ose you have algorithms with the two running times listed below. Suppose you have a computer that can perform 6 operations per second, and you need to compute a result in at most an hour of computation. For each of the algorithms, w

The travel time function of an algorithm has the form: f(n) = 3n^2 + 4n + 8  Prove that Big Oh is n^2 which is denoted by f(n) = O(n^2);

Given an unsorted array of integers, write a function in Python to find the length of the longest increasing subsequence (LIS) in the array. For example, given the array [10, 9, 2, 5, 3, 7, 101, 18], the LIS is [2, 3, 7, 101], which has a length of 4. Your solution should have a time complexity of O(n log n), where n is the length of the input array. Here's some code to get you started: def longest increasing_subsequence(arr): # TODO: implement function pass # example usage arr = [10, 9, 2, 5, 3, 7, 101, 18] print(longest_increasing_subsequence(arr)) # should print 4

Consider the following three sorting algorithms: Insertion Sort, Heapsort, and Quicksort. Here are three statements. A. Iam an incredibly fast sorting algorithm that runs in O(n log n) time on average, though my worst case run time is O(n2). B. I run very quickly for small values of n, but unfortunately am really slow when n is large. My average run time is O(n2). C. I am an in-place sorting algorithm whose average case and worst case running time is O(n log n). For each statement (A, B, C), determine the correct sorting algorithm.