Q2) Assume the insertion sort is applied on the array [44, 55, 88, 11, 55, 66]. What is the content of this array after three iterations of the outermost loop of the insertion m sort algorithm? I a) [11, 44, 55, 88, 55, 66] b) [44, 55, 11, 88, 55, 66]. c) [11, 44, 55, 55, 66, 88]. d) [11, 55, 77, 44, 66, 88].
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- Algorithms Assignment Quicksort is a divide and conquer algorithm that re-order the elements over the same input array (to be distinguished from the quicksort version that implements out-place re-ordering). There are two basic operations in the algorithm, swapping items in place and partitioning a section of the array. In light of this, write a report about the quicksort algorithm, which includes the following: • Discuss sorting as a problem and the algorithms used for sorting (briefly discuss merge-sort, insertion sort, etc.). • Discuss and explain the quicksort algorithm (Step, Pseudo-code). • Implement the algorithm using Java/Python and add comments to the code. Show the output of the algorithm (screenshots). • Analyze the best, worst and average case. Provide and analyze example inputs for the best, worst and average cases (use the implementation). Some good references: https://www.geeksforgeeks.org/quick-sort/ https://en.wikipedia.org/wiki/Quicksort1.""Implementation of the Misra-Gries algorithm.Given a list of items and a value k, it returns the every item in the listthat appears at least n/k times, where n is the length of the array By default, k is set to 2, solving the majority problem. For the majority problem, this algorithm only guarantees that if there isan element that appears more than n/2 times, it will be outputed. If thereis no such element, any arbitrary element is returned by the algorithm.Therefore, we need to iterate through again at the end. But since we have filtredout the suspects, the memory complexity is significantly lower thanit would be to create counter for every element in the list. For example:Input misras_gries([1,4,4,4,5,4,4])Output {'4':5}Input misras_gries([0,0,0,1,1,1,1])Output {'1':4}Input misras_gries([0,0,0,0,1,1,1,2,2],3)Output {'0':4,'1':3}Input misras_gries([0,0,0,1,1,1]Output None""".expl.Computer Science 1)What are the steps in the selection sort algorithm? Group of answer choices Split the array into two subarrays, sort each subarray, and append the two arrays together. Starting at index 0, search the entire array to find the smallest value and swap the smallest value with the value at index 0. 2)Suppose there an integer threshold such that the expression n2 is equal to the expression 9n-8 at that threshold, and is larger for all integers values larger than the threshold. What does this mean?
- AIM: Write a program to do Binary Search using a given Search Key in a Sorted Linear Array 'A' which has N values in it. Description: The binary search algorithm can only be used with sorted array and eliminates one half of the elements in the array being searched after each comparison. The binary search algorithm applied to our array A works as follows: Algorithm: (Binary Search) Here A is a sorted Linear Array with N elements stored in it in sorted order and SKEY is a given item of information to search. This algorithm finds the location of SKEY in A and if successful, it returns its location otherwise it returns -1 for unsuccessful. BinarySearch (A, N, SKEY) [Initialize segment variables.] 1. Set START=0, END=N-1 and MID=int((START+END)/2). 2. Repeat Steps 3 and 4 while START ≤ END and A[MID]+SKEY. 3. If SKEY< A[MID] Then Set END=MID-1. Else Set START=MID+1. [End of If Structure.] 4. Set MID=int((START +END)/2). [End of Step 2 loop.] 5. If A[MID] = SKEY then Set LOC= MID Else Set…Task using C language Write a program that checks both of the following conditions hold for a given array a1, a2, …, an. If the conditions hold, display “yes”, otherwise, display “no”. a1 < a2 < … < an For every i from 2 to n, ai isn’t divisible by ai-1. Requirements Follow the format of the examples below. The program reads in the number of elements of the array, for example, 4, then read in the numbers in the array, for example, 3 6 8 9. In the main function, declare the input array after reading in the number of elements of the array, then read in the elements. Examples (your program must follow this format precisely) Example #1 Enter the length of the input array: 7Enter the array elements: 2 5 4 1 6 9 12Output: no Example #2 Enter the length of the input array: 6Enter the array elements: 2 7 13 19 23 43Output: yes2 Problem Statement You are given