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- A graph is a collection of vertices and edges G(V, E). A weighted graph has weights (numbers, etc.) on every edge. A multigraph can have more than one edges between any vertices. Explain why a person should use a weighted graph instead of a multigraph. Give examples. An adjacency matrix might be a better choice for speeding up a program, however, it consumes huge memory for large graphs. How this situation can be improved? What programming constructs better suit graph representation? Explain with example1. Analyze the word finder with wild card characters scenario to form the algorithm and compute the time complexity. You are given a list of characters with size n, m. You need to read character data provided as input into this list. There is also a list of p words that you need to find in the given problem. You can only search in left, right, up and down direction from a position. There are two wild characters *' and '+' ,if there is any instance of wild card characters for example '+' appears you can match whatever character in your word that you are searching at this position (only one character). Similarly, if you got wildcard *' you can skip any number of characters ( A sequence of characters not necessary same in between the characters) but the last character should be matched in the given data. This means you are not allowed to match a first and last character with *' wildeard. Input: The first line of the input will give you two integers n and m. From the next line you will get…You have an array of 10,000 subject scores for a high-school exam and you want to find the scores that are ranked from 4900 to 5100 that is the 201 most middle-ranked scores. Precisely describe two alternative algorithmic ap proaches to doing this - one of which is, in terms of time complexity, more efficient than the other.
- The intersection of two sets contains the list of elements that are common to both, without repetition. As such, you are required to write an algorithm that finds and returns the intersection of two sets A and B. The sets A and B and the resulting intersection set are all lists. Assume the size of A is n and that of B is m. (a) Write an iterative algorithm that finds the intersection. (b) Prove the correctness of your algorithm; i.e. state its loop invariant and prove it by induc- tion. (c) Analyze the time complexity of your algorithm. (d) Think of a way to enhance the complexity of your algorithm by sorting both lists A and B before calculating their intersection. Write the enhanced version and prove that it has a better time complexity.Below are a number of statements about linear and binary search. A. Linear search systematically searches from beginning to end. B. Linear search as well as binary search works on both sorted and unsorted data sets. C. For linear search, T (n) = O (n) applies in the worst case. D. For linear search, T (n) = 0 (n) applies in the worst case, if the quantity is unsorted. E. For binary search, T (n) = O (log n) applies in the worst case. Indicate which of these is correct. a,b,d,e true a,b,c,d true a,c,d,e true a,e trueYou are advised to refer to the recommended textbook “Introduction to Algorithms (3rdedition) by Thomas H. Corman, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein”. Have areading through Chapter 04 and answer the following questions as a follow up exercise Compute big-oh of the given T(n) using the Iteration Method:
- Please do not give solution in image format thanku Implement the following recursively using sudo code: Suppose an elevator which is on a floor on n. For this elevator to go from the nth floor to the base(ground) floor, it should go to every floor under the nth floor. Let's consider an elevator on the 4th floor. This elevator 1st comes on the third(3rd) floor. 4th-> 3rd then 3rd-> 2nd then 2->1 and next 1->0(ground floor) The recursive equation defined is F(n)=1+F(n-1)suppose that n is not 2i for any integer i. How would we change the algorithm so that it handles the case when n is odd? I have two solutions: one that modifies the recursive algorithm directly, and one that combines the iterative algorithm and the recursive algorithm. You only need to do one of the two (as long as it works and does not increase the BigOh of the running time.)Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. Sierpinski.java When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle with the specified side length. public static double height(double length) // Draws a filled equilateral triangle with the specified side length // whose bottom vertex is (x, y). public static void filledTriangle(double x, double y, double length) // Draws a Sierpinski triangle of order n, such that the largest filled //…
- Let n be a positive integer and let MaxCrossing(n) be a function that returns the maximum number of line crossings that you can create by drawing n straight lines. Write down a recursive formula for MaxCrossing(n) and analyze the time complexity of the corresponding recursive algorithm. You must write a formal recursive formula including the base case and general recursive step.Write in python programming language: The Longest Subsequence Problem is a well-studied problem in Computer Science, where given a sequence of distinct positive integers, the goal is to output the longest subsequence whose elements appear from smallest to largest, or from largest to smallest. For example, consider the sequence S= [9,7,4,10,6,8,2,1,3,5]. The longest increasing subsequence of S has length three ([4,6,8] or [2,3,5]), and the longest decreasing subsequence of S has length five([9,7,4,2,1] or [9,7,6,2,1]). And if we have the sequence S = [531,339,298,247,246,195,104,73,52,31], then the length of the longest increasing subsequence is 1 and the length of the longest decreasing subsequence is 10. Question: Find a sequence with nine distinct integers for which the length of the longest increasing subsequence is 3, and the length of the longest decreasing subsequence is 3. Briefly explain how youconstructed your sequence. Let S be a sequence with ten distinct integers. Prove by…Given an unsorted array, A, of integers and an integer k, write a recursivejava code for rearranging the elements in A so that all elements less than or equal to k come before any elements larger than k. What is the running time of your algorithm on an array of n values.