Princess Nora Bint Abdulrahman University First Semester 1433/1434H
Faculty of Computer and Information Science Tutorial # 2
CS 411 : Algorithms Design and Analysis Recursion Tree
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Q: Regard to the recurrence equation below:
T(n) = 4T(n/2) +n
a. Draw the recursion tree.
b. Determine the number of nodes and cost at each level.
c. Determine the total cost for all levels (i.e. in summation form).
Steps:
1. Draw the tree based on the recurrence
2. From the tree determine:
a. # of levels in the tree
b. cost per level
c. # of nodes in the last level
d. cost of the last level (which is based on the number found in
2c)
3. Write down the summation using ∑ nota*on – this summation
sums up the cost of all the levels in the recursion tree
4. Recognize the sum or look for a closed form solution for the
summa*on created in 3). Use Appendix A.
5. Apply that closed form solution to your summation coming up
with your “guess” in terms of Big-O, or Θ, or Ω (depending on
which type of asymptotic bound is being sought).
