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1. Show that 3-SAT problem is in NP appealing to the definition of the NP class .

2. Finding a vertex cover of a graph, is a problem of finding a set of vertices of minimum size such that each edge in the graph is covered with at least one vertex. Formulate a decision version of the vertex cover problem.

3. Suppose A and B are two different decision problems and furthermore assume that problem A is polynomial-time reducible to problem B. If problem B is NP-complete, is problem A NP-complete ? Justify your answer.

Make powerpoint on insertion sort algorithm
Write a structured algorithm to prompt the user to enter the length of a square. Calculate the output and area of the square

Q2: As we know, the heuristic or approximation algorithms may not give an optimum solution to the problem but they are polynomial efficient.

(a) Propose an approximation algorithm for travelling salesman problem (TSP) and discuss about its time complexity and limitation. (6 marks)

(b) Give two example inputs, in which the algorithm in (a) gives the best and not-thebest solutions, respectively. The number of nodes should be between six and eight. (4 marks)

Write a structured algorithm to prompt the user to input the ages of four friends. The algorithm should allow the user to input the ages, find and print the average.
Write a structured algorithm to prompt the user to enter the length of a square. Calculate and output the area of the square.
What is the MAXimum number of swaps between heap elements required to construct a max heap of 9 elements using the O(n) BuildHeap(array)?
What is the MAXimum number of comparisons between heap elements required to construct a max heap of 12 elements using the O(n) BuildHeap(array)?
1. A hospital wants a program that records and monitors the temperature of each baby that is currently in its maternity unit. It wants to store the temperature of each baby; it will have 15 babies in the unit at a time.
• If a baby’s temperature is below 36.5 degrees, the program should alert a nurse with a suitable message.
• If a baby’s temperature is above 37.5 degrees, the program should alert a nurse with a suitable message.

Write an algorithm that the hospital could use to store and monitor the temperatures of the babies in the unit.  

The mainline logic of almost every produral program consists of three parts namely householdkeeping tasks,detail loop and end of job task. By making use of flowchart show how these parts can be implemented in the solution for question 2.1
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