An independent set in a graph G is a set S of vertices of G (so S is a subset of the vertex setV(G) of G) such that no two vertices from S are adjacent. A caterpillar is a tree T such thatthe graph obtained from T by removing all leaves is a path.Problem:Instance: a caterpillar TProblem: find the number of independent sets in TDesign a recursive algorithm based on Divide and Conquer strategy for solving this problem.Prove its correctness. Estimate the time complexity of the algorithm.

CODE IN PYTHON: def is_diff_two(values,diff):n = len(values)if(n==0):return False;temp =…

Answered: An independent set in a graph G is a…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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The BST remove algorithm traverses the tree from the root to find the node to remove. When the node being removed has 2 children, the node's successor is found and a recursive call is made. One node is visited per level, and in the worst-case scenario, the tree is traversed twice from the root to a leaf. A BST with N nodes has at least log2N levels and at most N levels. Therefore, the runtime complexity of removal is best case O(logN) and worst case O(N). Two pointers are used to traverse the tree during removal. When the node being removed has 2 children, a third pointer and a copy of one node's data are also used, and one recursive call is made. Thus, the space complexity of removal is always O(1)." I have to explain this clearly! and the advantages of the BST algorithim
Code: Prim’s MST algorithm.algorithm PrimMST (G) pre-cond: G is an undirected graph. post-cond: The output consists of a minimum spanning tree.
Yusuf: C X 0 F1 umn.instructure.com/courses/342857/external_tools/retrieve?display=full_width&url=https%3A%2F%2Fumn.quiz-Iti-iad-prod.instructure.com ... D 2 L Given: Member m = new Board Member(); What will be printed by: System.out.println(m.toString()); ۲ 3 F2 W .. ص X Output: Searching A at: Searching C at: Searching X at: Searching Et: S >>> س eturn -1 if The BTNodeGen instance method search(T s) in the class above is intended to return the depth of the data items in the tree if it is found, and r item s is not found in the tree. Given the tree below, show the output that will be produced if the main() fragment were run, assuming the tree, t, is the followi ng: # 3 r L E 20 F3 $ 4 ی D уу. ي Without actually re-writing the code, briefly describe two changes needed to make search(T s) give the correct output. R W F L. G 000 900 F4 in with this one. thi Gill 5 ق 67 5⁰ "A" (depth 1) "B" "C" (depth 2) // (depth 3) "D" "E" % & ។ 7 V 8 28 Y.2⁰. AA F7 غ ز * H IJ X U .... o: W E A CSV B…
In Python
Recursion Trees ----------------------- See Picture
4. please help me with this Data structure and algorithm
Create a binary linked tree, and traverse the tree by using the recursive function. The structure of the tree is as follows: //check pic// You should input the nodes in pre-order sequence. If a child of a node is NULL, input a space. Write the function of create binary tree, pre-order to print the nodes, in-order to print the nodes and post-order to print the nodes. Count the height of the tree. Hints: Header file typedef char ElemType; typedef struct node//define the type of binary tree node { }BTnode; Source file #include <stdio.h> #include <stdlib.h> #include "tree.h" BTnode * createTree()//create the binary tree，return the root { BTnode *tnode;// tnode is the root char elem; ;//input the character //if the input is a space，set the pointer as NULL Else// if the input is not a space，generate the binary node and create its left…
Recursion Trees Use the recursion tree method to determine the asymptotic upper bound of T(n). T(n) satisfies the recurrence T(n) = 2T(n-1) + n, and T(0)=0.
Please how do i solve this?
A good loop invariant would be “The entire tree is a heapexcept that nodei might not be greater or equal to both of its children. As well, thevalue of i’s parent is at least the value of i and of i’s children.” When i is the root,this is the precondition. The algorithm proceeds as in the recursive algorithm.Node i follows one path down the tree to a leaf. When i is a leaf, the whole tree isa heap.Write algorithm Heapify(r )
4-Clique Problem The clique problem is to find cliques in a graph. A clique is a set of vertices that are all adjacent - connected - to each other. A 4-clique is a set of 4 vertices that are all connected to each other. So in this example of the 4-Clique Problem, we have a 7-vertex graph. A brute-force algorithm has searched every possible combination of 4 vertices and found a set that forms a clique: https://en.wikipedia.org/wiki/Clique_problem You should read the Wikipedia page for the Clique Problem (and then read wider if need be) if you need to understand more about it. Note that the Clique Problem is NP-Complete and therefore when the graph size is large a deterministic search is impractical. That makes it an ideal candidate for an evolutionary search. For this assignment you must suppose that you have been tasked to implement the 4-clique problem as an evolutionary algorithm for any graph with any number of vertices (an n-vertex graph). The algorithm succeeds if it finds a…
Using the recursion tree method find the upper and lower bounds for the following recurrence (if they are the same, find the tight bound). T (n) = T (n/2) + 2T (n/3) + n.

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