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- 4. Consider the graph G, shown below, which is simply a copy of K5. 02 V3 5 V1 24 V5 How many distinct spanning trees does G have? (Hint: Break up your search by the isomorphism type of the tree, as discovered on the previous page. So for example, start by counting the paths of length 5 in G. Then proceed to the next type of tree with 5 vertices. The total number of trees is 125, but please use this answer only to check that your solution is complete!)Answer the following questions about treeB. a. What is the height of the tree? b. Which nodes are on level 3? c. Which levels have the maximum number of nodes that they could contain? d. What is the maximum height of a binary search tree containing these nodes? Draw such a tree. e. What is the minimum height of a binary search tree containing these nodes? Draw such a tree. f. What is the order in which the nodes are visited by an ignorer traversal? g. What is the order in which the nodes are visited by a preorder traversal? h. What is the order in which the nodes are visited by a postorder traversal?Given a binary tree, write a function to check if it is a valid binary search tree (BST). Discuss the approach you would take to validate the BST properties and handle edge cases.
- Java ... Yatin is playing PUBG and he has reached a place with a large staircase in front of him. And there is an enemy at each landing of the staircase. This is not the actual staircase. He is looking at the staircase from sideways. The staircase is analogous to a binary tree with each of its nodes as a landing of the staircase and each of its edges as stairs from one landing to another. Yatin wants to kill the maximum possible number of enemies. He can kill every person he can see from his position with his suppressed sniper gun. But he can see only the persons at the leftmost standing at each level and cannot see the rest. Before starting shooting them, he wants to know how many persons he can kill. He is busy keeping an eye on the enemies. So he wants you to find out the maximum number of people he can kill from that location by providing you with the analogous a binary search tree. [ Note: Players do not change their position after one player has died, i.e. the leftmost node…Exercise 8. In a red-black tree which is initially empty, we insert in order nodes with keys 1,2,3,4. Draw the tree after these insertions (single-circled nodes are black, and double-circled nodes are red).Consider the Binary Search Tree below: 50 25 20 35 70 90 15 23 100 30 45 65 75 05 150 (a) Give the order in which the nodes will be visited in a preorder traversal. (b) List all the nodes in level 3 of the tree. (c) How many leaf nodes does the tree have? (e) Is the given tree an AVL tree? If it is an AVL tree, discuss how it conforms to the definition of an AVL tree. If it is not an AVL tree, explain how u will change the tree into an AVL tree. (d) If we delete node 80, which node should be its replacement? you
- Is it possible for a minimum spanning tree to have a cycle? Why or why not?2. We are given a complete binary tree with height h and n nodes. The link between a node and its left child is labeled as 0 and the link between a node and its right child is labeled as 1. A path from the root to each external node at the last level can be labeled by an h-tuple (X1, X2, ..., xh) of 1s and Os that lie on its links. See the following example: 0 0 1 1 0 0 1 0 (0,0,0) (0,1,1)Find the canonical DFS code for the graph in Figure 11.12. Try to eliminate some codes without generating the complete search tree. For example, you can eliminate a code if you can show that it will have a larger code than some other code. Figure 11.12. Graph for Q1.
- Are you familiar with the characteristics of minimum spanning trees? C is taken for granted.Consider the Binary Search Tree below: (a) Give the order in which the nodes will be visited in a preorder traversal. (b) List all the nodes in level 3 of the tree. (c) How many leaf nodes does the tree have? (d) If we delete node 80, which node should be its replacement? (e) Is the given tree an AVL tree? If it is an AVL tree, discuss how it conforms to the definition of an AVL tree. If it is not an AVL tree, explain how you will change the tree into an AVL tree.Which of the following graphs are trees? (Tree or Not A Tree) 1. A graph G with V(G)={a,b,c,d,e} and E(G)={{a,b},{a,c},{d,e}} (Tree or Not A Tree) 2. A graph G with V(G)={a,b,c,d,e} and E(G)={{a,b},{b,c},{c,d},{d,e}} (Tree or Not A Tree) 3. A graph G with V(G)={a,b,c,d,e} and E(G)={{a,b},{a,c},{b,c},{c,d},{d,e}} (Tree or Not A Tree) 4. A graph G with V(G)={a,b,c,d,e} and E(G)={{a,b},{a,e},{b,c},{c,d},{d,e}}