Discrete Math help

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.