i need solution for lap 5 please

Exercise 1: Pre-sorting Consider the problem of nding the distance between the two closest numbers in an array of n numbers. (The distance between two numbers it and y is computed as Ix - yl .) a. Design a presortlng-based algorithm and implement it in your preferred language. b. Solve the above problem using brute-force approach. Implement in your preferred language. c. Compare the efficiency of the above two algorithms. Exercise 2: AVL Trees Construct AVL trees by inserting the elements successively, starting with the empty tree. a) 1, 2, 3, 4, 5, 6 b) 6, 5, 4, 3, 2, 1 c) a, 6, 5, 1, 2, 4 (Note: Observe the final trees and you will nd that although all of them have the same data, the tree are not necessarily the same.) Exercise 3: Multi-way Trees A way to reduce the height of tree and ensure balance is to allow multiple children of nodes. In your class you learned 2-3 trees which allows up to 2 keys in a node, and the number of children is equal to the number of keys + 1. Bitrees extend this concept to any arbitrary number of keys (usually number of keys is even and number of children (equal to number of keys+1) is odd). Assume we want to design a 5-way B-Tree. This will mean that there can be maximum 4 keys in a node, and if the number of keys becomes 5, we can split it into two (the same way we split 2-3 tree when number of keys becomes 3). Design a 5-way B-tree. Starting with an empty tree, insert the following keys in order. 2, 3, S, 7, 10, 50, 22, 44, 45, 55, 66, 68, 70, 17, 6, 21, 67