Algorithms Questions and Answers August 21, 2021

For each of the weighted graphs below, apply the algorithms of Kruskal and Prim to find a minimum spanning tree for the graph, and apply Dijkstras algorithm to find the distance between the vertices a and h, and a walk of that distance (a) a a 8 b 6 4 6 b 2 1 d 1 3 1 C 3 d 3 3 4 3 2 4 O 1 e 5 f 2 5 5 6 2 8 g 1 h 00 g 4 h Activate Wir Go to

AC=4 AD=7 AE=8 DC=6 CF=4 BD=8 BG=6 GC=2 DF=6 GE=4 BE=6 EF=8

SOLVE NETWORK WITH PRIM ALGORITHM AND YOUR DATA PRIM ALGORITHM (MNMUM SPANNING TREE) MSP districts B D

Consider an undirected graph that may have negative edge weights. (a) Will Kruskals algorithm still generate the minimum spanning tree If so, explain why. If not, give an example on which Kruskals algorithm will fail. (b) Will Prims algorithm still generate the minimum spanning tree If so, explain why. If not, give an example on which Prims

Assume that Prim and Kruskal have come together to design a new algorithm to find the minimum spanning tree where the edges are picked alternatively first using the Prims approach and the second using the Kruskals method. Write briefly the pseudo code of the algorithm, analyze its complexity and explain the MST found in the below graph using this

(a) Use the selection algorithm to find the second smallest (k2) of 5, 7, 4,15, 9, 8, 13. Show how the partition algorithm is applied in the selection algorithm. (b) Given a graph G(V,E), explain how the Prim minimum spanning tree (MST) algorithm can be applied to Construct an MST. For the following graph, show the cost of each stage, final cost,

4 Vphase prim Vine prim Iphase prim lline prim 5 Vine prim Iphase prim Calculate the unknowns for the three phase transformers Vphase prim lline prim 200 volts Vphase sec 208 volts Vine sec Iphase sec lline sec 5. Calculate the unknowns for the three phase transformers Vphase sec Vine sec Vphase load Iphase load Ratio Iphase sec lline sec Load

I. II. A 50 60 Consider the graph below 90 B E 120 D 80 50 70 F 40 140 Draw the minimum spanning tree by using Prims algorithm. You must show the order of picking the edges (or nodes). Draw the minimum spanning tree by using Kruskal algorithm. You must show the order of picking the edges (or nodes). Activate Wind

1. Using Dijkstra to solve following graphs. Show each answer from start vertex (a to g). 2. Using Prim to solve following graphs. Show each answer from start vertex (a to g). 3. Using Kruskal to solve following graphs.

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In the model below, a model is estimated for the premium amount of employees in a company operating on a bonus basis. In this company, different premium rate is applied for sales above 100 units. i 120 3Xi 2 (Xi X Di Y Sales Premium (TL) X Sales Quantity (Piece) X (Threshold Value) 100 units D0, up to 100 pieces D1, after 100 pieces. a) Draw

Given an undirected graph as shown below, show the process of finding the minimum spanning tree using Prim and Kruskal algorithms respectively

10 10 20 11 18 14 3

12 h 11 12 14 15 22 a b 18 3 k 14,Consider the graph shown on the right. The 12 edges in the figure are marked with letters a tol, and the numbers on the edges indicate the cost of the edges. Calculation Use Prim algorithm to calculate the minimum cost spanning tree the node marked with must be selected as the starting node. As a solution, only

1. Using prims algorithm starting with vertex "A", list the vertices of the graph below in the order they are added to the maximum spanning tree 2.Using Kruskals algorithm, list the edge of the maximum spanning tree of the graph fig -1 in the order they are added

For the below Graph (fig1), you will find the maximum spanning tree. 202209 (91 15 5 6 a 11. 17 10 Fig1 19 12 13 7 16 18 14

For the following linear programming formulation, Z 85x12 53x13 88x14 65x34 31x25 61x35 137x46 117x37 72X57 24X67 Determine a) the shortest path using the tree diagram and the Dijkstra algorithm. b) the minimal spanning tree using the Prim and the Kruskal algorithms.

