I need Very Urgent help in getting 2 small questions answered in Algorithms Desi

Question

I need Very Urgent help in getting 2 small questions answered in Algorithms Design and Analysis Assignments to be done today. If you are available to get it done soon, so please help with this and i have lots of other assignments to offer.

Problem 1 (25 points).
Solve the following recurrences by induction. First, expand the recursion tree up to four steps, in
order to guess a solution. Then prove your guess by induction. (In the following the initial condition
is always T(1) = 1, and you can assume n is a power of 4.)
(a) T(n) = T(n/4) + T(3n/4) + n.
(b) T(n) = T(n/4) + T(n/2) + n.
Problem 2 (25 points).
Suppose that you are given the problem of returning in sorted order the k smallest elements in an
array of size n, where k is much smaller than log(n), but much larger than 1.
a. Describe how selection sort, insertion sort, mergesort, and heapsort can be adapted to this
problem. Your description need not give the pseudo-code for the modified algorithms; it is
enough simply to describe what changes can be made, as long as your description is clear.
b. Find the worst-case running times of these algorithms as functions of k and n.

Explanation / Answer

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