Determine whether the two bipartite graphs below have a perfect matching. Justify your answer, either by showing a perfect matching or using Hall’s theorem to prove that it does not exist
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Determine whether the two bipartite graphs below have a perfect matching. Justify your answer, either by showing a perfect matching or using Hall’s theorem to prove that it does not exist.
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- python 8.7 LAB: Writing append and search methods (singly-linked list)Given main.py and a Node class in Node.py, complete the LinkedList class in LinkedList.py by writing the append() and search() methods. The search() method should return the Node whose data value matches a given key, and None if the key is not found. The search() method should also set the position of each Node searched in the LinkedList, starting with 1. Ex: If the input is: 12 23 59 37 923 212the output is: 12 found in list at position 1.If the input is: 12 23 59 37 923 268the output is: 68 not found in list.3) Implement the if __name__ == "__main__" : block at the bottom of this file to do the following: 3a) The if main block at the bottom should get the name of the highway graph file from the command line arguments. See the video in Python that explains how to get command line arguments. 3b) Call your parse_highway_graph_file function to parse that file, and to construct a WeightedGraph object from it. 3c) Write some code that outputs (with print statements) the degree of each vertex. You can have one vertex per line, indicating its id (just its 0-based index) followed by its degree. IMPORTANT: Your parse_highway_graph_file function should NOT produce any output. You will have code in your if main block that will have the print statements. The WeightedGraph class has a degree method, inherited from Graph that will return to you the degree of a vertex.Q.2. Implement a single linked list. Elements of this linked list should be of integer type, user would provide values as input for elements of this linked list. Which does not allow insertion of duplicate value to the list.
- 6.3.25 Develop a pair of TOY functions that implement a pushdown stack, passing the values to push and pop in R[B] and the address of the stack in R[A]. This question was taken from Computer science an interdisciplinary approach. NOTE: I don't need an answer with java or high-level language code but the TOY code as described in the book which has a specific set of opcodes in hexadecimal for eg 18AB; means that adding results of R[A] and R[B] and store them in R[8]. and so on...Java - Given list: ( 0, 8, 10, 16, 23, 49, 61, 74, 96 )**11.18** Java Solve (ArrayList of Character) Using the following header, create a method that produces an array list of characters from a string: toCharacterArray public static ArrayListCharacter> (String s) ToCharacterArray("abc"), for example, returns an array list containing the characters 'a', 'b', and 'c'.
- Write down a C++ program to implement the link list in the following way. a) Create an array taking 10 values from the user.b) Create a link list and fill it (insert nodes) with the array values.c) Display the link listd) Run the 9 commands given in the table on slide 9.e) Create functions for the following and implement these in order(i) Insert a new node in front of the list and display the list.(ii) Insert a new node at the end of the list and display the list(iii) Delete the first node from the list and display the list.(iv) Search for a value in the list (user entered). Note: The program must be well structured and properly commented.1. Implement a function insertBook(Book newBook) to add a book at the end of thelinked list.a. Ask the librarian to input all the necessary book information.b. Use the information to create a Book objectc. Pass through the Book object as the parameter to the functiond. Store the Book object into the Node objecte. “Link” the object with the rest of the linked list2. Implement a function insertBefore(Book newBook, int bookID) to add a book infront of another book given its bookID.a. Ask the librarian to input all the necessary book information.b. Use the information to create a Book objectc. Pass through the Book object and bookID as the parameter to the functiond. Search for the matching Book objecte. Store the Book object into the Node objectf. “Link” the object with the rest of the linked list3. Implement a function searchBook(int bookID) to search for a book by its bookIDcode and return the book object.a. Ask the librarian to input the bookID.b. If the book doesn’t exist display an…C programming fill in the following code #include "graph.h" #include <stdio.h>#include <stdlib.h> /* initialise an empty graph *//* return pointer to initialised graph */Graph *init_graph(void){} /* release memory for graph */void free_graph(Graph *graph){} /* initialise a vertex *//* return pointer to initialised vertex */Vertex *init_vertex(int id){} /* release memory for initialised vertex */void free_vertex(Vertex *vertex){} /* initialise an edge. *//* return pointer to initialised edge. */Edge *init_edge(void){} /* release memory for initialised edge. */void free_edge(Edge *edge){} /* remove all edges from vertex with id from to vertex with id to from graph. */void remove_edge(Graph *graph, int from, int to){} /* remove all edges from vertex with specified id. */void remove_edges(Graph *graph, int id){} /* output all vertices and edges in graph. *//* each vertex in the graphs should be printed on a new line *//* each vertex should be printed in the following format:…
- please complete the following in JAVA Implement the graph ADT using the adjacency list structure. thanks! also posting a similar question for adjacency matrix. have a good day!5. Construct a function C(V) that counts the number of basic operations for the following algorithm. Then place the algorithm in a time efficiency class. State any assumptions you make. public static ArrayList topologicalSort(Graph dag) { Queue q = new LinkedList(); ArrayList sortOrder = new ArrayList(); int[] inEdgeCounts = new int[dag.size()]; for(int i = 0; i < inEdgeCounts.length; i++) { inEdgeCounts[i] = 0; } for(int i = 0; i < inEdgeCounts.length; i++) { dag.getAdjList(i).stream().forEach((x) -> inEdgeCounts[x]++); } // Identify sources for(int i = 0; i < inEdgeCounts.length; i++) { if(inEdgeCounts[i] == 0) { q.add(i); } } while(!q.isEmpty()) { int currVertex = q.remove(); sortOrder.add(currVertex); ArrayList adjList = dag.getAdjList(currVertex); // Remove edges for this node for(Integer adjVertex:…PYTHON CODE: In order to beat AlphaZero, Grandmaster Hikaru is improving her chess calculation skills.Today, Hikaru took a big chessboard with N rows (numbered 1 through N) and N columns (numbered 1 through N). Let's denote the square in row r and column c of the chessboard by (r,c). Hikaru wants to place some rooks on the chessboard in such a way that the following conditions are satisfied:• Each square of the board contains at most one rook.• There are no four rooks forming a rectangle. Formally, there should not be any four valid integers r1, c1, r2, c2 (≠r2,c1≠c2) such that there are rooks on squares (r1,c1), (r1,c2 (r2,c1)and (r2,c2).• The number of rooks is at least 8N.Help Hikaru find a possible distribution of rooks. If there are multiple solutions, you may find any one. It is guaranteed that under the given constraints, a solution always exists.InputThe first line of the input contains a single integer T denoting the number of test cases. The first and only line of each test…