Suppose you have an array of n elements containing three distinct keys, true, false, and maybe. Give an O(n) algorithm to rearrange the list so that all false elements precede the maybe elements, which in turn precede all true elements. You may use only constant extra space.
Suppose you have an array of n elements containing three distinct keys, true, false, and maybe....
6. Give an efficient algorithm to rearrange an array of n keys so that all negative keys precede all nonne- gative keys. Your algorithm must be in-place meaning you cannot allocate another array to temporarily hold the items.
Do problem 4-20: Give an efficient algorithm to rearrange an array of n keys so that all the negative keys precede all the nonnegative keys. Your algorithm must be in-place, meaning you cannot allocate another array to temporarily hold the items. How fast is your algorithm?
Design an algorithm to rearrange elements of a given array of n real numbers so that all its negative elements precede all its positive elements. Your algorithm should be both time efficient and space efficient. (run the code in a programming language and present the running result)
Suppose that you are given an array of N elements. Develop an optimum algorithm that finds the minimum k elements of this array in at most nlogn time. Try your algorithm on an example N-sized array and some value of k.
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Problem 2 You are given an array A with n distinct elements. Implement an (n log n)-time algorithm that creates an array B where all elements are in range from 0 to n - 1 and where the order of elements is the same as in A. That is, 0 has the same index in B as the smallest element in A, 1 has the same index in B as the second smallest element...
1. Suppose that an array al] is a max-heap that contains the distinct integer keys 1, 2,.., N with N> 7. The key N must be in gl1] and the key N-1 must be in either al2) or al3) a. Give all possible positions for the key N-2 as a function of N. b. Repeat the same question for the key 2
3. Suppose you have an array of n random elements. You are required to perform n different searches on the array. What is best big-oh time for your entire task? Explain how to achieve that time. 4. Suppose you are given two sorted integer arrays int[] A and int[] B. Write a method that returns an array which contains only the common elements (elements that are present in both A and B) of these two sorted arrays. Indicate the big-Oh...
Suppose you are given an array A holding n distinct integers (negative values are allowed) in sorted order; in other words, A[i] < A[i + 1] for each i ∈ [0, n − 2]. We say the ith element is self referential if A[i] = i. Design an O(log n) time algorithm to determine if there is a self referencial element in the array. Your solution must include a) Statement of your algorithm in plain English. (Pseudo-code is optional.) b)...
Suppose that A is an array whose integer elements are organized into a max-heap. Also suppose that e is an integer. Write an algorithm IS-IN-MAX-HEAP(A, e) that tests if e is an element of A. Your algorithm must not change A, and it must not make copies of A. It must avoid visiting all elements of A where possible—so it must not use linear search. You may state your answer in English, in Cormen’s pseudocode notation, or in a programming...
5. A three-heap with n elements can be stored in an array A, where A[O] contains the root of the tree. a) Draw the three-heap that results from inserting 5, 2, 8, 3, 6, 4, 9, 7, 1 in that order into an initially empty three-heap. You do not need to show the array representation of the heap. You are only required to show the final tree, although if you draw intermediate trees. b) Assuming that elements are placed in...