1 -You are given an unsorted list containing 107 different items. You have been asked to find the 1000 most expensive items. To do so you have available two algorithms: Algorithm-A and Algorithm-B that work as follows: Algorithm-A performs a linear search on the list (with complexity O(n)) 1000 times. Algorithm-B first converts the list into an array, then sorts the array (operation that costs O(n lg n)), and finally returns the top 1000 items. Lets assume that searching for 100 items in the entire unsorted list takes 0.1 milliseconds, and lets assume that sorting 100 items also takes 0.1 milliseconds. Which algorithm should be used? Carefully explain why. Assume that the running time is made only by the dominant term

2-Given an array, explain whether after running Max-Heapify starting from the first element the final array will be a heap. Provide an array, corresponding to a heap of height 3, where the previous statement holds.