Use Kruskals algorithm to find a minimum spanning tree for the following graph. You can show just the final minimum spanning tree, but you should indicate the order in which the edges are added. b 6 1 f 7 2 11 4 9 bo 10 3 5 d h 1 8

H 1. Determine the minimum spanning tree of each graph using a) Prims Algorithm b) Kruskals Algorithm 2. Determine the shortest path tree of each graph using Dijkstras Algorithm. 13 16 5 a 7 7 8 6 b 10 13 14 10 5 e 12 B h

b 3 2 d f 2 2 8 3 h,a. b. Find a minimumcost spanning tree by Prims algorithm. Find a minimumcost spanning tree by Kruskals algorithm. c. Find a depthfirst spanning tree starting at a and at d. d. Find a breadthfirst spanning tree starting at a and at d. 2. Describe an algorithm to insert and delete edges in the adjacency list representation for

Consider the below graph. Part a:apply Depth First Search Algorithm starting with Vertex 1. Part b:apply Breadth First Search Algorithm starting with Vertex 1. Part c: apply Prims and Kruskal algorithm. Is the answer (MST) from both the algorithm is same?

10 7 5 5 LO 15 5 20 8 1 5 20 20 20 10 10 15, 9 10, 5 4 10 or 2 15 5 5 (10) 3 15 J

a. In a graph, explain what do we mean by the following terms and give examples Node degree, Diameter, Fault Tolerance, Regular Graph, Planer Graph b. Define the spanning tree and the minimum spanning tree, provide examples. c. Consider the following graph and show in details how the Prim and Kruskal algorithms work to provide the MST

Define what is the minimum spanning tree of a weighted graph. State the theorem that justifies the correctness of the greedy algo rithms of Prim and Kruskal for generating a minimum spanning tree. (20 marks) Trace Prims algorithm to find a minimum spanning tree of the following weighted graph, starting from vertex a. in

1.Suppose you only know Dijkstra's shortest path algorithm. Can you still use it in some innovative way to accomplish the same goal as that of all-pairs shortest path algorithm? 2.If you are asked to find a minimum spanning tree starting from a specific vertex, between Prim and Kruskal algorithm, which one you should choose? Explain your answer.

develop a graph of your home with 4 your other family houses in a city (but your house neither dormitory nor your boarding house). The graph represents the road distances (kms) of among all houses. Please calculate the Minimum Spanning Tree (MST) using Prim and Kruskal Algorithms and show your steps in constructing the MST. (30 marks),develop a

Every location is connected through a road and the distances are represented in every edges as shown by the following picture. Jenna 2 6. Harry Billy 13 Cassie Please calculate the Minimum Spanning Tree using Prim and Kruskal Algorithms and show your steps in constructing the MST.

There is a network given below. What is the length of the minimum spanning tree of this network (5 points) Which edges are included in the minimum spanning tree (15 points) You can use Kruskal or Prim algorithm. A 3 B 2 2 U E 9 9 8 8 7 F 18 5 H 10 3

Find a minimal spanning tree and its minimal cost with Kruskal algorithm. show all steps & back track. Find a minimal spanning tree and its minimal cost with Prim algorithm using Va as the source node. show all the steps & back track. Find the amount of spanning trees with the Kirchoffs Theorem. show all steps.

5 6 3 a

Consider the graph given above. Use Kruskals and Prims algorithms (for Prim start at J) to find the minimum spanning tree. a. For each algorithm provide the edges in the order they were selected. (6 pts) Kruskals algorithm Prims algorithm b. What is the total weight of the spanning tree ( 5pts) Total weight of the spanning tree for Kruskals

where d1 = 0, d2 = 6, d3 = 7. specify the steps of the algorithm. Consider A as the root of the tree, traverse the obtained tree using pre-order and post-order algorithms.

To find a minimal spanning tree using Kruskal or Prim algorithm in the following graph V A, B, C, D, E, F) and weights w(A, F) 4, w(A, B) 3, w(B, E) 4, w(F, D) d3, w(E, C) 10, w (B, C) 5, w(E, D) 9, w(B, F) 8, w(D, C) 5, w(C, F) d, w(F, E) d,

write a small program that executes the following graph algorithms in any language: 1. All-Pairs Shortest Path (Floyd-Warshall). It must ask for the vertices and edges for the user to enter them. As an output, deploy the resulting matrix. This will be done only for directed graphs. 2. Kruskal or Prim algorithm whatever you want to do. It must ask

Do all implementations and show in one Graph or tree: 1-Graph: BFS and DFS, Floyd-Warshall, Dijkstra, Prim AND Kruskal Algorithm 2-Tree: BST, AVL, min/max heap, Red Black Tree, Minimum Spanning Trees, Splay Trees (Insert, Delete, Find) 3-Hash Table write a java code.

