For this task, save your work in hw1.pdf, SumEven.javaThe first n even numbers are 0,2,4,..., 2(n-1). This task involves computing the sum of the first neven numbers and understanding their performance implications.Subtask I We begin by writing a function public static long sumEven(int n) that computes the sumof the first n even numbers by looping over the even numbers in that range and adding them up.At the top of your function, answer the following question as a comment block: Approximatelyhow many steps does this function need as a function of n?Subtask II Using the method discussed in Lecture 1, find a simple formula for the sum of the first n evennumbers. Please show your work. Derive it directly without referencing other formulas.Subtask III If we are to use this formula instead of what we have in the sumEven function, how many stepswould this implementation need when the input is n? Please answer this question in the PDF file.

To summarize:Subtask I: We implemented the function sumEven(int n) in Java, which calculates the sum…

Answered: For this task, save your work in…

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 8SA

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In python, Problem Description:Sheldon and Leonard are physicists who are fixated on the BIG BANG theory. In order to exchange secret insights they have devised a code that encodes UPPERCASE words by shifting their letters forward. Shifting a letter by S positions means to go forward S letters in the alphabet. For example, shifting B by S = 3 positions gives E. However, sometimes this makes us go past Z, the last letter of the alphabet. Whenever this happens we wrap around, treating A as the letter that follows Z. For example, shifting Z by S = 2 positions gives B. Sheldon and Leonard’s code depends on a parameter K and also varies depending on the position of each letter in the word. For the letter at position P, they use the shift value of S = 3P + K. For example, here is how ZOOM is encoded when K = 3. The first letter Z has a shift valueof S = 3 × 1 + 3 = 6; it wraps around and becomes the letter F. The second letter, O, hasS = 3 × 2 + 3 = 9 and becomes X. The last two letters…
Implement the vacuum cleaning agent function in Python/Java for the scenario described below: Consider two-dimensional Boolean array of size m x n (m and n can each be equal to 4) where m is the number of rows, and n is the number of columns. Obtain numerical positive integer values for m and n as inputs from the user. Generate random numbers and scale them down to either a “0” or a “1” according to whether they represent “Clean” or “Dirty”, respectively. After filling the array with 0s or 1s, start at some random array position indicating the initial position of the vacuum cleaner. First check if at that current position, there is the presence of a “Dirt” or not determined by whether 0 or 1 is filled in at that initial position of the vacuum cleaner. If there is a “Dirt”, clean it, and if there is no “Dirt” do a No-operation. After this is done, generate random numbers modulo 4 to obtain random numbers 0, 1, 2, 3 indicating whether to take a left, right, up or down correspondingly. If…
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