Suppose that A is an array whose integer elements are organized into a max-heap. Also suppose that e is an integer. Write an algorithm IS-IN-MAX-HEAP(A, e) that tests if e is an element of A. Your algorithm must not change A, and it must not make copies of A. It must avoid visiting all elements of A where possible—so it must not use linear search. You may state your answer in English, in Cormen’s pseudocode notation, or in a programming language.
Suppose that A is an array whose integer elements are organized into a max-heap. Also suppose...
5. A three-heap with n elements can be stored in an array A, where A[O] contains the root of the tree. a) Draw the three-heap that results from inserting 5, 2, 8, 3, 6, 4, 9, 7, 1 in that order into an initially empty three-heap. You do not need to show the array representation of the heap. You are only required to show the final tree, although if you draw intermediate trees. b) Assuming that elements are placed in...
1. Suppose that an array al] is a max-heap that contains the distinct integer keys 1, 2,.., N with N> 7. The key N must be in gl1] and the key N-1 must be in either al2) or al3) a. Give all possible positions for the key N-2 as a function of N. b. Repeat the same question for the key 2
Suppose that d ≥ 2 is an integer constant. In a d-ary tree, each node has at most d nonempty subtrees. For example, the trees discussed along with heaps had d = 2. We can represent a nearly complete d-ary tree with n nodes using an array whose indexes range from 0 to n−1. (This is different from Cormen’s arrays, whose indexes range from 1 to n.) Suppose that i is the index of a node in the array....
1. Suppose that d ≥ 2 is an integer constant. In a d-ary tree, each node has at most d nonempty subtrees. For example, the trees discussed along with heaps had d = 2. We can represent a nearly complete d-ary tree with n nodes using an array whose indexes range from 0 to n−1. (This is different from Cormen’s arrays, whose indexes range from 1 to n.) Suppose that i is the index of a node in the...
Java Program Create a class to store an array of with enough space to store 10 integer values. Using the principle of recursion, implement the following: *getSize : returns the size of the array. *get (i): returns the i-th element of the array. If the element does not exist, it throws a "NoSuchElementException” which is a subclass of Java class RunTimeException. *add (val): inserts value as the last element of the array. If necessary, double the size of the current...
Suppose you have a sorted array of positive and negative integers and would like to determine if there exist some value of x such that both x and -x are in the array. Consider the following three algorithms: Algorithm #1: For each element in the array, do a sequential search to see if its negative is also in the array. Algorithm #2:For each element in the array, do a binary search to see if its negative is also in the...
Suppose v is an array with 100 int elements. If 100 is assigned to v[100], what happens? Show the code. An array of 1000 integers is declared. What is the largest integer that can be used as an index to the array? Shows the code. Consider the declaration: int v[1]; What is the index of the last element of this array? Declare an array named a of 10 int elements and initialize the elements (starting with the first) to the...
3. [5 marks] Suppose T is a binary tree that stores an integer key value in each node. Assume the following notation/operations on a binary tree. » the key T.key is the root node's integer key value . the left child T.left is T's left subtree, which is possibly an empty tree (or null) the right child T.right is T's right subtree, which is possibly an empty tree (or null) (a) Write an efficient algorithm FINDMAxPrODuCT(T) in pseudocode that returns...
In Java, Implement a class MyArray as defined below, to store an array of integers (int). Many of its methods will be implemented using the principle of recursion. Users can create an object by default, in which case, the array should contain enough space to store 10 integer values. Obviously, the user can specify the size of the array s/he requires. Users may choose the third way of creating an object of type MyArray by making a copy of another...
A method called linearSearch(), which takes as parameters an array of int followed by three values of type int, and returns a value of type int. The first int parameter represents a key, the second int parameter represents a starting position, and the third int parameter represents an end position. If the key occurs in the array between the start position (inclusive) and the end position (exclusive), the method returns the position of the first occurrence of the key in...