Algorithm 6.1 Spanning Tree Algorithm 1: Input : G = (V, E)  unweighted connected graph G 2: Output : T = (V, ET )  spanning tree of G 3: V ← {s} 4: T ← Ø 5: while V = V do  continue until all vertices are visited 6: select an arbitrary edge (u, v) such that u ∈ T and v ∈ G \ T 7: V ← V ∪ {v} 8: ET ← ET ∪ {(u, v)} 9: end while make Python Implementation of given algorithm

Q: Exercise 11.11 An undirected graph G- (V, E) is called bipartite if it contains no odd cycle, i.e.,…

A: Attaching handwritten solution: Image1:

Q: 48 Given this tree: pAp PATE PVTE What is the length of the path from vertex F to vertex D? 2 QUE (…

A: The problem is based on the basics of trees data structures in programming languages.

Q: 1. Write a Program to implement DFS algorithm and print the DFS sequence for below graph start with…

A: def dfs(graph, start,visited = []):     if start in visited:         return…

Q: Give the following grapn z w 1) Give an adjacency list representation for G

A: Solution for 1st question is mentioned below.

Q: Algorithm 18.6: (P₁, 1st, cnt) agaDivide (Pold, d)

A: algorithm for given function step by step given in next step

Q: Implement the following on the given graph. Prepare adjancey list Implement Breadth first Search…

A: The Adjacency list nothing but a representation of the graph as an array of Linked lists. The index…

Q: ark all the correct statements. If u → v is a back edge, then pre [v] < pre [u] < post [u] < post…

A: Correct statements of the given statements

Q: Single source shortest path Algorithm 1. Implement the algorithm 2. Write comments 3. Screenshot…

A: The code was absolutely right The thing lacking was proper indentation which makes the code flow…

Q: Given the following search space (graph) 6. 4 1 7 3. 8 Find the sequence of states using: BFS…

A: I have answered the question in step 2.

Q: What is the running time of Depth First Search A) O(\E| + |V]) B) O(\E||V|) C) O(\V°) D) O(\E| +…

A: Let us the answers below,

Q: A graph G=(v, e) is a _______ graph, if we can partition V=L u R, s.t. all edges in E go between L…

A: We say that a directed edge points from the first vertex in the pair and points to the second vertex…

Q: Minimum Spanning Tree of a graph includes all its nodes Both the lazy and eager versions of Prims…

A: 1. Minimum Spanning Tree of a graph includes all its nodes. TRUE Explanation: Minimum Spanning Tree…

Q: What graph traversal algorithm uses a queue to keep track of vertices which need to be processed?

A: In computer science,  graph traversal alludes to the most common way of visiting every vertex in a…

Q: 6. Find a Steiner tree of the graph K, with the vertices b, j, d, h by listing the edges that form…

A: The solution is given in the next step

Q: For the next set of questions, consider the directed graph, G2, shown below. Assume that the…

A: The correct answer for the above mentioned question is given in the following steps for your…

Q: Spanning Tree Algorithm 1: Input : G = (V, E)  unweighted connected graph G 2: Output : T = (V, ET…

A: In this question we have to implement the given algorithm of spanning tree algorithm Let's code

Q: Algorithm 7.3 Dijkstra’s Algorithm 1: Input : G = (V, E, w)  connected, weighted graph G and a…

A: Write code for algorithm

Q: Luby’s Algorithm: 1. Input: G = (V, E) 2. Output: MIS I of G 3. I ← ∅ 4. V ← V 5. while V = ∅ 6.…

A: Initialize an empty set I to store the independent set and a set V containing all vertices.While the…

Q: Code: Prim’s MST algorithm. algorithm PrimMST (G)  pre-cond: G is an undirected graph.  post-cond:…

A: Code: Prim’s MST algorithm. The output consists of a minimum spanning tree.

Q: 5. Refer to the following given graph: 7 5 3 7 5 2 3 2 6 1 3 a) Show the adjacency matrix for the…

A: Given the graph , we have to show that adjacency matrix , breadth first traversal, shortest path…

Q: java binary tree:

A: Lets see the solution.

Q: Describe an algorithm to find the shortest path from a certain vertex in a graph to a certain other…

A: 1. Bellman Ford's Algorithm: Bellman Ford's algorithm is used to find the shortest paths from the…

Q: A Topological Sorting Algorithm The basic algorithm for topological sorting is straightforward: 1.…

A: A Topological Sorting AlgorithmThe basic algorithm for topological sorting is straightforward:1.…

Q: Q5. Figure below shows an unweighted graph of 6 vertices. Draw a spanning tree for the graph where…

A: Solution: Que-5)

Q: algorithm PrimMST (G)  pre-cond: G is an undirected graph.  post-cond: The output consists of a…

A: Because which edges are evaluated changes as the algorithm progresses, this is an adaptive greedy…

Q: Perform A* search on the following state space graph, starting at A and reaching G. Draw the search…

A: Given the state space graph we have to perform A* Search starting at A and reaching G.

Q: Algorithm 7.3 Dijkstra’s Algorithm 1: Input : G = (V, E, w)  connected, weighted graph G and a…

A: Given Dijkstra’s Algorithm Algorithm: 1: Input : G = (V, E, w)  connected, weighted graph G and a…

Q: Implement RBFS algorithm and draw the search tree for the following search space. (Assume start…

A: RBFS stands for Recursive Breadth first search and given graph contains 9 vertices that are S, A to…

Q: 4-Clique Problem The clique problem is to find cliques in a graph. A clique is a set of…

A: Introduction: A graph where no two vertices are connected by more than one edge, and no edge begins…

Q: Luby’s Algorithm: 1. Input: G = (V, E) 2. Output: MIS I of G 3. I ← ∅ 4. V ← V 5. while V = ∅ 6.…

A: Luby's Algorithm is a randomized algorithm for computing a Maximum Independent Set (MIS) in a graph.…

Q: 43. Find a Steiner tree of the graph K, with the vertices b, j, d, h by listing the edges that form…

A: According to the information given:- We have to find the Steiner tree of the graph K5

Q: Items cannot be updated or deleted in a Float is an example of a data type in Python. There can be…

A: I have provided solution in step2.

Q: 4 5

A: DFS traverse of first node i.e. 1 with minimum number in all the nodes- Now we have to select the…

Q: Divide and Conquer MST sider the following divide-and-conquer algorithm for computing minimum…

A: Suppose that we represent the graph G = (V, E) as an adjacency matrix. Give a simpleimplementation…

Q: A) show the discovery and finishing times of d and pi values that result from running breadth-first…

A: BFS: Breadth-first search is one amongst the best algorithms for looking out a graph and therefore…

Q: Luby’s Algorithm: 1. Input: G = (V, E) 2. Output: MIS I of G 3. I ← ∅ 4. V ← V 5. while V = ∅ 6.…

A: Luby's algorithm is a randomized algorithm that finds a maximum independent set (MIS) in an…

Q: 13 20 Show the execution of Dijkstra's shortest path algorithm, starting from vertex A. Draw the…

A:

Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.