Apply the following algorithms on the given graph example. 1) Kruskal 2) Prim 3) Dijkstra (Assume S is the root and directions shall be assigned independently by you) S 7 8 1 3 A 9 6 4 3 B 2 D 5 2 T Activate Win Go to Settings to

Write a JAVA program to Implement the Kruskal and Prim algorithm, for this they must create the Graph classes, Vertex and Edge, for the undirected graph.

A 5 16 9 3 2 D,(a) Find a minimum spanning tree in the given graph using Kruskals algorithm. List the edges in the order in which they are added, and draw the minimum spanning tree. (b) Find a minimum spanning tree in the given graph using Prims algorithm (rooted at any vertex of your choosing). List the edges in the order in which they are

A pipeline is to be built that will link eight cities. The cost (in hundreds of millions of dollars) of constructing each potential link depends on distance and is shown in the weighted graph below. Find a system of pipelines to connect all the cities and yet minimize the total cost. a. Show the SEQUENCE in Minimum spanning tree using Prim and

Based on Figure 2, find the minimal spanning tree and calculate the shortest distance of the tree using (a) (b) Kruskal Approach. Prim Approach, starts at C. 4 marks Activate,A O A 00 5 9 B E 7 5 Figure 2 F 00 6 G

Consider the following graph G. The label of an edge is the cost of the edge. b 6 DZ 3 10 12 5 1 a 4 2 7 14 8 d h 8 (a) Using Prims algorithm, draw a minimum spanning tree (MST) of the graph Also write down the change of the priority queue step by step and the order in which the vertices are selected. Is the MST drawn unique (i.e., is it the one

Prove that in any graph with edge-weights that are distinct (no pair of edges exists with the same weight), then both Prim and Kruskal must output the same MST, regardless of the starting node.

use DFS to traverse the graph in problem 2. use BFS to traverse the graph in problem 3.,Problem 2 Please use kruskal and prim to get minimum spanning tree. V4 V6 Problem 3 Please use Dijkstra to get the shortest path. 10 B 16 9 2 G 8 GA,use DFS to traverse the graph in problem 2. use BFS to traverse the graph in problem 3.,Problem 2 Please use

Apply (Dry Run) Greedy Algorithms on at least three example (values) of your own choice Prims Kruskal Dijkstra Max Compatible Activity Selection Coin Change Problem Huffman Coding L

Please fill in the following table for worst case time complexity of some common algorithms we have studied Algorithm Dijkstras Algorithm Kruskals Algorithm Prims Algorithm BinarySearch Matrix Multiplication (ordinary) Finding A Median of An Unsorted List FloydWarshall Algorithm Radix Sort Ordinary Binary Tree Insertion Balanced Binary Tree

Find the MST for the below graph considering that the edge V3-V7 must be in the MST. U both the Kruskals and Prims Algorithm. Explain the necessary steps you did.

D4 V4 V1 DS D1 V3 9 V5 V2 10. 9 05 V6 DZ h V7 03 V8 D4 V9

5. Find a minimum spanning tree for the graph in Figure 9.84 using Prims and Kruskals 30 Points D 4 6 A 5 H 4 2 3 E 4 2 1 B 11 I 3 3. 10 F 7 6 11 2 J 8 G Figure 9.84 Graph used in Exercise 9.15 a. Prims algorithm (show table with v, dv, known, path values). Show all steps. Start with Node A. Should include table as follows in the solution to show

information is 1 E W You are given 8 using 2 3 3 ed stored this way 16 a Write pseudocode this structure. weighted graph G where 10 So E can be Seen as a 2D array example, 11 a 1 2 0. 0 stores the weight of edges. R 8 lo c3 b e 16 of elges. In this Array W for either Prim or Kruskal

A weighted undirected graph is shown below (1) Using Prim algorithm, from vertex 1, draw step by step the construction of its MST (2) Using Kruskal algorithm, from vertex 1, draw step by step the construction of its MST 13 17 8 12 18 10

