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 5E
Program Plan Intro
To show that the solution of the exact recurrence relation 4.3 for merge sort is
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use change of variable to solve this recurrence .
find the best case for quick sort .
Use the substitution method to show that the recurrence defined by T(n) = 2T(n/3) + Θ(n) hassolution T(n) = Θ(n).
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.
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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- Solve the recurrence; T(n)=2T(n/2) + cn T(1) = carrow_forwardSolve the recurrence T(n) = T(; +5) + n².arrow_forwardUse divide-and-conquer algorithm for finding the position of the maximum element in an array of n numbers. Set up a recurrence relation for the above algorithm and solve it.arrow_forward
- Solve the recurrence by using repeated substitution. Show the work. T(n) = T(n-1) + narrow_forwardLet C(n) denote the number of comparisons performed by quicksort in sorting an array of size n in the worst case. Write the recurrence relation for C(n) and solve.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_forward
- Solve the following recurrences: (a) T(n) = 3T() +n² lg* n + 2narrow_forwardAlgorithm FHL Version of Schreier-Sims is O ( I f) 16), provided that the size of the initial generating set is O ( I ~ 14).arrow_forwardUse the substitution method to obtain the exact value of T(n) in the following recurrence. Show all computations. T(1) = 1, T(n)=T(n-1)+3n,n>1arrow_forward
- Please help me with this recurrence relation: B(0) = 1, B(n) = B(n −1) + n + 3 for n > 0 Use the method of unraveling to find a closed form for B(n).arrow_forwardGenerate all permutations of {1, 2, 3, 4} by the bottom-up minimal-change algorithm. Show the steps.arrow_forwardConsider the recurrenceT (n) = 2T (n/2) + n log n.Provide a detailed proof why Master Theorem does not apply for this recurrence.arrow_forward
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