In this question we will look at theInterval schedulingproblem. The problem consists of a set of tasks. Each of these tasks need to be executed in aspecific time interval. Two tasks are set to be compatible if their time intervals do notoverlap. The goal is to find the maximum set of compatible tasks so that as many taskspossible can be executed. For example consider the case of just three tasksTask start time end time Task 1 1 10 Task 2 2 5Task 3 7 9 Here the set consisting of Task 2 and Task 3 is the set consisting of marimum number of compatible tasks. It is maximum because if we select Task 1, then we cannot select either Task 2 or Task 3 as both of them have overlapping intervals with Task 1. Consider a greedy algorithm which always selects the shortest appointment first. Provide an example in tabular form with at least 5 tasks where this algorithm fails. List the order in which the algorithm selects the intervals, and also write down a larger subset of non-overlapping intervals than the subset output by the greedy algorithm.

Write a pseudocode solution for each of these problems. 1. design a while loop that lets that user enter a number. the number should be multiplied by 10, and the result stored in a variable named product. the loop should iterate as long as product contains a value less than 100. 2. design a do-while loop that asks the user to enter two numbers. the numbers should be added and the sum displayed. the loop should ask the user whether he or she wishes to perform the operation again. if so, the loop should repeat; otherwise it should terminate. 3. design a for loop that displays the following set of numbers: 0, 10, 20, 30, 40, 50 100. 4. design a nested loop that displays 10 rows of # characters. there should be 15 # characters in each row. 5. convert this for loop to a while loop. declare integer count for count = 1 to 50 display count end for 6. find the error in the following pseudocode. declare boolean finished = false declare integer value, cube while not finished display “enter a value to be cubed.” input value; set cube = value ^ 3 display value, “ cubed is “, cube end while

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Write a function balancechemical to balance chemical reactions by solving a linear set of equations. the inputs arguments are: reagents: symbols of reagents in string row array products: symbols of products in string row array elements: elements in the reaction in string row array elcmpreag: elemental composition of reactants in two dimensional numeric array elcmpprdcts: elemental composition of prducts in two dimensional numeric array hint: the first part of the problem is setting up the set of linear equations that should be solve. the second part of the problem is to find the integers from the solution. one way to do this is to mulitiply the rational basis for the nullspace by increasing larger integers until both the left-and right-side integers exist. for example, for the reaction that involves reacting with to produce and : reagents=["ch4", "o2"]; products =["co2", "h2o"]; elements =["c","h", "o"] elcmpreag=[1,4,0;