Question

Suppose that, even unrealistically, we are to search a list of 700 million items using Binary Search, Recursive (Algorithm 2.1). What is the maximum number of comparisons that this algorithm must perform before finding a given item or concluding that it is not in the list

“Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a problem into n subinstances of size n/3, and the dividing and combining steps take linear time. Write a recurrence equation for the running time T(n), and solve this recurrence equation for T(n). Show your solution in order notation.”

34. What is the time complexity T(n) of the nested loops below? For simplicity, you may assume that n is a power of 2, That is, n = 2k for some positive integer k. z = n; while (i>= 1){ while i > j = i; while (j <= n){ while loop > //Needs Θ(1). < body of th j=2*j; e e while 100 i = Li/2] ;

Answer 1

Search Using Binary Search Is The Fastest One When Comparing To The Others. In This Case We Have the Order of 700 Million Items Initially We Need Check the Middle Position of the List. Because If We Find That Searching Element in the First Half then We Can Neglect the Second Half. If We Continue This Repeatedly that is Recursively We Can Easily Find The Solution. Example: You have 700 million items and each item has the list of account numbers in the order. Now we need to look at the number 2100 is the 350th item. If the acc number will be 1008 we don't need to check the 349th item split it into half 351 to 700 that would be 175. Each time we need to split the records in this sequence 700 - 350 - 175 - 83 - 42 - 21 - 10 - 5 - 3 - 1