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 8.1, Problem 4E
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To show that lower bounds on the number of comparisons needed to solve the sorting problem is
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Consider a list L = {387, 690, 234, 435, 567, 123, 441}. Here, the number of elements n = 7, the number of digits l = 3 and radix r = 10. This means that radix sort would require 10 bins and would complete the sorting in 3 passes.
Algorithm to illustrates the skeletal procedure for the LSD first radix sort.
Take example given a list of queries, each consisting of three integers: a, b, and k. Your task is to perform a series of operations on an array of size n such that each element in the array is incremented by k in a specific range defined by a and b.
Develop a sort implementation that counts the number of different key values,then uses a symbol table to apply key-indexed counting to sort the array. (This methodis not for use when the number of different key values is large.)
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- The element being searched for is not in an array of 100 elements. What is the maximum number of comparisons needed in a sequential search to determine that the element is not there if the elements are completely unsorted?arrow_forwardSO You have been given two integer arrays/lists (ARR1 and ARR2) of size N and M, respectively. You need to print their intersection; An intersection for this problem can be defined when both the arrays/lists contain a particular value or to put it in other words, when there is a common value that exists in both the arrays/lists.Note :Input arrays/lists can contain duplicate elements.The intersection elements printed would be in the order they appear in the first sorted array/list (ARR1).Input format :The first line of input contains an integer 'N' representing the size of the first array/list.The second line contains 'N' single space separated integers representing the elements of the first the array/list.The third line contains an integer 'M' representing the size of the second array/list.The fourth line contains 'M' single space separated integers representing the elements of the second array/list.Output format :Print the intersection elements. Each element is printed in a separate…arrow_forwardGiven these 8 numeric values to be sorted using the recursive Mergesort algorithm: 92 63 24 18 69 27 64 43 The list that will be passed to the first call of the Mergesort algorithm will be the entire list of values above. Show the list that will be passed to the 5th call of the Mergesort algorithm.arrow_forward
- Given a string representing an array of strings, you will need to sort the given array with the following rules: • Strings should first be sorted based on their rate of occurrence, i.e. strings that are more frequent should appear earlier in the list • If two strings are tied in their occurrence, then they should be sorted by their alphabetical order Each string will be contained by single-quotations which are not part of the word. Additionally, all words will be lower-case. Spelling does NOT matter, nor do the words have to be "valid" or real words. Input will be given exactly as it appears, including brackets, quotations, spaces, and commas, all on a single line of input (I have spread them over many lines to aid reading, they are all on one line). Your output should consist of the words in their proper order followed by their frequency, as below. Feel free to use any methods we have learned in class to answer this, along with the vector or list STL and string…arrow_forwardIn the following Quick Sort algorithm, the last element in the array is selected as Pivot. We are going to select the Median of the data in the array as Pivot. Make the appropriate changes in the following algorithms. Indicate which line (line number) in each algorithm is to be modified and what are the changes. In the original algorithm, the complexity of Quick Sort is "n Log (n)". What would be the complexity with Median as Pivot? Why?arrow_forwardA deque DQUE is to be implemented using a circular one-dimensional array of size N. Execute procedures to:i) insert and delete elements from DQUE at either end;ii) implement DQUE as an output restricted deque;iii) implement DQUE as an input restricted deque;iv) for the procedures, what are the conditions used for testing whether DQUE is full (DQUE_FULL) and empty (DQUE_EMPTY)?arrow_forward
- Binary search necessitates the sorting of data before it can be used. If we start with unsorted data and sort it using selection sort, how many binary searches must we perform to be more efficient than sequential search on the unsorted data?arrow_forwardThe algorithm for finding all occurrences of a sequence in another sequence using the suffix array of the latter sequence can also be implemented in R in a straightforward way, Write R script for given statement.arrow_forwardA gap sort is an adaptation of the bubble sort technique that compares items that are i places or more apart from each other rather than nearby components every time through the list. For instance, the comparison between the first element and the (i + 1) element, the second element and the (i + 2) element, the nth element and the (n - i) element, and so on. A single iteration is completed after all the elements that can be compared have been evaluated. I is decreased by a number greater than one on the subsequent iteration, and the process is continued until i is less than one. Make use of a gap type.arrow_forward
- A variation of the bubble sort algorithm known as a gap sort examines elements that are some number I positions apart, where I is an integer less than n, rather than neighbouring elements each time through the list. The first element, for instance, would be compared to the element I + 1), the second element, to the element I + 2), the nth element, to the element (n - I and so on. Once all the components that can be compared have been done so, the iteration is finished. I am decreased by a factor greater than 1 on the following iteration, and the procedure continues until I is less than 1. Apply the gap filter.arrow_forward7. How many non-empty subsequences does a string of length n have? For example, for the sequence represented by the array [1,3,6,9], [1,3] is a subsequence, and [1,6] is a subsequence, but [6,1] is not. Notice that the order of the elements in a sequence must be preserved in any subsequence.arrow_forwardWrite a Java program to implement a binary search algorithm to search for a target element in a sorted array. Provide an explanation of your approach and the time and space complexity of your solution.arrow_forward
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