1. Draw the decision tree for the merge-sort algorithm for the input consisting of 3 numbers: a,b,c

2. Draw the 4 top levels of the decision tree for the merge-sort algorithm for the input consisting of 4 numbers: a,b,c,d

3. How many leaves does this tree have?

4. How amny levels does this tree have?

5. What is the number of comparisons needed to sort these 4 numbers by the merge-sort algorithm in the worst case?

6. What is the number in the best case?

7. Is there an algorithm that in the worst case sorts 4 numbers with a smaller number of comparisons?

Justify the answers to all of these questions