to every other element. When the input is the array [2, 9, 5, 4, 6
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Randomized quicksort compares individual pairs of elements but it does not necessarily compare every element to every other element. When the input is the array [2, 9, 5, 4, 6], what is the probability that randomized quicksort compares 2 and 4 directly to each other? Give an exact answer.
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- Create a quicksort based on splitting a random sample of five items from the subarray according to their medians. Place the sample's elements at the correct ends of the array so that only the median is used for partitioning.To evaluate the impact of the adjustment in contrast to the default method and median-of-3 partitioning (see the preceding exercise), do doubling tests.Extra points Create a median-of-five method that employs no more than seven comparisons for every given input.Using heapsort to sort [10,5,10,5] and [5,10,5,10], on which of the two arrays, the relative order of all the elements of the same values will be preserved? Can you show a working behind your answer? Options are: 1. only [10,5,10,5] 2. only [5,10,5,10] 3. none 4. bothcreate a plan for implementation Instead of the binary-search-based linearithmic technique, TwoSumFaster employs a linear algorithm to count the pairings that sum to zero once the array is sorted. Then, using a similar concept, create a quadratic method for the 3-sum issue.
- Implement a quicksort based on partitioning on the median of a random sample of five items from the subarray. Put the items of the sample at the appropriate ends of the array so that only the median participates in partitioning. Run doubling tests to determine the effectiveness of the change, in comparison both to the standard algorithm and to median-of-3 partitioning (see the previous exercise). Extra credit : Devise a median-of-5 algorithm that uses fewer than seven compares on any input.Create a quicksort based on splitting a random sample of five items from the subarray according to their medians. Place the sample's items at the correct ends of the array so that only the median is used for partitioning. To evaluate the impact of the adjustment in contrast to the default algorithm and median-of-3 partitioning (see the preceding exercise), do doubling tests.Extra points Create a median-of-five algorithm that employs no more than seven comparisons for every given input.The worst-case scenario for the fast sort algorithm occurs when each partition consists of a single empty subarray, all partitions are of equal size, and the selection of the pivot element is indeterminate. Are the elements in the initial array completely randomized?
- Run mergesort for huge random arrays and determine empirically, as a function of N (the total of the two subarray sizes for a given merge), the average length of the other subarray when the first subarray exhausts.Write a bottom-up mergesort that makes use of the array's order by carrying out the following steps each time it needs to locate two arrays to merge: locate the first element in an array that is smaller than its predecessor, then locate the next, and finally merge them to form a sorted subarray. Consider the array size and the number of maximal ascending sequences in the array while analysing the running time of this method.Write out the algorithm (pseudocode) to find K in the ordered array by the method that compares K to every fifth entry until K itself or an entry larger than K is found, and then, in the latter case, searches for K among the preceding four. How many comparisons does your algorithm do in the worst case?
- Which methods/actions in the Sorted Array can be made significantly more efficient compared to the Unsorted Array? Why is this? In other words, what can be done in the Sorted Array implementation to radically improve the efficiency that can't be done in an Unsorted Array?When we apply the mergesort on a 12-element array, how many comparisons do we need for the worst case? Ans:Implement an algorithm that returns the X closest items to a value V, for any array of integer elements. V may or may not be present in the array. Its solution must be O(nlogn). (phyton or Java). Note: The proposed solution must use the divide-and-conquer strategy.