a number n. There is an array of strings that contains all the binary strings of length n where each string represents the plantation system where '1' represents plant A and '0' repres According to research if any two plant A comes together then they will stop the growth of the neighbors also. Your task is to find the number of plantations in which growth will not be affected. Note-Since the answer can be too long, return the answer modulo 1e9+7. Constraints: 1 <= n <= 100000 B Rules E Finish Input Format The first line contains an integer n. Output Format Print k-the number of strings satisfying the condition. Sample Testcase #0 Testcase Input Light Theme Java Testcase Output ENG € 40 IN
- bool ok(int q[]) which takes an array q and returns true if the array represents a valid configuration of the eight queens and returns false otherwise. 4. Write a functionSection A: Multiple Choice Questions : Q1: Consider searching element 45 using binary search in an array A [ ] = { 23, 34, 45, 67, 78, 54, 87, 91 }. The returned index would be a) Index [0] b) Index [2] c) Index [3] d) None of these Q2: In the context of recursive search a) Recursion terminates when the item is found b) Same function is called again and again c) Slower than iterative search d) All options are correct Q3: Which one of the following is an approach for a systematic trial and error to search an item? a) Binary search b) Backtracking c) Recursion d) Iteration Q4: In terms of time efficiency, the following method is ____. public int function(int n) { int result = 1; for (int k = 1; k returnType methodName(methodParameters) c) methodModifiers returnType methodName (methodParameters) d) methodModifiers returnType methodName(methodParameters) Q8: Given a function f(n) = n2 + 20n on an input parameter n, which of the following is true a) f(n)=O(1) b) f(n)=O(n) c)…*Data Structures and Algorithm Professor Holmes came up with the idea of a sorting algorithm that he calls Trinary Sort which he claims is asymptotically faster than merge sort, despite being similar in logic. Unlike merge sort, trinary sort splits the input list into three roughly equal parts at each step of the recursion as long as the list is splittable (i.e., has at least 3 elements in this case). The merge operation, similar to what it does in mergeSort, takes three already sorted subarrays, and merges them. (a) In merge sort, merge operation makes exactly n−1 comparisons in total to merge two lists of size n/2 in the worst case, which takes O(n) time. How many comparisons will the merge operation of Trinary sort make in the worst case to merge three sublists of size (n/3) (give an exact number)? Why? What would be the asymptotic bound? (b) What is the total running time of the Trinary Search algorithm? Show it using the tree expansion method.
- True or False For each statement below, indicate whether you think it is True or False If you have an array with no “holes”, the append function performs at O(1) Inserting an element at the front and shifting all elements performs significantly worse than appending an element at the end of the list For the insert function, if the array is empty, there are no comparison operations that need to be performed and you can immediately add the new element Binary search can be used on an unsorted array to significantly improve its performance from O(n) to O(1) Because the update algorithm depends on using linear search, its performance is O(1) in the worst case scenario True If you search for and delete an element in an unsorted array and then shift the rest of the elements to fill the hole, the worst case performance is O(n) If you search for and delete an element in an unsorted array and then move the last element to fill the hole, the worst case performance is O(n)Problem 14: Sequential Search: You are required to write a function that can search in an array in a sequential way. The function should return the index of the item that matches the search in case of a successful search, or -1 in case of search failure.True or False For each statement below, indicate whether you think it is True or False If you have an array with no “holes”, the append function performs at O(1) Inserting an element at the front and shifting all elements performs significantly worse than appending an element at the end of the list For the insert function, if the array is empty, there are no comparison operations that need to be performed and you can immediately add the new element Binary search can be used on an unsorted array to significantly improve its performance from O(n) to O(1)