Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 4.4, Problem 2E
Program Plan Intro
To determine the good asymptotic upper bound of the recurrence relation
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Use a recursion tree to determine a good asymptotic upper bound on therecurrence T(n) = 3T(n/2) + n. Use the substitution method to prove your answer.
For each of the following recurrences, verify the answer you get by applying the master method, by solving the recurrence algebraically OR applying the recursion tree method.
T(N) = 2T(N-1) + 1
T(N) = 3T(N-1) + n
Use a recursion tree to determine a good asymptotic upper bound on the recurrence T(n)=4T(n/2+2)+n. Use the substitution method to verify your answer.
Chapter 4 Solutions
Introduction to Algorithms
Ch. 4.1 - Prob. 1ECh. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5E
Ch. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.6 - Prob. 1ECh. 4.6 - Prob. 2ECh. 4.6 - Prob. 3ECh. 4 - Prob. 1PCh. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Prob. 6P
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- Use a recursion tree to determine a good asymptotic upper bound on following recurrences. Please see Appendix of your text book for using harmonic and geometric series. a) T (n) = T(n/5) + O(n)2 b) T (n) = 10T(n/2) + O(n)2 c) T (n) = 10T(n/2) + Θ (1) d) T (n) = 2T (n/2) + n/ lg n e) T (n) = 2T (n - 1) + Θ (1)arrow_forwardFor each of the following recurrences, verify the answer you get by applying the master method, by solving the recurrence algebraically OR applying the recursion tree method. T(N) = 4T(N/2) + n2logn T(N) = 5T(N/2) + n2/lognarrow_forwardAnswer the following for the recurrence T(n) = T( n / 2 ) + T( n / 4 ) + n. (a) Use the Recursion Tree method to guess the upper-bound. (b) Prove by induction the upper-bound obtained in the previous question (problem a).arrow_forward
- Please explain!! Solve the recurrence: T(n)=2T(2/3 n)+n^2. first by directly adding up the work done in each iteration and then using the Master theorem. Note that this question has two parts (a) Solving IN RECURSION TREE the problem by adding up all the work done (step by step) andarrow_forwardGive the uppor-bound for the recurrence T(n)=2π(n/2)+n∧2, using the Recursion Tree method. You must show at least 3 levels of the tree, and give the explicit log base when using the tree height!arrow_forwardfor the following problem we need to use a recursion tree. so we can determine an asymptotic upper bound on therecurrence T(n) = 3T(n/2) + n. the substitution method must be used to solve.arrow_forward
- Solve using the recursion tree: T(n) = 2T(n-1) + c, where c is a positive constant, and T(0)=0.arrow_forwardUsing the recursion tree method find the upper and lower bounds for the following recurrence (if they are the same, find the tight bound). T (n) = T (n/2) + 2T (n/3) + n.arrow_forwardUsing a recursion tree, show the process how to solve the following recurrence in terms of the big O representation. Use the substitution method to verify your result. T(n) = T(n/2)+T(n/3)+cnarrow_forward
- Please explain Solve the recurrence: T(n)=2T(2/3 n)+n^2. first by directly adding up the work done in each iteration and then using the Master theorem. Note that this question has two parts (a) Solving IN RECURSION TREE the problem by adding up all the work done (step by step) and (b) using Master Theoremarrow_forwardUse recursion tree to guess a bound, then proof it using induction. Finally, use master theorem (if applicable) to directly get the bound. Try to make your bounds as tight as possible. T(n) = 2T(n/2) + n T(n) = 2T(n-2) + narrow_forwardA recursive algorithm is designed in such a way that for size n it divides it into 2 subproblems in the ratio 3:2 and it takes linear time to integrate the solution from the 3 subproblem, what will be the recurrence relation of this.arrow_forward
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