I only need help with the second group of questions (#2). I have my answers but

Question

I only need help with the second group of questions (#2). I have my answers but I'd like to see if I'm correct. Please help and thank you.

Update: I used the recursion tree from https://www.chegg.com/homework-help/questions-and-answers/cmsc-451-homework3-1-shown-code-insertion-sort-consisting-two-recursive-methods-replace-tw-q30769385?trackid=3fc59e06&strackid=59495649&ii=5

Shown below is the code for the insertion sort consisting of two recursive methods that replace the two nested loops that would be used in its iterative counterpart: 1. void insertionSort (int array[]) insert (array, 1); void insert (int[] array, int i) if (i 0 && array [i - 1] > value) array [i] insert array [1-1]; shift (array, value, 1-1); return insert; Draw the recursion tree for insertionsort when it is called for an array of length 5 with data that represents the worst case. Show the activations of insertionsort, insert and shift in the tree. Explain how the recursion tree would be different in the best case. 2. Refer back to the recursion tree you provided in the previous problem. Determine a formula that counts the numbers of nodes in that tree. What is Big-O for execution time? Determine a formula that expresses the height of the tree. What is the Big-0 for memory?

Explanation / Answer

The execution time for the worst case complexity is O(N^2)

The maximum space complexity is O(logn)

The height of the tree is determined by the formula: 2T(n/2)+O(1)

So, the time complexity will be O(N)

Big O notation is used in Computer Science to describe the performance or complexity of an algorithm. Big O specifically describes the worst-case scenario, and can be used to describe the execution time required or the space used (e.g. in memory or on disk) by an algorithm.

The number of nodes in the recursion tree = 2^h+1 - 1 = 2^log(n)+1 - 1

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