a. Study the algorithm below and implement quickSort method . Additionally you will also need to implement the "partition" method. After sorting print both the unsorted array and sorted array and also the time it takes to complete sorting.
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- Given n distinct integers on an array and a positive integer K. step1. choose any two integers x and y in the array which differ by at most K, i.e. |x − y| ≤ K. step2. remove the smaller of the two chosen integers. one move is consisting of the two steps above. task is to make moves in this way until no longer able to do so. in some cases, may be unable to make even a single move. Design an algorithm which runs in O(n log n) time and finds the longest sequence of moves. Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English In some initial states, has no valid moves. For example, if n = 5, K = 1 and the numbers are 1, 3, 5, 7, 9, then cannot make any moves and the longest sequence of moves is simply the empty sequence. Use the greedy method.Assume that we have an array in Figure 1. We apply only six steps (rounds) of the outerloop in the bubble sort. Show the content of the array after each round. Note that youneed to show six arrays, one for each round. Please be careful that we need the contentsof the outer loop (not the inner loop)Calculating the Minimum Sum Path in a Triangle (LeetCode Problem)Given a triangle array, return the minimum path sum from top to bottom. For each step, you may move toan adjacent number of the row below. More formally, if you are on index i on the current row, you maymove to either index i or index i + 1 on the next row. public static int minSumPathMemo(int[][] triangle)This method will calculate the minimum sum path in the triangle using the top down strategy. Note thismethod MUST BE recursive and you will need to create a recursive helper method. public static int minSumPathBottomUp(int[][] triangle)This method will calculate the minimum sum path in the triangle using the bottom up strategy. Note thismethod CANNOT be recursive and you should not create any additional helper functions. Extra Challenge: Could you do this using only O(n) extra space where n is the total number of rows in thetriangle? This is method signature class below: package dynamic; public class MinSumPath {…
- Simulate binary search Use array {1, 2, 3, 4, 5, 6, 7} to simulate binary search of 3. For each iteration, you need to write down the value of first, last, and middle after the execution of this statement: middle = (first + last) / 2 follow the loop until you get the search result. After you are done, update the BinarySearchDemo.java class to use this array for search. Compare the print out result to your simulation result.Write a program that takes 20 elements of array from user at run time. Find maximum element of array and swap it with last element of array. Display before and after swappingarray.Question 1: The following algorithm takes an unsorted array of integer numbers as input and sorts it in descending order, by repeatedly doing the following: • first, it searches in the whole array for the greatest element. • it then puts this element to the beginning of the array. • then, it searches the whole array excluding the first element for the greatest value and puts it to the second position. Implement the algorithm according to two different strategies: A. By using the method shiftRight(int[] A, int i, int j): if the maximum element is found in position j and needs to be put into position i, then (i) shift A to the right, starting from position i, while remembering the element in position j that will be overridden; (ii) copy the remembered element to position i. B. By using the method swap(int[] A, int i, int j): if the maximum element is found in position i and needs to be put into position j, then use swap to exchange the element in position i with the element in position…
- Implement the following method to sort the columns in a twodimensional array. A new array is returned and the original array is intact.public static double[ ][ ] sortColumns(double[ ][ ] m) Write a test program that prompts the user to enter a 4 X 4 matrix of doublevalues and displays a new column-sorted matrix. Here is a sample run: Enter a 4−by−4 matrix row by row:0.15 0.875 0.375 0.225 ↵Enter0.55 0.005 0.225 0.015↵Enter0.30 0.12 0.4 0.008 ↵Enter0.07 0.021 0.14 0.2 ↵EnterThe column−sorted array is0.07 0.005 0.14 0.0080.15 0.021 0.225 0.0150.30 0.12 0.375 0.20.55 0.875 0.4 0.225Implement the following method to sort the rows in a two-dimensionalarray. A new array is returned and the original array is intact.public static double[][] sortRows(double[ ][ ] m)Write a test program that prompts the user to enter a 4 x 4 matrix of doublevalues and displays a new row-sorted matrix. Here is a sample run: Enter a 4−by−4 matrix row by row:0.15 0.875 0.375 0.225 ↵Enter0.55 0.005 0.225 0.015 ↵Enter0.30 0.12 0.4 0.008 ↵Enter0.07 0.021 0.14 0.2The row−sorted array is0.15 0.225 0.375 0.8750.005 0.015 0.225 0.550.008 0.12 0.30 0.40.021 0.07 0.14 0.2Given two arrays that are full of integers, recursively merge these two arrays into one large array. The large array should have items from the first array in even indices (0,2,4 ...) and items from the second array in odd indices (1,3,5 ...). Only use recursion to complete this task. You cannot change the method header. public void mergeArrays(int[] arrayOne, int[] arrayTwo, int[] mergedArray){ // Your code here }
- Given an array with n objects colored red,white or blue, sort them so that objects of the same colorare adjacent, with the colors in the order red, white and blue. Here, we will use the integers 0, 1, and 2 to representthe color red, white, and blue respectively. Note:You are not suppose to use the library's sort function for this problem.""".Develop an implementation of insertion sortthat moves larger elements to the right one position with one array access per entry,rather than using exch(). Use SortCompare to evaluate the effectiveness of doing so.Develop an implementation of insertion sortthat moves larger elements to the right one position with one array access per entry,rather than using exch(). Use SortCompare to evaluate the effectiveness of doing so.In the "Common Array Algorithms" section, you learned how to find the position of an element in an array. Suppose you want to find the position of the second match. You could remove the first match and start over, but that would be wasteful. Instead, adapt the algorithm from that section so that it starts the search at a given position, not zero. Complete the following code.