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Both Quicksort and Insertionsort have the time complexity O (n2) in the worst case. Which of the following statements is correct?
A. Place of insertion is faster than average Quicksort, regardless of the value of 'n'.
B. Choosing the first element as a pivot is a very effective strategy for Quicksort.
C. Both Quicksort and Insertion sort are usually implemented as recursive
D. Insertion sort is generally faster than Quicksort for smaller values of n (<20 elements).
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- One-friend recursion vs iteration.1. Your task is to accept a tuple a1, a2, ... , an and return the reversed tuple an, an−1, ... , a1. Being lazy, you will only strip off an element from one end or add an element back onto one end. But you have recursive friends to help you. Provide both a paragraph containing the friend’s explanation of the algorithm, and the recursive code.2. Now suppose that you have a stack, but no friends. (See Chapter 3). Quickly sketch an iterative program that solves this same problem. Be sure to include loop invariants and other the key steps required for describing an iterative algorithm.3. Trace each of these two programs. Step by step, compare and contrast their computations on a computer. i already uploaded this question 3 times and getting wrong answer so if you don't know right answer dont write rubbih ans otherwise you will get downvoteOne-friend recursion vs iteration.1. Your task is to accept a tuple a1, a2, ... , an and return the reversed tuple an, an−1, ... , a1. Being lazy, you will only strip off an element from one end or add an element back onto one end. But you have recursive friends to help you. Provide both a paragraph containing the friend’s explanation of the algorithm, and the recursive code.2. Now suppose that you have a stack, but no friends. (See Chapter 3). Quickly sketch an iterative program that solves this same problem. Be sure to include loop invariants and other the key steps required for describing an iterative algorithm.3. Trace each of these two programs. Step by step, compare and contrast their computations on a computer. i already uploaded this question 3 times and getting wrong answer so if you don't know right answer dont write rubbih ans otherwise you will get downvote don't copy bartleby old or chegg its wrongOne-friend recursion vs iteration.1. Your task is to accept a tuple a1, a2, ... , an and return the reversed tuplean, an−1, ... , a1. Being lazy, you will only strip off an element from one end oradd an element back onto one end. But you have recursive friends to help you.Provide both a paragraph containing the friend’s explanation of the algorithm,and the recursive code.2. Now suppose that you have a stack, but no friends. (See Chapter 3). Quickly sketchan iterative program that solves this same problem. Be sure to include loop invariants and other the key steps required for describing an iterative algorithm.3. Trace each of these two programs. Step by step, compare and contrast their computations on a computer.
- The Tower of Hanoi is a puzzle where n disks of different sizes arestacked in ascending order on one rod and there are two other rods with nodisks on them. The objective is to move all disks from the first rod to thethird, such that:- only one disk is moved at a time- a larger disk can never be placed on top of a smaller oneWrite a recursive function that outputs the sequence of steps needed tosolve the puzzle with n disks.Write a test program in C++ that allows the user to input number of disks andthen uses your function to output the steps needed to solve the puzzle.Hint: If you could move up n−1 of the disks from the first post to thethird post using the second post as a spare, the last disk could be moved fromthe first post to the second post. Then by using the same technique you canmove the n−1 disks from the third post to the second post, using the firstdisk as a spare. There! You have the puzzle solved. You only have to decidewhat the nonrecursive case is, what the recursive…) Implement a quicksort with a 2k-sample-size-based sample. The sample should be sorted first, after which you should set up the recursive procedure to split the sample based on its median and to shift the two halves of the remaining sample to each subarray so they can be utilised in the subarrays without needing to be sorted again. The name of this algorithm is samplesort.The Binary Search algorithm works by testing a mid-point, then eliminating half of the list. In this exercise, you are going to take our binary search algorithm and add print statements so that you can track how the search executes. Inside of the recursive binary search function, add print statements to print out the starting, ending, and midpoint values each time. Then as you test a value, print out the results, either too high, too low, or a match. Sample Output Starting value: 0 Ending value: 9 Testing midpoint value: 4 Too high! Starting value: 0 Ending value: 3 Testing midpoint value: 1 Too low! Starting value: 2 Ending value: 3 Testing midpoint value: 2 Match! public class BinaryExplorer { public static void main(String[] args) {int[] testArray = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; binaryRec(testArray, 8, 0, testArray.length - 1); } /*** Add Print statements to the binaryRec method:* * Print Starting, ending, and midpoint values.