Data Structures and Algorithms in Java
6th Edition
ISBN: 9781118771334
Author: Michael T. Goodrich
Publisher: WILEY
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Expert Solution & Answer
Chapter 4, Problem 7R
Explanation of Solution
a)
Running time of
It is given that the running time of algorithm A is
Reason:
- If the
Explanation of Solution
b)
Running time of Algorithm A in worst case:
It is given that the worst-case running time of algorithm A is
Reason:
- It is important to note that the worst case running time is always greater than or equal to the average case running time
Expert Solution & Answer
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Students have asked these similar questions
Running Time Analysis: Give the tightest possible upper bound for the worst
case running time for each of the following in terms of N. You MUST choose your
answer from the following (not given in any particular order), each of which could be reused
(could be the answer for more than one of a) – f)):
O(N2), O(N3 log N), O(N log N), O(N), O(N2 log N), O(N5), O(2N), O(N3),
O(log N), O(1), O(N4), O(NN), O(N6)
2. Algorithm A has a running time described by the recurrence T(n) = 7T(n/2) + n². A
competing algorithm B has a running time described by the recurrence T(n) =
aT (n/4) + n². What is the largest integer value for a such that B is asymptotically faster
than A? Explain your answer.
Another recursive algorithm is applied to some data A = (a₁, ..., am) where
m = 2* (i.e. 2, 4, 8,16 ...) where x is an integer ≥ 1. The running time T is
characterised using the following recurrence equations:
T(1) = c when the size of A is 1
T(m) = 2T (2) + c otherwise
Determine the running time complexity of this algorithm.
Chapter 4 Solutions
Data Structures and Algorithms in Java
Ch. 4 - Prob. 1RCh. 4 - The number of operations executed by algorithms A...Ch. 4 - The number of operations executed by algorithms A...Ch. 4 - Prob. 4RCh. 4 - Prob. 5RCh. 4 - Prob. 6RCh. 4 - Prob. 7RCh. 4 - Prob. 8RCh. 4 - Prob. 9RCh. 4 - Prob. 10R
Ch. 4 - Prob. 11RCh. 4 - Prob. 12RCh. 4 - Prob. 13RCh. 4 - Prob. 14RCh. 4 - Prob. 15RCh. 4 - Prob. 16RCh. 4 - Prob. 17RCh. 4 - Prob. 18RCh. 4 - Prob. 19RCh. 4 - Prob. 20RCh. 4 - Prob. 21RCh. 4 - Prob. 22RCh. 4 - Show that 2n+1 is O(2n).Ch. 4 - Prob. 24RCh. 4 - Prob. 25RCh. 4 - Prob. 26RCh. 4 - Prob. 27RCh. 4 - Prob. 28RCh. 4 - Prob. 29RCh. 4 - Prob. 30RCh. 4 - Prob. 31RCh. 4 - Prob. 32RCh. 4 - Prob. 33RCh. 4 - Prob. 34RCh. 4 - Prob. 35CCh. 4 - Prob. 36CCh. 4 - Prob. 37CCh. 4 - Prob. 38CCh. 4 - Prob. 39CCh. 4 - Prob. 40CCh. 4 - Prob. 41CCh. 4 - Prob. 42CCh. 4 - Prob. 43CCh. 4 - Draw a visual justification of Proposition 4.3...Ch. 4 - Prob. 45CCh. 4 - Prob. 46CCh. 4 - Communication security is extremely important in...Ch. 4 - Al says he can prove that all sheep in a flock are...Ch. 4 - Consider the following justification that the...Ch. 4 - Consider the Fibonacci function, F(n) (see...Ch. 4 - Prob. 51CCh. 4 - Prob. 52CCh. 4 - Prob. 53CCh. 4 - Prob. 54CCh. 4 - An evil king has n bottles of wine, and a spy has...Ch. 4 - Prob. 56CCh. 4 - Prob. 57CCh. 4 - Prob. 58CCh. 4 - Prob. 59CCh. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - Perform an experimental analysis to test the...Ch. 4 - Prob. 63P
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Similar questions
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- 1. If I prove that an algorithm takes Θ(n2) worst-case time, is it possible that it takes O(n) on some inputs? 2. If I prove that an algorithm takes Θ(n2) worst-case time, is it possible that it takes O(n) on all inputs?arrow_forwardAlgorithm X has a growth rate that is proportional to n ∗ n ∗ n . What is the function that represents the growth rate of algorithm X? What is the order of algorithm X?arrow_forwardState True or false, for each of the following statements, and briefly explain why no points will be given even for a correct solution if no justification is presented. resented. 1. For all asymptotically positive f(n).f(n) + O(f(n)) = (f(n)) 2. The worst-case running time and expected running time are equal to within constant factors for any randomized algorithm. 3. There exists a data structure to maintain a dynamic set with operations Insert (x,S), Delete(x,S). and member? (x,S) that has an expected running time of O(1) per operation. 4. Let A₁, A₂ and A3 be three sorted arrays of n-real numbers (all distinct). In the comparison model constructing a balanced binary search tree of the set A₁ U A₂ U A3 requires Q(nlogn) time. 5. If dynamic programming problem satisfies the optimal-substructure property, then a locally optimal solution is globally optimal.arrow_forward
- Heuristics Prove or disprove: If h1(n), ..., hk(n) are admissible, so is h(n) = h1(n) + ... + hk(n)arrow_forwardConsider the following functions as time complexities of some algorithms. (a) First write the worst-case runtime of each algorithm in Big-O notation. (b) Then arrange functions from low to high (Consider their Big-O notations as you arrange them; as n grows, the function that grows slower should come sooner than the one that grows faster). (c) Arbitrary, select TWO of arrangements in part (b) and for each one of them justify why you have chosen such an ordering for the corresponding function. Provide formal proof. For example if fl<=f2<= f3<= f4<=f5 you may choose to formally justify why (1) fl<=f2 and why (2) f4<=f5 . fI(n)=n², f2(n)=210 nlogn, f3(n)=3", f4(n)=n, f5(n)=1, f6(n)=5*logn, f7(n)= n", f8(n)=4 n*n, f9(n)=2log(n³)arrow_forward3.1-6 Prove that the running time of an algorithm is O(g(n)) if and only if its worst-case running time is 0(g(n)) and its best-case running time is 2(g(n)).arrow_forward
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