In today's Lab we will explore a specific way to perform a Depth First Search  (DFS) of a given Graph [Ref : Figure 1]. You will implement the traversal using one of the two ways stated below :  [1] With Recursion.  When you follow the traversal process as specified - the complexity of the solution will be linear as shown below. Time Complexity: O(V + E), where V is the number of Vertices and E is the number of Edges respectively. Space Complexity: O(V )

Please help me make a a t square fractal using recursion. if you can please also make a sierpenski triangle ( and comment it). You do not have to comment the first task.

*Discrete Math In the graph above, let ε = {2, 3}, Let G−ε be the graph that is obtained from G by deleting the edge {2,3}. Let G∗ be the graph that is obtain from G − ε by merging 2 and 3 into a single vertex w. (As in the notes, v is adjacent to w in the new if and only if either {2,v} or {3,v is an edge of G.) (a)  Draw G − ε and calculate its chromatic polynomial. (b)  Give an example of a vertex coloring that is proper for G − ε, but not for G. (c)  Explain, in own words, why no coloring can be proper for G but not proper for G − ε. (d)  Draw G∗ and calculate its chromatic polynomial. (e)  Verify that, for this example,PG(k) = PG−ε(k) − PG∗ (k).

No plagarism please! Correct and detailed answer will be Upvoted else downvoted. Thank you!

b3

Problem 1. Construct a non-recursive procedure capable of reversing a single linked list of n elements, which runs in O(n) time. Can the same be achieved in (n) time? If so, construct it.

Please help solve the python problem, thank you

Consider the following multiplication problem: Given an integer list (an array) of size n, we want to calculate the product of all numbers in the list and display the result. (a) Define an instance of a problem in general. (b) Specify two different instances of the multiplication problem defined above. (c) What is the solution for each instance in part (b). How did you come up with that solution?

Program in C++

Personal project Q5. This question is concerned with the design and analysis of recursive algorithms. You are given a problem statement as shown below. This problem is concerned with performing calculations on a sequence ? of real numbers. Whilst this could be done using a conventional loop-based approach, your answer must be developed using a recursive algorithm. No marks will be given if your answer uses loops. FindAverageAndProduct(a1, ...., an) such that n > 1 Input: A sequence of real values A = (a1, ..., an) Output:, A 2-tuple (average, product) containing the average (average) of all the values and the product (product) of all the values of the elements in A. Your recursive algorithm should use a single recursive structure to find the average and product values, and should not use two separate instances of a recursive design. You should not employ any global variables. (a) Produce a pseudo code design for a recursive algorithm to solve this problem.   (b) Draw a call-stack…