* * Print when you find a match* * Print if you are…
- The Binary Search algorithm works by testing a mid-point, then eliminating half of the list. In this exercise, you are going to take our binary search algorithm and add print statements so that you can track how the search executes. Inside of the recursive binary search function, add print statements to print out the starting, ending, and midpoint values each time. Then as you test a value, print out the results, either too high, too low, or a match. Sample Output Starting value: 0 Ending value: 9 Testing midpoint value: 4 Too high! Starting value: 0 Ending value: 3 Testing midpoint value: 1 Too low! Starting value: 2 Ending value: 3 Testing midpoint value: 2 Match!One-friend recursion vs iteration. 1. Your objective is to receive the tuple a1, a2,..., a and return the tuple an, an1,..., a1 that has been inverted. You will only take an element off of one end or put an element back on one end because you are being lazy. But you have friends in recursion who can assist you.Please provide the recursive code as well as a paragraph with the friend's description of the algorithm.2. Now imagine that you lack friends but have a stack. Quickly design an iterative programme to address this issue. Include loop invariants and other crucial stages that are necessary to describe an iterative method.3. Trace both of these scripts separately. On a computer, step by step compare and contrast their calculations.Iteration versus one-friend recursion. 1. Your job is to accept the tuple a1, a2,..., a and return the tuple an, an1,..., a1 that has been reversed. You will only take an element off of one end or put an element back on one end because you are being indolent. But you have allies in recursion who can assist you.Please include the recursive code as well as a paragraph with the friend's description of the algorithm. 2. Now imagine that you lack pals but have a stack. (Refer to Chapter 3. Quickly design an incremental programme to address this issue. Include loop invariants and other crucial stages that are necessary to describe an iterative algorithm. 3. Trace both of these scripts separately. Compare and contrast their computerised calculations step by step.
- Question 6 Suppose you are writing an algorithm to merge k sorted arrays of size n into a single sorted array of size kn. You write an algorithm to do so that (1) makes a recursive call to merge the first k/2 arrays, (2) makes another recursive call to merge the remaining k/2 arrays, then (3) merges the results from the calls in (1) and (2). Suppose the cost of merging two sorted arrays of sizes a and b is a+b. Suppose you are sitting at the root of the recursion tree, where the last two arrays of size kn/2 will be merged. What will be the total cost of the algorithm at this level of the tree? Give your answer as an expression in terms of n and k (in simplest form). nk*log(nk) Question 7 Given the recursive algorithm above for merging k sorted arrays, what will be the total cost of the algorithm at the bottom of the recursion tree (the sum of the work performed at the leaves)? You can assume that k is a power of 2. Give your answer as a simplified expression in terms of n and k.Let n be a positive integer and let MaxCrossing(n) be a function that returns the maximum number of line crossings that you can create by drawing n straight lines. Write down a recursive formula for MaxCrossing(n) and analyze the time complexity of the corresponding recursive algorithm. You must write a formal recursive formula including the base case and general recursive step.Q4. Recursion Find how many possible combinations that a number can be decomposed into the multiple of integers (smaller than the number itself) by a recursion function.Suppose we have a positive number Y as input, and it need to be decomposed into the multiple of several integers, Yi, where each Yi, is smaller than Y(e.g., Y=Y1∗Y2∗ Y3∗...∗Yn). In addition, these decomposed integers can only be arranged in an ascending order (Y1