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242-535 ADA: 3. Insertion Sort1 Objective o asymptotic analysis of insertion sort Algorithm Design and Analysis (ADA) 242-535, Semester 1 2014-2015 3. Insertion Sort

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242-535 ADA: 3. Insertion Sort2 1. What is Sorting? 2. Insertion SortOverview

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242-535 ADA: 3. Insertion Sort3 Input: sequence of numbers. Output: permutation such that a'1 a'2 a'n Example: Input: 8 2 4 9 3 6 Output: 2 3 4 6 8 9 1. What is Sorting?

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242-535 ADA: 3. Insertion Sort4 o Sort a list of names. o Organize an MP3 library. o Display Google PageRank results. o List RSS feed in reverse chronological order. o Find the median. o Find the closest pair. o Binary search in a database. o Identify statistical outliers. o Find duplicates in a mailing list. o Data compression. o Computer graphics. o Computational biology. o Supply chain management. o Load balancing on a parallel computer. o... Sorting is Essential obvious applications problems become easy once items are in sorted order non-obvious applications

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242-535 ADA: 3. Insertion Sort5 Applications have different sorting needs: o Stable? o Parallel? o Deterministic? o Keys all distinct? o Multiple key types? o Linked list or arrays? o Large or small items? o Is your array randomly ordered? o Need guaranteed performance? Different Sorting Needs

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242-535 ADA: 3. Insertion Sort6 Internal sorts o Insertion sort, selection sort, bubblesort, shaker sort o Quicksort, mergesort, heapsort, samplesort, shellsort o Solitaire sort, red-black sort, splaysort,,... External sorts o Poly-phase mergesort, cascade-merge, oscillating sort String/radix sorts o Distribution, MSD, LSD, 3-way string quicksort Parallel sorts o Bitonic sort, Batcher even-odd sort o Smooth sort, cube sort, column sort o GPUsort Many Different Sorting Algorithms

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2. Insertion Sort I NSERTION -S ORT (A, n) A[1.. n] for j 2 to n dokey A[ j] i j 1 while i > 0 and A[i] > key doA[i+1] A[i] i i 1 A[i+1] = key pseudocode sorted ij key A:A: 1n

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Example of Insertion Sort 824936

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242-535 ADA: 3. Insertion Sort19 void insertionSort(int[] A) // A[0.. n-1] { (1) for (int j = 1; j < num.length; j++) { // start with 1 (not 2) (2) int key = num[j]; (3) int i = j - 1; (4) while((i >= 0) && (A[i] < key)) { (5) A[i+1] = A[i]; (6) i--; (7) } (8) A[i+1] = key; (9) } } Insertion Sort Java Code

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242-535 ADA: 3. Insertion Sort20 Insertion Sort Structure Tree for 1-9 3 3 block 1-9 while 4-7 2 2 5 5 8 8 block 4-7 6 6

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242-535 ADA: 3. Insertion Sort21 Lines 2, 3, 5, 6, 8: each is O(1) Block of 4-7 = O(1) + O(1) = O(1) For of 4-7 is: = O( (n-1) * 1) = O(n-1) = O(n), simplified Block of 1-9 = O(1) + O(1) + O(n) + O(1) = O(n) For of 1-8 is: = O( (n-1) * n) = O(n 2 - n) = O(n 2 ), simplified this is the hard part assume the worse case where the loop has to move the most elements) this is the hard part assume the worse case where the loop has to move the most elements)

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242-535 ADA: 3. Insertion Sort22 What can T() be? o Best case -- inner loop body never executed T(n) is a linear function o Worst case -- inner loop body executed for all previous elements T(n 2 ) is a quadratic function o Average case tricky Analyzing Insertion Sort