Chpater 10: Sorting

Internal Sort:

Bubble　　　　　 O(n2)

Selection　　　　 O(n2)

Insertion　　　　O(n2)

Shell　　　　　　O(nlogn)

Merge　　　　　　O(nlogn)

Heap　　　　　　O(nlogn)

Quick Sort　　　　O(nlogn)

Tree Sort(BST)　　O(nlogn)

Linear Sorting:

Counting Sort  　　O(n)

BUcket Sort　　　　O(n)

Radix Sort　　　　O(n)

External Sorting:

K chunks of data need to be sorted and a K-way merge has to be completed.     Assembly Line

Problems:

pro22: Nearly Sorted.  Given a array of n elements, each which is at most K positions from its target position, devise an algorithm that sort in O(nlogK).

Insert the first K elements into a binary heap of size K. Insert the next element from the array into the heap, and delete the minimum element from the heap.\

pro35: Nuts and Bolts. We are given a box which contains bolts and nuts. Assume that there are n nuts and n bolts and that each nut matches exactly one bolt. By trying to match a bolt and a nuts we can see which one is bigger, but we cannot compare two bolts or two nuts directly.

We can use divide-and-conquer to solve. Pick a random bolt B[i], Using this bolt to rearrange the array of nuts into three groups of elements:

• 　　Nuts smaller than B[i]
• 　　Nuts matches B[i]
• 　　Nuts larger than B[i]