Give an equation to calculate the minimum number of nodes in a complete binary tree of height h. This means that every height 1,..,h-1 is completely full.
the minimum number of nodes in a complete binary tree of height h means All h-1 levels are completely full and last level have one node minimum number of nodes in a complete binary tree of height h = 2^0 + 2^1 + …. 2^(h-1) - 1 = 2^h - 1
Give an equation to calculate the minimum number of nodes in a complete binary tree of...
Trees and Heaps 1. Show that the maximum number of nodes in a binary tree of height h is 2h+1 − 1. 2. A full node is a node with two children. Prove that the number of full nodes plus one is equal to the number of leaves in a nonempty binary tree. 3. What is the minimum number of nodes in an AVL tree of height 15? 4. Show the result of inserting 14, 12, 18, 20, 27, 16,...
Refer to the definition of Full Binary Tree from the notes. For a Full Binary Tree T, we use n(T), h(T), i(T) and l(T) to refer to number of nodes, height, number of internal nodes (non-leaf nodes) and number of leaves respectively. Note that the height of a tree with single node is 1 (not zero). Using structural induction, prove the following: (a) For every Full Binary Tree T, n(T) greaterthanorequalto h(T). (b) For every Full Binary Tree T, i(T)...
2. A complete binary tree is defined inductively as follows. A complete binary tree of height 0 consists of 1 node which is the root. A complete binary tree of height h +1 consists of two complete binary trees of height h whose roots are connected to a new root. Let T be a complete binary tree of height h. Prove that the number of leaves of the tree is 2" and the size of the tree (number of nodes...
(2 points) A full binary tree has a start node, internal nodes, and leaf nodes. The number of leaf nodes of this binary tree is 256. a) What is the height of the tree? b) How many internal nodes are in this tree?
Show that the tree height of a height-balanced binary search tree with n nodes is O(log n). (Hint: Let T(h) denote the fewest number of nodes that a height-balanced binary search tree of height h can have. Express T(h) in terms of T(h-1) and T(h-2). Then, find a lower bound of T(h) in terms of T(h-2). Finally, express the lower bound of T(h) in terms of h.)
Program in JAVA: A Perfect binary tree is a complete binary tree with all levels fully filled. Add a method in the BST class to return true if the tree is a perfect binary tree.(Hint: The number of nodes in the nonempty perfect binary tree is 2 raised to the power of height - 1) (/** returns true if the tree is a perfect binary tree, boolean isPerfectBST() **/)
A binary search tree includes n nodes and has an height h. Check all that applies about the space complexity of TREE-MINIMUMX) TREE-MINIMUM () 1 while x. left NIL 2 3 return x x x.left O it is e (lg n) ■ it is 0(h). D it is e (1) ■ It is in place ■ it is Θ (n) A binary search tree includes n nodes and has an height h. Check all that applies about the space complexity...
A binary tree is a complete binary tree if all the internal nodes (including the root node) have exactly two child nodes and all the leaf nodes are at level 'h' corresponding to the height of the tree. Consider the code for the binary tree given to you for this question. Add code in the blank space provided for the member function checkCompleteBinaryTree( ) in the BinaryTree class. This member function should check whether the binary tree input by the...
2. A regular binary tree is a binary tree whose internal nodes all have two subtrees (left and right). In other words, all their nodes have either zero subtrees (in which case they are leaves) or two subtrees (in which case they are internal nodes). Suppose that you have a boolean function that tells you, for each node of the tree, whether it is a leaf or not (call it: leaf(n), for node n). a) Write a recursive function that...
Form a recurrence relation for the minimum number of full nodes F(h) in a AVL tree. A node is full if it has exactly two children