am_lect_23 - The worst case occurs when b is not in the...

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Algorithms Consider an array a 1 , a 2 , …, a n of numbers, and suppose we want to know if a particular number b appears in the list. The following algorithm returns the first position i for which a i = b (if such an i exists), and returns 0 if no such i exists 1: LinearSearch(a 1 , a 2 , . .., a n : array of reals, b:real) 2: for i := 1 to n 3: if a i = b then 4: return i 5: end if 6: end for 7: return 0 // did not find b in the array! Running time analysis: Line 1 runs once, Lines 2-6 run at most n times each, Line 7 runs at most once. Hence, the running time is O (1) + O ( n ) + O (1) which is O ( n )
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Worst case analysis vs. Average case analysis Notice that the analysis on the previous page is a “worst-case” analysis.
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Unformatted text preview: The worst case occurs when b is not in the array, and the loop executes exactly n times, and the final line (Line 7) also gets executed. Alternatively, we could do an average case analysis that assumes something about how likely it is for b to be in the array, and where it is likely to be if it is in the array. We will almost always do a worst-case analysis, but if we knew that b was definitely in the array and was equally likely to be at any location i , we could compute the average number of times the loop executes as: Hence, the average running time is also O ( n )...
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This note was uploaded on 12/24/2010 for the course CS CS 173 taught by Professor Fleck during the Spring '10 term at University of Illinois, Urbana Champaign.

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am_lect_23 - The worst case occurs when b is not in the...

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