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 4.5, Problem 3E
Program Plan Intro
To show that the solution of the binary search recurrence relation
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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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- What is the complexity of the following recurrence?arrow_forward1. Use the substitution method to show the recurrence: T(n) = 4T(n/2) + (n) has solution T(n) = O(n²)arrow_forward4. Consider the recurrence: T(n) = T(n/2) + T(n/4) + n, T(m) = 1 for m <= 5. Use the substitution method to give a tight upper bound on the solution to the recurrence using O-notation.arrow_forward
- Consider the following recurrence: T(1)=1; T(n) = 2.T()+n, for n> 1, n a power of 3. =..... Find T(27) by substitution, starting with n = 1, n = 65 2 169 29 15 6arrow_forwardUse the substitution method to show that the recurrence defined by T(n) = 2T(n/3) + Θ(n) hassolution T(n) = Θ(n).arrow_forward4.5-3 Use the master method to show that the solution to the binary-search recurrence T(n) = T(n/2) + ©(1) is T(n) = O(lgn). (See Exercise 2.3-5 for a description of binary search.)arrow_forward
- For each of the following recurrences, give an expression for the runtime T(n) if the recurrence can be solved with the Master Theorem. Otherwise, indicate that the Master Theorem does not apply. For all cases, we have T(x) = 1 when x ≤ 100 (base of recursion). Ex.) T(n) = 3T(n/3) + √n We have nlog, a T(n) = O(n). a) T(n) = 5T(n/3) +2023n¹.6 b) T(n) = 9T(n/3) + 1984n² = n. Since f(n) = O(n¹-) (for any € < 1/2), we are at case 1 and n³ c) T(n) = 8T(n/2) + log n 4 d) T(n) = 16T(n/2) + n² log³ narrow_forwardSolve the recurrence by using repeated substitution. Show the work. T(n) = T(n-1) + narrow_forwardSolve the following recurrences: (a) T(n) = 3T() +n² lg* n + 2narrow_forward
- 1. Use the substitution method to verify that the upper bound solution to the recurrence: T(n) = 3T ([n/4])+(n²) is O(n²). Otherwise, if O(n²) is not the solution, find the correct solution to the above recurrence.arrow_forwardCan the master method be applied to the recurrence T(n) = 4T(n²) + n²logn Why or why not? Give an asymptotic upper bound for this recurrence.arrow_forwardPractice Exercise #3: For each of the following recurrences, give an expression for the runtime T (n) if the recurrence can be solved with the Master Theorem. Otherwise, indicate that the Master Theorem does not apply. 1. T(n) = T + 2⁰ 2. T(n) = √2T) + logn 3T (+2 3. T(n) = 4. T(n) = 64T() -n²lognarrow_forward
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