given two integers n and k. You are approached to pick greatest number of particular integers from 1 to n so that there is no subset of picked numbers with aggregate equivalent to k.    A subset of a set is a set that can be gotten from starting one by eliminating a few (potentially all or none) components of it.

1. Both mergesort and quicksort uses divide and conquer paradigm to sort unsorted list. (a) Imagine you want to write the quicksort algorithm to sort an array into non-increasing order. Write down the partition algorithm that is used in the divide phase in the quicksort algorithm. Show that the time complexity of this algorithm is 0(n). (b) Identify the worst case situation in the naive quicksort algorithm and show that in the worst case situation its time complexity is O(n2)

Course: Algorithm Project: We will use the defintion of of n-Queens Problem from the chapter Backtracking.  In this project you need to describe Problem and Algorithm and Indicate input and output clearly.  Analyze and prove the time complexity of your algorithm. Implement the algorithm using backtracking(including writing testing case).illustrate key functions with comments indicating: What it does, what each parameter is used for, how it handles errors etc. Indicate the testing scenarios and testing the results in a clear way. Make sure source is commented appropriately and structured well.

JAVA - How do I make this a random pull of participants instead of just a participant +1? I want the purchaser to be the same as it was input in the array, but then want the gift to be random. If that isn't possible, making both random would work as well, but either way the giver and receiver can't be the same person.The output should be something like this:a will purchase a gift for d (age: 2)b will purchase a gift for c (age: 3)c will purchase a gift for a (age: 4)d will purchase a gift for b (age: 2) import java.util.Random; public class ExchangeResults{public static void main(String[] args){UserInput userinput = new UserInput();Participant[] participants = userinput.inputParticipants();   System.out.println("Exchange Results");//PRINT MATCHESshuffleParticipants(participants);} //MAKE RANDOM MATCHESpublic static void shuffleParticipants(Participant[] participants){for (int i = 0; i < participants.length-1 ; i++){Participant p1 = participants[i];Participant p2 =…

I need the code from start to end with no errors and the explanation for the code ObjectivesJava refresher (including file I/O)Use recursionDescriptionFor this project, you get to write a maze solver. A maze is a two dimensional array of chars. Walls are represented as '#'s and ' ' are empty squares. The maze entrance is always in the first row, second column (and will always be an empty square). There will be zero or more exits along the outside perimeter. To be considered an exit, it must be reachable from the entrance. The entrance is not an exit.Here are some example mazes:mazeA7 9# # ###### # #   ## # # #### #     ## ##### ##       ########## RequirementsWrite a MazeSolver class in Java. This program needs to prompt the user for a maze filename and then explore the maze. Display how many exits were found and the positions (not indices) of the valid exits. Your program can display the valid exits found in any order. See the examples below for exact output requirements. Also, record…

Assume you are playing a card game using a standard 52-card deck. You are dealt a hand of cards that are all the same suit, spades. You are dealt first a 5, then a 3, then 8, and finally 4. You first took the 5 into your hand. Then you put the three before the 5. Next you put the 8 behind the 5. Finally, you put the 4 between the 3 and 5. Which sorting algorithm is most similar to how you sorted your hand?  Group of answer choices   1. Quick Sort 2. Insertion Sort 3. Merge Sort 4. Selection Sort

Note that you can only use recursion to solve Q1  and you cannot use any loop. You are free to add helper methods, but you are not allowed to change the method header.Question 1: Crazy seriesIn this session, you need to implement the crazy series method. In the crazy series, you will be given a starting number. Then, you need to times 2 for each number until the number is greater than 100. After the number is greater than 100, you need to divide 3 until we reach the number is less than 5. Note that the input number must be greater than 0, and you are not allowed to use loop here.For example,crazySeries(10) should return ArrayList [10.0, 20.0, 40.0, 80.0, 160.0, 53.333333333333336, 17.77777777777778, 5.9259259259259265, 1.9753086419753088]crazySeries(5) should return ArrayList [5.0, 10.0, 20.0, 40.0, 80.0, 160.0, 53.333333333333336, 17.77777777777778, 5.9259259259259265, 1.9753086419753088]crazySeries(1) should return ArrayList [1.0, 2.0, 4.0, 8.0, 16.0, 32.0, 64.0, 128.0,…

ONLY IF STATEMENTS ALLOWED!!!! NO RANGE FUNCTION, NO SETS, NO LISTS, NO LOOPS, ETC Angela loves reading books. She recently started reading an AI generated series called “Harry Trotter”. Angela is collecting books from the series at her nearest bookstore. Since the series is AI generated, the publishers have produced an infinite collection of the books where each book is identified by a unique integer. The bookstore has exactly one copy of each book. Angela wants to buy the books in the range [l,r], where l ≤ r. As an example, the range [−3,3] means that Angela wants to buy the books  − 3,  − 2,  − 1, 0, 1, 2, and 3. Dan also loves the series (or maybe annoying Angela – who knows, really), and he manages to sneak into the bookstore very early to buy all of the books in the range [d,u], where d ≤ u. When Angela later visits, sadly she will not find those books there anymore. For example, if Angela tries to buy books [−2,3] and Dan has bought books [0,2], Angela would only receive books…