Suppose we implement the tree-based union-find data structure, but we don't use the union-by-size it is...
Suppose we have 20 singleton sets, numbered 0 through 19, and we call the operation union(find(i),find(i + 5)), for i = 0, 1, 2, . . . , 14. Draw a picture of a tree-based representation of the sets that result, assuming we don’t implement the union-by-size and path compression heuristics.
Suppose we want to implement a circular queue using an array that has an initial capacity (maximum number of elements) MAX. A circular queue is like a regular queue except that elements can be enqueued or dequeued by wrapping around it. Assume we enqueue on the tail and dequeue from the head. An example circular queue with sample operations is shown below: head head tail head tail tail head Enqueue(9) a) Write a program in C that implements this circular...
Suppose a binary tree data (in tiny written size) is stored in an array (A) as given below and root is placed at “0”index. Note the array indices are in larger written size (0 to 74). Show the traversal data of the given tree for a) In-Order Traversal b) Post Order Traversal A 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 3 28 13 36 15 9 22 44 7 10 75 33 19 15...
Suppose we have an array-based queue (circular buffer) of size 6: int data[6]; int front = 0, back = 0; void enqueue(int x) { data[back] = x; back = (back + 1) % 6; } void dequeue() { front = (front + 1) % 6; } and we perform the following series of queue operations: enqueue(1); dequeue(); enqueue(2); dequeue(); enqueue(7); enqueue(3); enqueue(5); dequeue(); dequeue(); enqueue(4); enqueue(6); Write the state of the queue array after each operation, and at the end,...
Weird recursion tree analysis. Suppose we have an algorithm that on problems of size n, recursively solves two problems of size n/2, with a “local running time” bounded by t(n) for some function t(n). That is, the algorithm’s total running time T(n) satisfies the recurrence relation T(n) ≤ 2T(n/2) + t(n). For simplicity, assume that n is a power of 2. Prove the following using a recursion tree analysis (a) If t(n) = O(n log n), then T(n) = O(n(log...
1.Fix any tree T on 10 vertices. Draw the recursion tree of the algorithm Find-size-node when run on the input T with a being the root of T. Can you use this to give a bound on the running time of T? 2. Consider the following problem. Check-BST • Input: A binary tree T • Output: 1 if T is a binary search tree, and 0 otherwise. Give an efficient algorithm for this problem. 3.Give a recursive algorithm for the...
You must implement a BlockedList class that implements the List interface. You may use any of the classes in JCF or in the textbook code. The constructor for this class takes an integer block size b and the implementation should have the following performance characteristics: a) get(i) and set(i,x) should run in O(1) time per operation b) add(i,x) and remove(i) should run in O(b+ min{i, n-i}/b) amortized time per operation. Any solution matching this specification is acceptable. However, the runtime...
C++ Question 1 5 pts A binary heap's structure is an AVL tree a complete binary tree a particular case of binary search tree a sparse tree Question 2 5 pts When using a hash table with quadratic probing, and the table size is prime, then a new element can always be inserted if the table is at least half empty the table is full the table is at least half full the table is larger than any data value...
Use R to find to find the answers to the problems 2. (25 points) Suppose that we have a sample of size n 64, we know the population standard deviation is σ 48, and we are considering a normally distributed population, we want to test the hypotheses: Ho : μ-200 Hi 200 We are going to use a z-test because σ is known. We will use a significance level of:-0.05. (a) What is the critica z value? In other words,...