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 7E
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 the recurrence T(n)=4T(n/2+2)+n. Use the substitution method to verify your answer.
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.
Use a recursion tree to determine a good asymptotic upper bound on the recurrenceT(n) = 3T(n/3) + n.You can assume that n is a power of 3.Show all your work.
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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- please draw recursion tree and solve the recursion tree for the worst case T(n) <= T(n/7) + T(10n/14) + narrow_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_forwardUse the recursion tree method to guess tight asymptotic bounds for the recurrence T(n)=4T(n/2)+n. Use substitution method to prove it.arrow_forward
- Answer 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_forwardDraw a recursion tree for a recurrence and use the Substitution Method to prove the solution. ( make a sample question )arrow_forwardUse the recursion tree method to solve the following recurrence T(n) by finding the tightest function f(n) such that T(n) = O(f(n)). T(n) ≤ 4.T(n/3) +0(n³)arrow_forward
- 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_forwardSolve using the recursion tree T(n) = 4T(n-1) + c, where c is a positive constant, and T(0)=0.arrow_forwardProblem 3. Use recursion tree to solve the following recurrence. T(n) = T(n/15) +T(n/10) +2T(n/6) + /narrow_forward
- Generate the recursion tree for TOH problem with no. of discs=5.arrow_forwardSolve tower of Hanio problem for N = 4, 5 & 6 using recursion. The call of recursion is as follows: F(N, Source, Destination, Auxiliary).arrow_forwardr Examples: Find the tight bound of the following recursive functions, T(n). T(n)=9T(n/3) +n T(n)= T(2n/3) +1 ● T(n)=3T(n/4)+nlogn ● T(n) = 2T (n/2)+nlogn T(n)=2T(n/2) + O(n) • T(n)=8T(n/2) +0(n²) ● T(n) = 7T(n/2) + O(n²)arrow_forward
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