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Unformatted text preview: 1 Sorting  Introduction z Sorting is simply the ordering of your data in a consistent manner. (e.g., cards, telephone#s, student names) z Each element is usually part of a collection of data called a record . z Each record contains a key , which is the value to be sorted, and the remainder of the record consists of satellite data . z Assumptions made here: – Integers – Use internal memory 2 Sorting  Introduction z There are several easy algorithms to sort in O ( n 2 ), such as insertion sort. z There is an algorithm, Shellsort , that is very simple to code, runs in o ( n 2 ), and is efficient in practice. z There are slightly more complicated O ( n log n ) sorting algorithms. z Any generalpurpose sorting algorithm requires Ω ( n log n ) comparisons. 3 Introduction z Internal vs. External Sorting Methods z Different Sorting Methods – Bubble Sort – Insertion Sort – Selection Sort – Quick Sort – Merge Sort – Shell Sort – Radix Sort 4 Introduction z Types of Sorting – Singlepass – Multiplepass z Operations in Sorting – Permutation – Inversion (Swap) – Comparison 5 Permutation z A permutation of a finite set S is an ordered sequence of all the elements of S , with each element appearing exactly once. z For example, if S = { a , b , c }, there are 6 permutations of S : abc , acb , bac , bca , cab , cba . z There are n ! permutations of a set of n elements. 6 KPermutation z A kpermutation of S is an ordered sequence of k elements of S , with no element appearing more than once in the sequence. z The twelve 2permutations of the set { a , b , c , d } are ab, ac, ad, ba, bc, bd, ca, cb, cd, da, db, dc . 7 Inversion z An inversion in an array of numbers is any ordered pair ( i , j ) having the property that i < j but a [ i ] > a [ j ]. z For example, the input list 34, 8, 64, 51, 32, 21 has nine inversions, namely (34,8), (34,32), (34,21), (64,51), (64,32), (64,21), (51,32), (51,21) and (32,21). z Notice that this is exactly the # of swaps that needed to be performed by insertion sort . 8 Preliminaries z Internal SortEach algorithm will be passed an array containing the elements and an integer containing the # of elements. z ValidityWe will assume that N , the # of elements passed to our sorting routines, has already been checked and is legal. z OrderingWe require the existence of the “<“ and “>” operators, which can be used to place a consistent ordering on the input. 9 Bubble Sort z It is done by scanning the list from one end to the other, and whenever a pair of adjacent keys is found to be out of order, then those entries are swapped....
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 Fall '06
 CJYuan
 Sort

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