Data structures (xii) Sort

First, the quick sort

I have learned to sort

Divide and rule

Pivot Point

pivot：

Quick Sort

Bad news: in the original sequence, the pivot point there is not necessarily ...

Prerequisites: // pivot points must be already in place although not vice versa

derangement： 2 3 4... n 1

In particular: in the ordered sequence, all the elements are all pivot points; or vice versa

Quick sort is all the elements one by one into an axis point of the process

Question: How to exchange? How high the cost?

Configuration pivot point

Select the pivot point as a candidate training object, the first element typically queued m

Configuration used in the process and lo hi, the sequence is divided into three portions L, U, G

L is a prefix of any element not exceed a candidate axis points, G is a suffix, any element not less than a pivot point candidate

U is the sequence between the two, an element composed of an unknown size

The initial state of the entire sequence is U, L and G are empty

After startup, alternating attempts to hi to lo measured and moved, so that they are close to each other

lo with every step, a L unit to expand, Hi and G is, in this process, U is added to the elements of L or G,

Finally, Hi and lo refer to the same location, the pivot points previously selected candidates placed there, a real pivot point

Monotonicity + invariance

Initial situation, L and G are empty, pivot less than or equal to L G, satisfy NATURAL

U header elements have been removed as an axis point candidate backed up, it may be considered idle

generally:

Lo assumed idle, the left expanding subsequence G, as long as the end of the element _elem [hi] axis is not less than the candidate points, it is decremented by one unit for hi

Thus the original elements included in the G, the new elements of the last still meet these conditions, continue to fall under G until the end of the element at some point no longer meets the conditions

Hi lo element unit is transferred to the end of the idle, hi becomes idle

Further investigation _elem [lo], to expand the L, the first element until the pivot point candidate lo does not exceed in value

Hi lo will be transferred to the

Examples

The first shaft element 6 is taken as the candidate point to be cultured, then remove the backup, the unit is regarded as idle logically

At this time, i.e. first examine the end of the element 7, the shaft is greater than the candidate points 6, classified into G

The new end element 6 is less than 1, to be classified in the L sequence, is transferred to this purpose lo 1 at idle, i.e., the position of the first element

Extended to the right, 3 less than 6, and then expand, 8 is greater than 6,

Transferred to the position hi, lo idle

5 on the left side is less than 6, proceeds to lo, hi idle

6 is smaller than the right side, the right side is less than 5 6

6 is larger than 9 right, go hi, lo idle

4 is less than 6 left, go lo

右侧的U只剩下一个元素，此处应放6，是轴点