Implement it and write a report to compare the performance of the two algorithms.,A 5 B 6 2 1 C 2 D 5 3 E F

On the following graph run the following algorithms and show all the steps of the algo rithm. At the end write what is the output of the algorithm and the number of its steps. 2 10 8 2 3 Y W (a) Dijkstra (source s) (b) Prims (c) Kruskal

In the following graph has 8 nodes, please determine the minimum spanning tree (MST) with how to describe a spanning tree (including the steps) and calculate the total weight at a minimum use the method: (a) Prim (b) Kruskal

a 2 3 2 6 b f 5 0.0 3 g 3 6 d H h

Construct MST for the given graph, using Prims and Kruskals algorithm. Take A as start vertex for vertex oriented algorithm (Step by step solution is required) 22 20 B 10 2 6 11 H

It is required to control the average voltage of a 3 ohms and 20uH inductive load connected to a 12VDC source. They have IRLZ44N mosfets, whose characteristics are: VDS of 55VCd, IDSon 47A, VGSon of 3.25Vcd, an RDon of 22mohms, a Qc of 48nF and a Ton of 11ns. Design the control stage to control the load with an LVT mcu at a frequency of 20KHz with

If given a 01 knapsack problem, in which items order does not change when they are arranged in ascending order by weight or in descending order by value. Provide an efficient algorithm to find the optimal solution for this particular problem, and give arguments about the correctness of your algorithm. Apply Kruskal and Prims Algorithms on the

Use Prim algorithm to find MST of following graph and verify by Kruskal algorithm. 3 00 3 1 3 2

M 1 1 d 1 weights ab 2 bc 2 ac 8 bd 1 cd be de cf Spanning tree minimum 2 6 1 I 3 To Find the weighted graph ot Apply the Kruskal algorithm step by step Apply the Prim Algorithm step by step (Storting in the above vertex a

use MST approached propsed by Prim & Kruskal to find the MST of the following diagram and then compare their Time Complexity.

a 6 2 8 3 2 d 2 15 8 00 8 4 f (20 h 2 9 4 19 14

The time complexity FloydWarshalls algorithm is O(n). Is this ever better than simply running the Dijkstras singlesource shortest path algorithm from every node Note that the best time complexity for Dijkstras single source shortest path is 0(m n log n) when a Fibonacci heap are used to store distances). Briefly explain your answer. Hint you

Calculate the Minimum Spanning Tree (MST) process separately, starting from node A, using the Prim and Kruskal algorithms in the graph below. Note Write the edges in the order they were added to the MST. Use node names to represent edges. Example (AB), (BE),7 6 (A) 2 12 D C 1 B 11 1513 10 (E) 3 G 14 8 F (H) 9

Let G(V,E) be an undirected graph with n vertices and m edges such that G has two vertices s and t where the shortest path from s to t has length strictly more than n/2. Then, prove that there must be a vertex w V {s,t} such that every path from s to t must pass through w. Furthermore, assuming that G is given to you in the adjacency-list

Given a graph G , along with the DFS algorithm (Graph depth-first search with a stack), please do the following: a. Show the Adjacency List representation of the graph G. b. Assume that the start node is 0 (i.e., node = 0). Demonstrate a step-by-step, manual desk-check execution of the DFS algorithm - showing the values of all variables and

1 0 2 3 6 4 5

Write the output from the following code. for (int i 0 i

Your task is to design and implement an algorithm that searches a collection of documents. You have the freedom to select the data structures and algorithms that you consider to be more efficient for this task. Of course, you will have to justify your decisions. First, you will process the documents and store their content(i.e. words) in the data

For the HMEQ dataset, you are given a target variable BAD. Your task is to apply any binary classification algorithm to the dataset, employing a suitable training and test split. Use a linear regression model to model the LGD based on the independent variables provided in the dataset. BAD LOAN MORTDUE VALUE REASON JOB YOJ DEROG DELINQ CLAGE NINQ

Determine the value for c so that lim f(x) exists. X3 f(x) 1 3xc, for x 3 x7, for x3 The value of c is

According data sheet of zener diode IN4736. The data sheet gives Vz 5.1 at test current 40 mA when Izk 10 mA and Izm 60 mA 1) what is the impedance of zener diode 2) what is the voltage across the zener diode when current (a) 30 mA (b) 50mA 3 Marks

