Question

Given a non-decreasingly sorted array A[p..q] and a number x, consider the following algorithm Search. SEARCH(A, p, q, x) 1 if A[q] ? x 2 return -1 3 if p == q 4 return p 5 else 6 mid = \lfloor(p + q)/2\rfloor 7 if A[mid] ? x 8 return SEARCH(A, mid + 1, q, x) 9 else 10 return SEARCH(A, p, mid, x) (1) (4pts) Run Search(A, 1, 6, 7) on array A[1..6] = <2, 3, 5, 6, 8, 9>. Find the final return value by listing all the recursive calls made to Search, along with the input p and q values of each call. Note that index starts from 1. (2) (2pts) Analyze the best-case running time of algorithm Search, in terms of n, size of the input array A[p..q] and give a tight bound (using \Theta) on it. (3) (4pts) Write a recurrence relation describing the worst-case running time of algorithm Search, in terms of n, and solve the recurrence to give a tight bound (using \Theta) on it.

          Given a non-decreasingly sorted array A[p..q] and a number x, consider the following
algorithm Search.
SEARCH(A, p, q, x)
1 if A[q] ? x
2	return -1
3 if p == q
4	return p
5 else
6	mid = \lfloor(p + q)/2\rfloor
7	if A[mid] ? x
8		return SEARCH(A, mid + 1, q, x)
9	else
10		return SEARCH(A, p, mid, x)
(1) (4pts) Run Search(A, 1, 6, 7) on array A[1..6] = <2, 3, 5, 6, 8, 9>. Find the final
return value by listing all the recursive calls made to Search, along with the input p
and q values of each call. Note that index starts from 1.
(2) (2pts) Analyze the best-case running time of algorithm Search, in terms of n, size
of the input array A[p..q] and give a tight bound (using \Theta) on it.
(3) (4pts) Write a recurrence relation describing the worst-case running time of
algorithm Search, in terms of n, and solve the recurrence to give a tight bound
(using \Theta) on it.

Given a non-decreasingly sorted array A[p..q] and a number x, consider the following
algorithm Search.
SEARCH(A, p, q, x)
1 if A[q] ? x
2 return -1
3 if p == q
4 return p
5 else
6 mid = ⌊(p + q)/2⌋7 if A[mid] ? x
8 return SEARCH(A, mid + 1, q, x)
9 else
10 return SEARCH(A, p, mid, x)
(1) (4pts) Run Search(A, 1, 6, 7) on array A[1..6] = <2, 3, 5, 6, 8, 9>. Find the final
return value by listing all the recursive calls made to Search, along with the input p
and q values of each call. Note that index starts from 1.
(2) (2pts) Analyze the best-case running time of algorithm Search, in terms of n, size
of the input array A[p..q] and give a tight bound (using Θ) on it.
(3) (4pts) Write a recurrence relation describing the worst-case running time of
algorithm Search, in terms of n, and solve the recurrence to give a tight bound
(using Θ) on it.

Added by Cheryl M.

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