We want to arrange the n numbers stored in any array such that all negative values occur before all positive ones. 

What is the minimum number of exchanges required in the worst case?

What are the functions represented in the graph below?

  Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3, and f4?
  f1(n) = 2n
  f2(n) = n(3/2)
  f3(n) = n*log(n)
  f4(n) = nlog(n)
Choice 1 : f3, f2, f4, f1
Choice 2:  f3, f2, f1, f4
Choice 3:  f2, f3. f1, f4
Choice 4:  f2, f3, f4, f1

What is the big O time complexity for finding if a value is in a binary search tree?

1. O(N)
2. O(log(N))
3. O(1)
4. O(2^N)

What is the solution of the following recurrence

T(n) = T(n/4) + T(n/2) + cn2
T(1) = c
T(0) = 0
where c is a positive constant
1. O(n3)
2. O(n2)
3. O(n2 log n)
4. O(nlog n)

The answers to the questions of this quiz are my own and I pledge to not use any outside sources or people to help me.  By clicking True I pledge that I will not cheat

Let G be an undirected graph. Consider a depth-first traversal of G, and let T be the resulting depth-first search tree. Let u be a vertex in G and let v be the first new (unvisited) vertex visited after visiting u in the traversal. Which of the following statements is always true?

Your friends are starting a security company that needs to obtain licenses for n different pieces of cryptographic software. Due to regulations, they can only obtain these licenses at the rate of at most one per month.

Each license is currently selling for a price of $100. However, they are all becoming more expensive according to exponential growth curves: in particular, the cost of license j increases by a factor of r_j > 1 each month, where r_j is a given parameter. This means that if license j  is purchased t months from now, it will cost $100 r_j^t_.

We will assume that all the price growth rates are distinct; that is, r_i ≠ r_j for licenses i ≠ j (even though they start at the same price of  $100).

Given that the company can only buy at most one license a month, in which order should it buy the licenses so that the total amount of money it spends is as small as possible?

Provide the complexity of your algorithm

Which type of proof would you use for proving that your algorithm is optimal? State clearly what you need to prove, considering the type of proof you would use. 

Run Prim’s algorithm starting on node A.

Fill the table below by indicating the order in which the edges are added to the MST under construction, and the final node labels.