(Recursive binary search) The binary search algorithm given in this chapter is nonrecursive. Write and implement a recursive version of the binary search algorithm. Also, write a version of the sequential search algorithm that can be applied to sorted lists. Add this operation to the class orderedArrayListType for array-based lists. Moreover, write a test program to test your algori

can someone help me with this in C++ (not Java) create a program that reads in two matrices from two different text files. Should use a singly or double linked list to store the two matrices and perform the following operations on them: - Add, Subtract, Mulitply, Transpose, and Determinant Requirements: Use singly or doubly linked list date structures only: - No other library methods or existing collection framework. - No use of Array, ArrayList, List, or Vectors for storing. - No two-dimensional arrays. - Input files can only be read Exactly Once for all operations. For the determinant operation, you may augment your linked list node to retain row/column id and employ recursion to directly implement the standard method for computing determinant of a matrix. You are encouraged to design your own node representation (e.g., each node element has two pointers: one to its next right and another to its next bottom element that facilitate both horizontal and vertical traversals like one gets…

Modify the recursive Fibonacci function to employ the memoization technique discussed in this chapter. The function creates a dictionary and then defines a nested recursive helper function named memoizedFib. You will need to create a dictionary to cache the sum of the fib function. The base case of the fib function is the same as before. However, before making any recursive calls, the helper function looks up the value for the function’s current argument in the dictionary (use the method get, with None as the default value). If the value exists, the function returns it and skips any recursive calls. Otherwise, after the helper function adds the results of its two recursive calls, it saves the sum in the dictionary with the current argument of the function as the key. Note: The program should output in the following format: n      fib(n) 2       1 4       3 8       21 16      987 32      2178309 ---------------------------------------------------------------------------------- def…

(a)    Write a method   public static void insert(int[] a, int n, int x)          that inserts x in order among the first n elements of a, assuming these elements are arranged in ascending order.   Do NOT use arraylists.   x is the last element in a. n does not include x. (b)    Using the insert method from Part (a), write a recursive implementation of Insertion Sort.