element

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描写叙述：又一次排序，使得[nth,last)内没有不论什么一个元素小于[first,nth)内的元素，

但对于[first,nth)和[nth,last)两个子区间内的元素次序则无不论什么保证。

思路：

1.以 median-of-3-partition 将整个序列切割为更小的左、右子序列

2.假设 nth 迭代器落于左序列，就再对左子序列进行切割，否则就再对右子序列进行切割

3.直到切割后的子序列长大于3，对最后这个待切割的子序列做 Insertion Sort

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复杂度：O(n)

源代码：

template <class RandomAccessIterator>
inline void nth_element(RandomAccessIterator first, RandomAccessIterator nth,
                        RandomAccessIterator last) {
  __nth_element(first, nth, last, value_type(first));
}

template <class RandomAccessIterator, class T>
void __nth_element(RandomAccessIterator first, RandomAccessIterator nth,
                   RandomAccessIterator last, T*) {
  while (last - first > 3) {
    //採用 median-of-3-partition 。參数：(first,last,pivot)
	//返回一个迭代器，指向切割后的右段第一个元素
	RandomAccessIterator cut = __unguarded_partition
      (first, last, T(__median(*first, *(first + (last - first)/2),
                               *(last - 1))));
    if (cut <= nth) //假设  nth 落于右段，再对右段实施切割
      first = cut;
    else  //假设 nth 落于左段。对左段实施切割
      last = cut;
  }
  __insertion_sort(first, last); //对切割后的子序列做 Insertion Sort
}

template <class RandomAccessIterator, class T>
RandomAccessIterator __unguarded_partition(RandomAccessIterator first,
                                           RandomAccessIterator last,
                                           T pivot) {
  while (true) {
    while (*first < pivot) ++first;
    --last;
    while (pivot < *last) --last;
    if (!(first < last)) return first;
    iter_swap(first, last);
    ++first;
  }
}

演示样例：

int A[] = {7, 2, 6, 11, 9, 3, 12, 10, 8, 4, 1, 5};
const int N = sizeof(A) / sizeof(int);

nth_element(A, A + 6, A + N);
copy(A, A + N, ostream_iterator<int>(cout, " "));
// The printed result is "5 2 6 1 4 3 7 8 9 10 11 12".