1. State the size of the input in big-Oh. For example, if the input to an algorithm is an array of size k, then the input size is O(k).

2. Derive the cost function for the algorithm. Be sure to show your work. You can use O(1) to denote all constants.

3. State the complexity of the algorithm in Big-Oh. The complexity MUST be stated in terms of input-size.

Problem: Root of the Problem

input: integer n

output: closest integer that is the square root of n

l = 1

h = n

while l < h

r = (l + h) / 2

s = r * r

if s == n

break

if s < n

l = r

else

h = r

return s

Problem: Last Resort?

input: A[k] // 1D array of size k, k is a power of 2

output: sorted array A

B = array(k)

size = 1

while size <= k / 2

count = (k / 2) / size

for i = 0 ... count

combine(A, i * size * 2, size, B)

for i = 0 ... k

A[i] = B[i]

size = size * 2

return A

def combine(A, start, size, B)

h = start

i = start

j = start + size

end = start + size

while (i < end) and (j < end + size) i

f A[i] <= A[j]

B[h] = A[i]

i = i + 1

else B[h] = A[j]

j = j + 1

h = h + 1

if j < end + size

i = j

end = end + size

while i < end

B[h] = A[i]

i = i + 1

h = h + 1