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 9.1, Problem 1E
Program Plan Intro
To show that the second smallest of n elements that can be found with
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Solve the recurrence T(n) = T(; +5) + n².
When we apply the mergesort on a 12-element array, how many comparisons do we need for the worst case? Ans:
Solve the recurrence by using repeated substitution. Show the work.
T(n) = T(n-1) + n
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Introduction to Algorithms
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- Suppose you have to compute AG sum(C)(r) as well as A,B Gsum(C)(r). Describe how to compute these together using a single sorting of r.arrow_forward1. Use the substitution method to show the recurrence: T(n) = 4T(n/2) + (n) has solution T(n) = O(n²)arrow_forwardSuppose arrays A and B are both sorted in increasing order and both contain n elements. What is the time complexity to find the median of A U B, i.e., the set of elements in A or B?arrow_forward
- Discuss a method for determining the rank of an element K in the array LIST[1:n].How can method PARTITION be utilised to solve the same problem effectively? What are the temporal complexities of the stated methods?arrow_forwardSolve the following recurrences: (a) T(n) = 3T() +n² lg* n + 2narrow_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
- Show that T(n) = 0(n³) where T(n) = n²arrow_forwardComputer Science for python The SELECT algorithm uses median of sub-medians as the pivot (let us call it s). Show that if n ≥ 140, then at least ⌈n/4⌉ elements are greater than p and at least ⌈n/4⌉ elements are less than parrow_forwardUse two ways to count the number of r-combinations of[n]={1,2,…,n}that contains 1 or 2 or 3. First, separate cases with Case 1 counting all r-combinations of [n] that contains 1 , Case 2 counting all r-combination of [n] that contains 2 but not 1 , and Case 3 counting allrcombination of [n] that contains 3 but not 1 or 2 . Second, count all r-combinations of [n] not containing any of1,2,3and use the subtraction rule.arrow_forward
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