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 4.3, Problem 9E
Program Plan Intro
To find the solution of the recurrence relation
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Give the solution for T(n) in the following recurrence. Assume that T(n) is constant for small n. Provide brief justification for the answer.
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How many lines will the following function write? Write the recurrence relation of each and solve using the Master theorem. Give your answer as a function of n (in the form Θ( · )).
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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- Expand the following recurrence to help you find a closed-form solution, and then use induction to prove your answer is correct. T(n) = T(n−1) + 5 for n > 0; T(0) = 8.arrow_forwardHow many lines does his algorithm print? Write a recurrence and solve it. function printaton(n: an integer power of 2) { if n > 1 { printaton(n/2) printaton(n/2) printaton(n/2) for i = 1 to n ^ 4 do printline("are we done yet?") } } Use Master's theorem to obtain an asymptotic solution. Derive an exact solution by expanding the recurrence.arrow_forwardDe ning T(0) = a; T(1) = b; T(2) = c, and T(n + 3) = (1=3)(T(n + 2) + T(n + 1) + T(n)) for n >= 0, solve for the limit T(n) as n -> ∞. Show your work.arrow_forward
- Give an asymptotic estimate, using the Θ-notation, of the number of letters printed by the algorithms given below. Give a complete justification for your answer, by providing an appropriate recurrence equation and its solution. algorithm printAs(n) if n < 4 then print ("A") else for j <-- 1 to n^2 do print ("A")arrow_forwardGive an asymptotic estimate, using the Θ-notation, of the number of letters printed by the algorithms given below. Give a complete justification for your answer, by providing an appropriate recurrence equation and its solution.arrow_forwardHow many lines does his algorithm print? Write a recurrence and solve it.function printaton(n: an integer power of 2) { if n > 1 { printaton(n/2) printaton(n/2) printaton(n/2) for i = 1 to n ^ 4 do printline("are we done yet?") }} a. Use Master's theorem to obtain an asymptotic solution. b. Derive an exact solution by expanding the recurrence.arrow_forward
- Solve following recurrence with iterative substitution: T(n)= 2T(n/2)+c *O(1)arrow_forwardImplement the function by simplifying and creating a truth table. F(W,X,Y,Z)= ((W^X)) | (~(Y&Z)) where ^ (XOR), | (OR), ~ (inverse) and &(AND)arrow_forwardProve or disprove each of the following Θ(log n)^k = O(n) where k is any constant larger than 1, hint: what is the derivative oflnk n?arrow_forward
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