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 8.2, Problem 4E
Program Plan Intro
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Given an n-element sequence of integers, an algorithm executes an O(n)-time computation for each even number in the
sequence, and an O(logn)-time computation for each odd number in the sequence. What are the best-case and worst-case
running times of this algorithm? Why? Show with proper notations.
Consider a function f: N → N that represents the amount of work done by some algorithm as follow:
f(n) = {(1 if n is oddn if n is even)┤
Prove or disprove. f(n) is O(n).
Please show proof or disproof
The number of operations executed by algorithms A and B is 100n2 and 4n4, respectively. Determine n0 such that A is better than B for n > n0
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- Write an algorithm to find longest common subsequence that runs in approximately O(n 2 ). Show how to improve it to O(nlog 2 n).arrow_forwardGiven a sorted array of n comparable items A, and a search value key, return the position (array index) of key in A if it is present, or -1 if it is not present. If key is present in A, your algorithm must run in order O(log k) time, where k is the location of key in A. Otherwise, if key is not present, your algorithm must run in O(log n) time.arrow_forwardThe first time you run algorithm A on a dataset of n elements; it is faster than algorithm B. The second time you run algorithm A on a dataset of n elements; it is slower than algorithm B. Explain how this is possible. Give an example for algorithm A and algorithm B.arrow_forward
- Consider a function f: N → N that represents the amount of work done by some algorithm as follow: f(n) = {(1 if n is oddn if n is even)┤ A. Prove or disprove. f(n) is O(n).arrow_forwardGiven two sorted arrays A and B, design a linear (O(IA|+|B|)) time algorithm for computing the set C containing elements that are in A or B, but not in both. That is, C = (AU B) \ (AN B). You can assume that elements in A have different values and elements in B also have different values. Please state the steps of your algorithm clearly, prove that it is correct, and analyze its running time. Pls give the code in C++, or very clear steps of the algorithmarrow_forward4 points Given an n-element array X of integers, Algorithm A executes an O(n3.4)-time computation for each even positive number in X, an Oin2.3-time computation for each odd positive number in X, and an O(n2.5)-time computation for each negative number in X. What are the best-case and worst-case running times of Algorithm A? Justify your answer. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac) BIUS Paragraph V Arial 10pt EVE 2 IXO QFS3Earrow_forward
- The average time complexity for an algorithm can be found by adding the best time and worst time and dividing that answer by 2. O True Falsearrow_forwardLet Tk (n) denote the value returned by A(k, n). This gives T0(n) = 2 + n, T1(0) = 0, Tk (0) = 1 for k ≥ 2, and Tk (n) = Tk−1(Tk (n − 1)) for k > 0 and n > 0.arrow_forwardimplement Running time algorithm Careful(n) pre-cond: n is an integer. post-cond: Q(n) “Hi”s are printed for some odd function Qarrow_forward
- 7. Suppose that you have two different algorithms for solving a problem. To solve a problem of size n, the first algorithm uses exactly n(log2 n) operations and the second algorithm uses exactly n3/2 operations. As n grows, which algorithm uses fewer operations?arrow_forwardGiven an n-element array X of integers, Algorithm A executes an O(n) time computation for each even number in X and an O(log-n) time computation for each odd number in X. What are the best case and worst case for running time of algorithm C?arrow_forwardThe number of operations executed by algorithms A is 5n^2 and by algorithm B is 30n^3. Determine n0 such that B is better than A for all n > n0.arrow_forward
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