In the binary search algorithm, what are the four cases you have to consider at each iteration and what do you have to do in each case?
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(a) In the binary search
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- Design and Analysis of Algorithms Consider the following description of a recursive algorithm:“The algorithm splits the input in three equal parts in constant time, process each part recursively and finally combines the solution in linear time”.Formulate a recurrence and solve it to compute total execution time of the algorithm.(Note: You can use any method for solving the recurrence.)Algorithm problem w/ recurrence: Frying pancakes: a small pan can only hold two pancakes at a time. Each pancake needs to be fried on both sides. Frying one side takes 1 minute, no matter how many pancakes are on the pan. Consider this recursive algorithm: If n <= 2, fry the pancakes or the two pancakes together on each side. If n > 2, fry any two pancakes together on each side and then apply the same process recursively to the remaining n-2 pancakes. a. Set up and solve the recurrence for the amount of time this algorithm needs to fry n pancakes. b. Explain why this algorithm does not fry the pancakes in the minimum time for all n > 0. c. Give a correct recursive algorithm that executes the task in the minimum amount of time. > I was not sure how to start this. I have had trouble with recurrence in the past. Also from the work that I did do, I didn't know how there could be a better algorithm. Thanks in advance9. Voting Suppose that the votes of n people for different candidates (where there can be more than two candidates) for a particular office are the elements of a sequence. A person wins the election if this person receives a majority of the votes. * Devise a divide-and-conquer algorithm that determines whether the two candidates who received the most votes each received at least n/4 votes and, if so, determine who these two candidates are. (NOTE: Please elaborate and explain briefly and please do not provide or copy answer from the internet or from chegg.)
- PLEASE USE BINARY SEARCH AND C LANGUAGE SIR, THX. The Famous Gauss You must know about Gauss, the famous mathematician. Back in late 1700’s, he was at elementary school. Gauss was asked to find the sum of the numbers from 1 to 100. The question was assigned as “busy work” by the teacher. He amazed his teacher with how quickly he found the sum of the integers from 1 to 100 to be 5050. Gauss recognized he had fifty pairs of numbers when he added the first and last number in the series, the second and second-last number in the series, and so on. For example:(1 + 100), (2 + 99), (3 + 98), ..., (50 + 51). Each pair has a sum of 101 and there are 50 pairs. History repeats itself. Jojo’s teacher assign a “busy work” to the students. The teacher believes that there will be no shortcut to finish this task in a minute. The teacher gives N integers A1, A2, ..., AN to the students. The teacher also gives Q questions. Each question contains two integers L and R asking the sum of all Ai where L…Sequential and binary search algorithms have pros and cons.What are the binary search algorithm's sole requirements?
- Question-3 There are n number of students in a class.Assume a teacher enters and wants to shake hand according to an algorithm: Algorithm (X) à 2n a) Write a recursive function to solve this problem for any number of students also calculate the time complexity of your code, along with an idea what might be the best technique to solve this problem other than recursion. b) Consider this Algorithm-Z , Taking list of integer as input List Of Integer: X(Integer: number) List Of Integer: Y Integer: i = 2 While (i< number) While (number Mod i == 0) Y.Add(i) number = number / i End While i = i + 1 End While If (number > 1) Then Y.Add(number) Return Y End X (i) Explain what Algorithm Z is doing? (ii) Analyze the complexity of Algo-Z and then write an algorithm Better-Algo-X that does exactly the same thing but with a strictly better time complexityQuestion-3 There are n number of students in a class. Assume a teacher enters and wants to shake hand according to an algorithm: Algorithm (X) à 2n a) Write a recursive function to solve this problem for any number of students also calculate the time complexity of your code, along with an idea what might be the best technique to solve this problem other than recursion. b) Consider this Algorithm-Z , Taking list of integer as input List Of Integer: X(Integer: number) List Of Integer: Y Integer: i = 2 While (i < number) While (number Mod i == 0) Y.Add(i) number = number / i End While i = i + 1 End While If (number > 1) Then Y.Add(number) Return Y End X (i) Explain what Algorithm Z is doing? (ii) Analyze the complexity of Algo-Z and then write an algorithm Better-Algo-X that does exactly the same thing but with a strictly better time complexityTrue or false Any iterative function can be implemented recursively. Typically, recursive sorts are more efficient than iterative sorts.