Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 2.3, Problem 5E
Program Plan Intro
To write the pseudo code of either recursive or iterative binary search and also explain that the worst case running time complexity of binary search is
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4. Consider the function IndexEqual(A,i.j) that returns true if there exists an index x (i sx sj)
such that A[x] = x; otherwise, retums false. You may assume A is a sorted integer array in
which every element is unique.
a. Write an efficient recursive algorithm for IndexEqual(A,i.j).
b. What is the situation resulting in the best-case running time of your function, and give
an expression for that running time?
c. What is the situation resulting in the worst-case running time of your function, and give
an expression for that running time in terms of n, where n=j-i+1?
The recursive algorithm below takes as input an array A of distinct integers, indexed between s andf, and an integer k. The algorithm returns the index of the integer k in the array A, or ?1 if the integerk is not contained within A. Complete the missing portion of the algorithm in such a way that you makethree recursive calls to subarrays of approximately one third the size of A.• Write and justify a recurrence for the runtime T(n) of the above algorithm.• Use the recursion tree to show that the algorithm runs in time O(n).FindK(A,s,f,k)if s < fif f = s + 1if k = A[s] return sif k = A[f] return felseq1 = b(2s + f)=3cq2 = b(q1 + 1 + f)=2c... to be continued.else... to be continued.
Question 2: Implement sequential search and binary search algorithms on your computer.
Note down run time for each algorithm on arrays of size (1, 250, 500, 750, 1000, 1250,
1500, 5000). For both algorithms, store the values 0 through n - 1 in order in the array,
and use a variety of random search values in the range 0 to n - 1 on each size n. Graph the
resulting times. When is sequential search faster than binary search for a sorted array?
Solution:
Input
Size(N)
Search Element
Execution Time for
Execution Time for
Sequential Search(n)
Binary
Search(logn)
Chapter 2 Solutions
Introduction to Algorithms
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