The top chord of a trussed roof is drawn below. Using graphic statics, generate the geometry for the bottom chord such that no internal diagonal members are required and that the top chord has constant force of 40 Kips in each element. Remember to correctly label the freebody diagram using Bows notation, and draw your load line at an appropriate

A radar system transmits the pulse p(t) given below. The radar receiverdetector is based on an LTI system with impulse response defined by h(t) p(Tt). a. Draw h(t) p(Tt), the impulse response of the radar receiver. Show your steps. Clearly label your plots. b. The input to the radar receiver is the received waveform r(t) defined below. Determine

A private company called AFH580S PTY (Ltd) generates electricity and supplies it to the main grid using superheated steam. The company employs cogeneration to meet various heating requirements. The water-steam mixture at the exit from the turbine is condensed and transformed into condensate at a temperature of 210C. This condensate, with a

The magnetic poles on the rotor can be either salient pole or cylindrical pole, make a high level comparison between then? Support you answer with draw. -The brushless exciter used to supply dc power to the field winding, draw the schematic diagram of the brushless exciter? And the how the generator filed current is controlled? -Mention the theory

1. Show the truth table of a fulladder 4 pts 2. Construct a 4bit binary adder circuit using four full adders. Label all inputs and outputs. 6 pts 3. Implement the Sum and Carry outputs of a full adder using a 3x8 decoder (with active high outputs) and 2input OR gates...

Suppose you have these related classes class Car extends Vehicle ... class Bus extends Vehicle ... Which is the sub class and which is the super class in this declaration Define Two different objects by applying Polymorphism.

Implement the ADT deque in Python, using the Python deque from the COLLECTIONS module. The interface to implement is like the ADT queue plus two methods for inserting and deleting elements at the end. You can call those methods enqueueEnd(item) and dequeueEnd(). You can add a comment in your code for specifying the two methods in your

Calculate the flux integral. Jg(34 3zk). Nds where S is z y with 0x2,0 y 1, N oriented upward f(31 32k). Nds 4,Calculate the flux integral. Jg(34 3zk). Nds where S is z y with 0x2,0 y 1, N oriented upward f(31 32k). Nds 4

A resource has a capacity of 30 units and use of the resource is desired by 5 users. The users A, B. C, D, and E have demands of 6, 8, 12, 24, and 2 units, respectively. Determine the allocation of the resource on the basis of maxmin fair sharing. You may assume that users may utilize fractions of resource units if required. Repeat the question,

What are Web sites & URL(s)?. Explain how data is organized on a magnetic tape?

Show that the SET-COVER problem is in NP.

Prove that the problem SAT, which takes an arbitrary Boolean formula S as input and asks whether S is satisfiable, is NP-complete. If you are proving a problem is in NP-Complete, you must - a. Prove that the problem is in NP (state the verification problem, give and explain an algorithm to verify a certificate in polynomial time, and prove its

Is the following distributive law valid or invalid? Provide your answer. Hint: use a truth table to get the answer for each side of the equation. x XOR (y + z) = (x XOR y) + (x XOR z) Draw the logic diagram of a 2-bit encoder, a circuit with four input lines, exactly one of which is high at any instant, and two output lines whose 2-bit binary

Consider the 2SAT version of the CNFSAT problem, in which every clause in the given formula S has exactly two literals. Note that any clause of the form (a V b) can be thought of as two implications, ( b) and ( a). Consider a graph G from S, such that each vertex in G is associated with a variable, x, in S, or its negation, . Let there be a

function After then, compare the cost for SOP and POS forms. 12 x3x4 00 01 11 10 Find the minimalcost SOP and POS forms for the following f (x, x2, x3, x4) m (0,5,6,7,8,13,15) D(2,10) SOP 00 01 11 10 12 x3 x4 a) Minimalcost SOP f(x, X2, x3, x4) b) Cost for the SOP c) Minimalcost POS f(x1, X2, x3, x4) d) Cost for the POS 00 01 11 10 00 POS 01

Is this multivariable Boolean theorem correct X+(XY) = X+Y (Hint: Create truth table)? a. There is no such theorem b. TRUE c. FALSE

In the practical work of the laboratory for the configuration of the op amp, the connected circuits are as below. Solve the problem. Consider the circuit shown in Figure 02. Find the value of voltage measured by the voltmeter. (CL03) i. 3 3 1 Volt 16 20 Figure 02 Voltmeter

