Prove that the running time of an algorithm is (g (n)) if and only if its worst case running time is O(g (n)) and its best case running time is (g (n)) ...

According to asymptotic theorem For any two functions fn and ...

Prove that the running time of an algorithm is (g (n)) if and only if its worst-case

Question:

Prove that the running time of an algorithm is Θ(g (n)) if and only if its worst-case running time is O(g (n)) and its best-case running time is Ω(g (n)).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Introduction to Algorithms

ISBN: 978-0262033848

3rd edition

Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest

Question Posted: Feb 24, 2020 12:02 PM

See More Questions

Show that f (n) is O(g(n)) if and only if g(n) is ( f (n)).
a. Prove that the running time of Shellsort is (N2) using increments of the form 1, c, c2, . . . , ci for any integer c. b. Prove that for these increments, the average running time is (N3/2).
Prove that the running time of Shellsort, using the increment sequence suggested by Hibbard, is (N3/2) in the worst case. Hint: You can prove the bound by considering the special case of what...
A clinical study is established to determine if the results of a screening stress test can be used as a predictor of the presence of heart disease. The study enrolls 100 participants who undergo a...
(a) Explain how pyrrole is isoelectronic with the cyclopentadienyl anion. (b) Specifically, what is the difference between the cyclopentadienyl anion and pyrrole? (c) Draw resonance forms to show the...
The fund(s) for which budgetary comparisons would potentially be included in the basic financial statements are a. General Fund. b. all Special Revenue Funds. c. major Special Revenue Funds. d. Items...
Chicago Prime Packers Inc. was a US corporation with its principal place of business in Colorado. Northam Food Trading Company was a Canadian corporation with its principal place of business in...
One of New England Airs top competitive pri-orities is on- time arrivals. Quality VP Clair Bond decided to person-ally monitor New England Airs performance. Each week for the past 30 weeks, Bond...
How to create a relational model from DDL statements and how you save a relational model design.?
Imagine that Howard has asked you to write some queries to help him make better use of his data. For each information request below, write a single query that provides the answer set. When a task...
We can apply the iteration operator ? used in the lg ? function to any monotonically increasing function f (n) over the reals. For a given constant c ? ?, we define the iterated function f * c by...
Show that the golden ratio and its conjugate both satisfy the equation x 2 = x + 1.
Draw a level 0 data flow diagram (DFD) for the process of buying glasses in Exercise A, Chapter 4.
For each of the sample spaces you have defined above, indicate whether the sample space is finite, countably infinite, or uncountably infinite. Justify your answers.
Girlfriend Collective wants customers to love its products and wear them with pride. Designing for an audience that cares about where clothes come from, as well as how they look and fit, the founders...
Formulate a linear programming model from a description of a problem.
Assume that there is an increase in the demand for money at every interest rate. Using a diagram, show what effect this will have on the equilibrium interest rate for a given money supply.
Consider Table 7-3 but suppose that the market basket is composed of 100 oranges, 50 grapefruit, and 200 lemons. How does this change the pre-frost and post-frost price indexes? Explain. Generalize...
The error involved in making a certain measurement is a continuous rv X with pdf a. Sketch the graph of f (x). b. Compute P(X > 0). c. Compute P (1 < X < 1). d. Compute P(X .5). 09375(4 x2) -2sxs2...
The Ranch 888 Noodle Company sells two types of dried noodles:ramen, at $6.50 per box, and chow fun, at $7.70 per box. So farthis year, the company has sold a total of 110,096 boxes ofnoodles,...
Design a circular positional list ADT that abstracts a circularly linked list in the same way that the positional list ADT abstracts a doubly linked list.
There is a simple algorithm, called bubble-sort, for sorting a list L of n comparable elements. This algorithm scans the list n1 times, where, in each scan, the algorithm compares the current element...
Redo Exercise C-7.51 assuming L is implemented with an array list. Exercise C-7.51 There is a simple algorithm, called bubble-sort, for sorting a list L of n comparable elements. This algorithm scans...
Solve (2.4 x 10-5) X 875 (2.5 x 107) x (2.8 x 107)
assume there are no outliers. Draw the boxplot for the following frequency table. You may X f rf cf crf 3 7 0.1228 7 0.1228 4 11 0.1930 18 0.3158 5 9 0.1579 27 0.4737 618 6 0.1053 33 0.5789 10 0.1754...
Find the partial derivative of the regularized least squares problem: {) (w + x) (wo + w x ( ) + w x ( ) } + |/\||[w1, w2]|| with respect to wo, w, and w2. Although there is a closed-form solution to...

Prove that the running time of an algorithm is (g (n)) if and only if its worst-case

Question:

Step by Step Answer:

According to asymptotic theorem For any two functions fn and ...View the full answer

Introduction to Algorithms

Students also viewed these Computer science questions