Kruskal's Algorithm: Kruskal's algorithm is a minimum-spanning-tree algorithm which finds an edge of the least possible weight that connects any two trees in the forest. This algorithm is a Greedy Algorithm. The steps to find a MST using this algorithm are as follows: Sort all the edges in non-decreasing order of their weight. Pick the smallest edge. Check if it forms a cycle with the spanning tree formed so far. If cycle is not formed, include this edge. Else, discard it. Repeat step2 until there are (V-1) edges in the spanning tree. Example with 10 vertices and 20 weighted edges:

Given a binary tree T and a source node s in it, provide the pseudocode for an iterative algorithm to traverse T starting from s using breadth-first traversal, also known as level-order traversal. Each node in T contains an integer key that can be accessed. Each time a node is visited, its key should be printed. Note: You do not have to implement your algorithm.

In the worst-case scenario, binary tree sort employing a self-balancing binary search tree requires O(n log n) time.

Write Kruskal’s algorithm with the union–find data structure incorporated is as follows. pre-cond: G is an undirected graph. post-cond: The output consists of a minimal spanning tree.

Let T be a binary search tree with n nodes, in which n> 0. When T is linear, the search algorithm makes key comparisons, in the unsuccassful case.

Draw the binary search tree if the pre-order and in-order traversals of that binary search tree are given as below: Pre-order traversal: 7, 4, 2, 3, 6, 5, 12, 9, 8, 11, 19, 15, 20 In-order traversal: 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 19, 20

In a binary search tree, to remove a node N that has parent P and one child C, we do the following: Group of answer choices If C is the right child of N, we make C the right child of P, and if C is the left child of N, we make C the left child of P If C is the right child of N, we make C the left child of P, and if C is the left child of N, we make C the right child of P If N is the left child of P, we make C the left child of P and if N is the right child of P, we make C the right child of P If N is the left child of P, we make C the right child of P and if N is the right child of P, we make C the left child of P none of the above

Is there a special reason why Prim's method always produces a Minimum Spanning Tree?

Suppose we have the following Binary Search Tree. 12 4 16 14 18 10 11 Algorithm Write up. Write an algorithm to determine the leaf nodes of the given tree reclusively. Output: The leaf nodes of the given tree are: 29 11 14 18

Cliques The Clique problem is finding the subsets of vertices all adjacent to each other. The maximum clique is the largest complete subgraph with every vertex connected by an edge. Cliques are studied in social networks, bioinformatics, and computational chemistry. Describe the brute force algorithm to find the maximum clique. What algorithm complexity class is the brute force solution to the clique problem? What time complexity is the brute force algorithm to find the maximum clique? How does the graph of a clique differ from the graph of a social network influencer? List the number of algorithm steps for graphs with the following vertex count: 10,100,1000

Show that, in UPGMA algorithm, a node is always lies above its child nodes.

Given a sorted array of n comparable items A, create a binary search tree from the items in A which has height h <= log: n. Your algorithm must create the tree in O(n) time.