Find the admittance Yab in the circuit seen in Fig.P9.250. Express Yab in both polar and rectangular form. Give the value of Yab in millisiemens. Figure P9.25 ao b 12.8 HE Yah m 13.6 2 m 60 3j1202 j 4 502 10 22 a

Lucy Lane maintains a savings deposit with Monarch Credit Union. This past year Lucy received $10.75 in interest earnings from her savings account. Her savings deposit had the following average balance each month: January $450 July $450 February 350 August 425 March 300 September 550 April 550 October 600 May 225 November 625 June 400 December 500

Question:

Frank the frog dabbles in prognostications. He has projected the number of flies that will be around his lilypad loft on each of the following n days. Thus, d days from now, there will be fa flies around his lilypad. Frank also is quite sleepy, and likes to rest for days at a time. The more he rests, the hungrier he gets. If Frank has rested for r

EXPLAIN ALGORITHM?

Consider a two sngine plane in a oneoutoftwo logic configuration. When both engines A and B are fully energized they share the total load and the failure time densities are f(t) and. f(t). If either one fails, the survivor must carry the full load and its failure density becomes g (1) 9r.8, (t). 1. Derive an expression for the reliability of the

A rectangular plate of composite material is formed with unidirectional fibres orientated at 15 degrees to the longitudinal axis. The composite material has properties in the principal material directions of E 285 GNm, E 45 GNm, V12 0.28, V21 0.37 and G2 75 GNm. A stress of 140 MNm is applied to the plate on the longitudinal direction What is

Given the following code fragment for (int i n i n ii2) sum What would the bigo notation be Please explain why or how you got to that answer i. O(log n) ii. O(n) iii. O(n2) iv. O(2n)

a) Specify the following queries in SQL on the database schema of Figure 1.2. a. Retrieve the name of each course and the instructor who taught that course. If an instructor taught a course more than one time, remove the redundant information. b. For each section of those courses offered by CS department, retrieve the course number, semester,

Find the integral. (3x87x37) dx xx4 7x C 7 9x 3x4 7x C 9x7x47x C Ox3x4 7x C Ox O

Write a Python program to remove the middle node from the linked list.

Write the code for GGCDof n numbers using recursion? Write a code to print a polynomial and evaluate it. Write a program for insertion sort.

a) Specify the following queries in SQL on the database schema of Figure 1.2. a. Retrieve the name of each course and the instructor who taught that course. If an instructor taught a course more than one time, remove the redundant information. b. For each section of those courses offered by CS department, retrieve the course number, semester,

What is the big O notation for the following code def f(nums) for i in range (1en (nums)) if i len (nums) 4 print(hi) else for j in range (len (nums)) print (numsj)

Consider the following program segment. Describe the asymptotic execution time as a function of n using bigO notation for i 1 to n do for j 1 to i do constant time operation

What is the Big O notation for the following code low 0 high len(arr) 1 while low x high mid1 else return mid return 1

What is the big O notation for the following code def f(nums) for k in range (len (nums) len (nums) len (nums)) i len (nums) while i 0 print(a0) i 1 2

Consider the following program fragment, which has a time complexity that is a function of n. What is its time complexity using BigO notation. int sum 0 for (int k 0 k

Given the following function def funl (L, M ) if len (L)

Whats the output after the following code is executed int number 6 while (number 0) number number 3 System.out.print(number )

The Java program Tangled is designed to check how well you can follow instructions as a computer would execute them. a) List the functionmethod names in the order in which the computer executes the functionsmethods. b) What is the output when Tangled is compiled and executed public class Tangled public static void main(String args) int a 10

(a) Use the binomial theorem to prove the following ( (b) Use the binomial theorem to prove the following 3100 (100) (100) 2(120) 2 (190) 23 (100) 299 (100) 2100 99 Solution 26. .

a. Find the address accessed by each of the following instructions. If DS 0100H, BX 0120H, DATA 0140H, and SI 0050H and real mode operation 1. MOV DATASI, ECX 2. MOV BL, BXSI b. Descriptor contains a base address of 00260000H, a limit of 00110H, and G 1, determine starting and ending locations are addressed by the descriptor for a Core2.

5. This question is about disjoint set. (20) G H M T S Z W