Given a sorted array arr[] of size N. Find the element that appears only once in the array. All other elements appear exactly twice. 
Example 1:
Input:
N = 11
arr[] = {1, 1, 2, 2, 3, 3, 4, 50, 50, 65, 65}
Output: 4
Explanation: 4 is the only element that appears exactly once.

Given a sorted and rotated array A of N distinct elements which is rotated at some point, and given an element key. The task is to find the index of the given element key in the array A.
Example 1:
Input: N = 9 A[] = {5, 6, 7, 8, 9, 10, 1, 2, 3} key = 10
Output: 5
Explanation: 10 is found at index 5.

Given a sorted array of size N and an integer K, find the position at which K is present in the array using binary search.
Example 1:
Input:
N = 5
arr[] = {1 2 3 4 5} 
K = 4
Output: 3
Explanation: 4 appears at index 3.

Given 2 sorted arrays Ar1 and Ar2 of size N each. Merge the given arrays and find the sum of the two middle elements of the merged array.
Example 1:
Input: N = 5, Ar1[] = {1, 2, 4, 6, 10}, Ar2[] = {4, 5, 6, 9, 12}
Output: 11
Explanation: The merged array looks like {1,2,4,4,5,6,6,9,10,12}. Sum of middle elements is 11 (5 + 6).

Quick Sort is a Divide and Conquer algorithm. It picks an element as pivot and partitions the given array around the picked pivot. Given an array arr[], its starting position low and its ending position high.
Implement the partition() and quickSort() functions to sort the array.
Example 1:
Input: N = 5, arr[] = { 4, 1, 3, 9, 7}
Output: 1 3 4 7 9

Given an array arr[], its starting position l and its ending position r. Sort the array using merge sort algorithm.
Example 1:
Input: N = 5, arr[] = {4 1 3 9 7}
Output: 1 3 4 7 9

Given two sorted arrays arr1 and arr2 of size N and M respectively and an element K. The task is to find the element that would be at the k’th position of the final sorted array.
Example 1:
Input: arr1[] = {2, 3, 6, 7, 9}, arr2[] = {1, 4, 8, 10}, k = 5
Output: 6
Explanation: The final sorted array would be - 1, 2, 3, 4, 6, 7, 8, 9, 10. The 5th element of this array is 6.