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Algorithm Analysis

Consider searching algorithms on the following array of data:

[22 21 9 4 16 2 10 14 20 31 26 19 17 28 8 13]

Suppose you want to implement a searching algorithm to see if the data set contains the number 19. Demonstrate how the search would go if you used:

?A sequential search

?A binary search

State the runtime for each of the searches, in this example, and for general data sets of size n. Address the issue of the order of the data in binary searching.

Suppose an algorithm that processes a data set of size 8 has a runtime of 72. The same algorithm has a runtime of 110 when applied to a data set of size 10; and when applied to a data set of size 20, it has a runtime of 420. Using big-O notation, state the runtime for this algorithm for the general case of a data set of size n.

Suppose you develop an algorithm that processes the first element of an array (length of n), then processes the first 2 elements, then the first 3 elements, and so on, until the last iteration of a loop, when it processes all elements. Thus, if n = 4, the runtime would be 1 + 2 + 3 + 4 = 10.

Create a table that depicts the runtime for arrays of length 1 to 10. Would you expect the general runtime to be O(n), O(n2), O(n3), or some other function of n? Explain.

Explanation / Answer

Binary Search

Binary Search is an incredibly powerful technique for searching an ordered list. It is familiar to everyone who uses a telephone book!

The basic algorithm is to find the middle element of the list, compare it against the key, decide which half of the list must contain the key, and repeat with that half.

Two requirements to support binary search:

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