Write algorithm method code that demonstrates the Fibonacci search process. The amount of data elements in this case, n, is such that: i) Fk+1 > (n+1); and ii) Fk + m = (n +1) for some m ≥ 0, where Fk+1 and Fk are two consecutive Fibonacci numbers.

in java

Given an integer array A[1..n] you are to list the k smallest elements. What method will you use when (i)k=0(1) Explain why you chose the algorithm you chose for parts (i)

Consider sorting n numbers stored in array A[1:n] by first finding the smallestelement of A[1:n] and exchanging it with the element in A[1]. Then find thesmallest element of A[2:n], and exchange it with A[2]. Then find the smallestelement of A[3:n], and exchange it with A[3]. Continue in this manner for thefirst n-1 elements of A. Write pseudocode for this algorithm, which is knownas selection sort. What loop invariant does this algorithm maintain? Why does itneed to run for only the first n-1 elements, rather than for all n elements? Give theworst-case running time of selection sort in big theta notation. Is the best-case runningtime any better?

Quick sort the list L = {A, B, N, M, P, R}. What are your observations? How canthe observations help you in determining the worst-case complexity of quick sort?

The algorithm: –In an array of n elements, go to index [n/2] –If the record there is the one you want, you are done –If the record value there is smaller than your search value, all records less than the current record can be ignored – set your search range of elements to [n/2+1…n] and return to step 1 –Otherwise, set your range of elements to [0…(n/2)-1] and return to step 1 –Repeat this loop until you have 0 elements (record is not found) or record is found Short answer Another approach to the update algorithm is to perform use the delete function for the old value and if it is successful, call the insert function using the new value. Explain in your own words if you think this approach is significantly better, worse, or in the same category as the algorithm discussed in the slides, and why.

True or false? The best-case number of comparisons needed to conduct a linear search of an array of n integers is n. True False

The algorithm below searches for the maximum in an input array A. Assume A is a random sequence containing n distinguishable real numbers, what is the probability for line #4 to be executed exactly once? (The phrase "random sequence" here means the n numbers can appear in any order with equal chance.) mymax(A, n) { 1: max = A[1]; 2: for i = 2:n 3: if A[i] > max 4: max = A[i); 5: end; 6: end; 7: return max; }

Let A = [n, n − 1, n − 2, . . . , 3, 2, 1] be an array where the first n positive integers are listed in decreasing order. Determine whether Heapsort or Quicksort sorts this array faster.For this question, assume the Quicksort pivot is always the right-most element.

an array of integers nums sorted in ascending order, find the startingand ending position of a given target value. If the target is not found in thearray, return [-1, -1]. For example:Input: nums = [5,7,7,8,8,8,10], target = 8Output: [3,5]Input: nums = [5,7,7,8,8,8,10], target = 11Output: [-1,-1].