Agent Bond and Agent Carter have agreed on a way to covertly communicate a positive integer...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Agent Bond and Agent Carter have agreed on a way to covertly communicate a positive integer within the range of 1 to n. Bond will send a sequence of n positive integers A[1], A[2], ..., A[n] to Carter. Upon receiving the sequence, Carter will attempt to look for the presence of increasing arcs in the sequence. A subsequence A[i], A[12],, A[im], where 1 <m <n, is considered an increasing arc whenever the following conditions hold: 11 and im ≤n, = i₁ <i₂ < <im, and A[i] A[i+1] for 1 <j <m. For example, suppose the following sequence of positive integers are given: 7,2, 33, 8, 11, 17, 1,5,9 The following are some of the increasing arcs for this sequence: 7,33 7,8, 11, 17 7,8,9 7,9 (1) (3) (4) A longest increasing arc is an increasing are that is the longest within the given se- quence (i.e., m is maximized). For example, (2) is the longest increasing arc: it has a length of 4. The positive number that Bond intends to send to Carter covertly is the length of the longest increasing arc. That means Carter, upon receiving a sequence from Bond, will have to recover the length of the longest increasing are in order to com- plete her mission and save humanity. Design an efficient algorithm that Carter can use to find the length of the longest increasing are from any given sequence of positive integers. Justify the correctness and analyze the running time of your algorithm. Agent Bond and Agent Carter have agreed on a way to covertly communicate a positive integer within the range of 1 to n. Bond will send a sequence of n positive integers A[1], A[2], ..., A[n] to Carter. Upon receiving the sequence, Carter will attempt to look for the presence of increasing arcs in the sequence. A subsequence A[i], A[12],, A[im], where 1 <m <n, is considered an increasing arc whenever the following conditions hold: 11 and im ≤n, = i₁ <i₂ < <im, and A[i] A[i+1] for 1 <j <m. For example, suppose the following sequence of positive integers are given: 7,2, 33, 8, 11, 17, 1,5,9 The following are some of the increasing arcs for this sequence: 7,33 7,8, 11, 17 7,8,9 7,9 (1) (3) (4) A longest increasing arc is an increasing are that is the longest within the given se- quence (i.e., m is maximized). For example, (2) is the longest increasing arc: it has a length of 4. The positive number that Bond intends to send to Carter covertly is the length of the longest increasing arc. That means Carter, upon receiving a sequence from Bond, will have to recover the length of the longest increasing are in order to com- plete her mission and save humanity. Design an efficient algorithm that Carter can use to find the length of the longest increasing are from any given sequence of positive integers. Justify the correctness and analyze the running time of your algorithm.
Expert Answer:
Answer rating: 100% (QA)
This Question is similar to Longest Common Subsequence Algorithm a7 2 33 8 11 17 1 5 9 step1 ... View the full answer
Related Book For
Discrete Mathematics and Its Applications
ISBN: 978-0073383095
7th edition
Authors: Kenneth H. Rosen
Posted Date:
Students also viewed these computer network questions
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
The Crazy Eddie fraud may appear smaller and gentler than the massive billion-dollar frauds exposed in recent times, such as Bernie Madoffs Ponzi scheme, frauds in the subprime mortgage market, the...
-
1. A projectile is launched in a vertical plane, at an angle 0 with initial velocity vo. It must be caught in a frictionless circular tube of radius R in such a way that the trajectory of the...
-
In fighting forest fires, airplanes work in support of ground crews by dropping water on the fires. A pilot is practicing by dropping a canister of red dye, hoping to hit a target on the ground...
-
Suppose that {xn} and {yn} are real sequences. a) Prove that provided that none of these sums is of the form - . b) Show that if limn xn exists, then and c) Show by examples that each of the...
-
Hooters Restaurant in Myrtle Beach, South Carolina, used an alternative dispute resolution program, a program to resolve disputes outside the traditional court system. Employees of Hooters had to...
-
High-low method, regression analysis. Anna Martinez, the financial manager at the Casa Real restaurant is checking to see if there is any relationship between newspaper advertising and sales revenues...
-
4. Find the missing angle. 16 22 5. When you are a certain distance from the base of a building, the top of the building is at an angle of 60. When you move 30 m further away, the angle is 45. How...
-
A network consists of the activities in the following list. Times are given in weeks. Activity Preceding A B C D E F -- A A, B C D Time 8 3 7 3 4 9 (a) Draw the network diagram. (b) Calculate the ES,...
-
In May there are 6,000 people classified as unemployed and the size of the labor force is 80,000. Between May and June two events take place: i) 1000 graduates join the labor force and start looking...
-
Why are the notes important for understanding an organizations financial statement?
-
Differentiate between the direct and the indirect methods for preparing and presenting the statement of cash flows.
-
Why are financial statements usually presented with more than 1 year of data?
-
Why might the excess of revenues over expenses be of particular interest to a financial statement user, rather than the increase in net assets without donor restrictions?
-
What are the three steps in investment analysis?
-
Although courts in the provinces may be described differently, the provinces generally maintain three levels of courts- Provincial Court (small claims in a civil context), Superior Court and a Court...
-
Why should you not model a decision variable as a random variable with a probability distribution?
-
Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0, 1), (1, 1), (1, 2), (2, 0), (2, 2), and (3, 0). Find the a) Reflexive closure of R. b) Symmetric closure of R.
-
Represent pictorially that x log x iso (x2) by graphing x log x, / x2, and x log x/x2. Explain how this picture shows that x log x is o(x2).
-
Find gcd(92928, 123552) and lcm(92928, 123552), and verify that gcd(92928, 123552) lcm(92928, 123552) = 92928 123552.
-
Do any problems arise when translating physical assets and economic events into monetary units? Give one or two illustrations to support your answer.
-
Entries for the Warren Clinic 2015 income statement are listed below in alphabetical order. Reorder the data in proper format. Depreciation expense General/administrative expenses Interest expense $...
-
Brandywine Homecare, a not-for-profit business, had revenues of \($12\) million in 2015. Expenses other than depreciation totaled 75 percent of revenues, and depreciation expense was \($1.5\)...
Study smarter with the SolutionInn App