Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 8.4, Problem 1E
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To illustrate the operation of BUCKET-SORT on the array
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- Given an array of integers arr, sort the array by performing a series of pancake flips. In one pancake flip we do the following steps: Choose an integer k where 1 <= k <= arr.length. Reverse the sub-array arr[0...k-1] (0-indexed). For example, if arr = [3,2,1,4] and we performed a pancake flip choosing k = 3, we reverse the sub-array [3,2,1], so arr = [1,2,3,4] after the pancake flip at k = 3. Print out the k-values corresponding to a sequence of pancake flips that sort arr. Example 1: Input: arr = [3,2,4,1] Output: 4, 2, 4, 3 Explanation: We perform 4 pancake flips, with k values 4, 2, 4, and 3. Starting state: arr = [3, 2, 4, 1]. After 1st flip (k = 4): arr = [1, 4, 2, 3] After 2nd flip (k = 2): arr = [4, 1, 2, 3] After 3rd flip (k = 4): arr = [3, 2, 1, 4] After 4th flip (k = 3): arr = [1, 2, 3, 4], which is sorted. Another potential solution is: Output = 3, 4, 2, 3, 1, 2, 1, 1 with a similar explanation. All potential solutions that solve the problem are…arrow_forwardCreate a bottom-up mergesort that takes advantage of array order by doing the following each time it has to identify two arrays to merge: locate a sorted subarray (by incrementing a pointer until it finds an entry in the array that is smaller than its predecessor), then locate the next, and finally merge them. Examine the algorithm's running time in terms of array size and the number of maximal rising sequences in the array.arrow_forwardConsider the array L = 387, 690, 234 435 567 123 441 as an example. The number of components in this case is 7, the number of numbers is 3, and the radix is 10. This suggests that radix sort would require 10 bins and 3 cycles to complete the sorting. shows how the radix order is followed by the list. Each key is probably thrown into the garbage bin facing down. Each bin is turned into a key when the output to the is to be attached to the phrase: at the end of the bin.arrow_forward
- Given an unsorted array A of size N that contains only positive integers, find a continuous sub-array that adds to a given number S and return the left and right index(1-based indexing) of that subarray. In case of multiple subarrays, return the subarray indexes which come first on moving from left to right. Note:- You have to return an ArrayList consisting of two elements left and right. In case no such subarray exists return an array consisting of element -1. Code please.arrow_forwardGiven an unsorted array A of size N that contains only positive integers, find a continuous sub-array that adds to a given number S and return the left and right index(1-based indexing) of that subarray. In case of multiple subarrays, return the subarray indexes which come first on moving from left to right. Note:- You have to return an ArrayList consisting of two elements left and right. In case no such subarray exists return an array consisting of element -1.code.arrow_forwardExplain step-by-step, showing all possible detail, how a binary search algorithm works on the array {1, 2, 3, 4, 5, 6, 7, 8} searching for the values of 5 and 12.arrow_forward
- Using an unsorted array to implement a map would allow an O(log2N) get operation (where N is the number of elements in the map). Group of answer choices True False also explain why?arrow_forwardIllustrate (step by step) the operation of COUNTING-SORT on the array A = {6, 2, 0, 1, 3, 4, 6, 3, 2}.arrow_forwardApply quick sort on array [5, 4, 3, 1, 6, 7, 11, 9, 2, 10, 8]. Assuming the pivot value selected on the first pass of the sort is 8, what is the content of the array after the first pass of "Partition" around pivot completes? [8, 4, 3, 1, 6, 7, 2, 5, 11, 10, 9] [3, 1, 2, 4, 5, 8, 6, 7, 11, 10, 9] [5, 4, 3, 1, 2, 7, 11, 9, 6, 10, 8] [5, 4, 3, 1, 6, 7, 2, 8, 11, 10, 9]arrow_forward
- 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. botharrow_forwardWrite 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 entry 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 algorithm.arrow_forwarda. Show step-by-step application of the Selection sort algorithm for the array given below. What is the time complexity of this algorithm? 20 12 10 15 2 b. Consider the below array and show all steps for carrying out one partition of quick sort algorithm. Consider first element as the pivot element. 54 26 93 17 77 31 44 55 20arrow_forward
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