Write a backtracking algorithm for the n-Queens problem that uses a version of procedure expand instead of a version of procedure checknode.

The PARTITION(A) procedure inputs an array A, and takes the fınal element x = A[r] as the pivot element. The output is an array where all elements to the left of x are less than x, and all elements to the right of x are greater than x. An example is provided on pg. 172 of the textbook. In this example, A = [2,8,7,1,3,5,6,4]. The pivot element is x=4 (highlighted in red). The end result of PARTITION is [2,1,3,4,7,5,6,8]. Notice that all elements to the left of 4 are less than 4, and all elements to the right of 4 are greater than 4. I strongly encourage you to go through this example, step by step. Let A = [1,2,7,8,9,6,3,4,5]. Determine PARTITION(A).

A majority element is an element that makes up more than half of the items inan array. Given a positive integers array, find the majority element. If there is no majority element,return -1. Do this in O(N) time and 0(1) space.Input: 1 2 5 9 5 9 5 5 5Output: 5

The optimised bubble sort offers none of the following benefits over conventional sorts for items that have already been sorted.

Write pseudocode for a divide-and-conquer algorithm for finding the position of the largest element in an array of n numbers.