Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 5.3, Problem 5E
Program Plan Intro
To prove that the probability that all elements are unique is at least
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Let T be a sorted array of n elements. An element x is said to be a majority element in T if the number of elements i, with T[i] = x, is greater than n/2.
Give an algorithm (code or pseudo-code) that can decide whether T includes a majority element (it cannot have more than one), and if so, find it. Your algorithm must run
in linear time.
For any input array of n 3-digit numbers, prove that Radix Sort is guaranteed to correctly sort these n numbers, with the algorithm running in O(n) time.
Algorithm FHL Version of Schreier-Sims is O ( I f) 16), provided that the size of the initial generating set is O ( I ~ 14).
Chapter 5 Solutions
Introduction to Algorithms
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- What is the obvious limit-to the problem of finding the median of a given array of n-elements? Is this obvious lower bound a TIGHT lower bound, why?arrow_forwardLet A be a random permutation of [a,b,c,d,e,f,g,h]. Determine the probability that exactly 12 comparisons are required by Merge Sort to sort the input array A. Clearly and carefully justify your answer.arrow_forwardGiven an array of numbers X₁ = {x₁, x2, ..., n } an exchanged pair in X is a pair xi, xj such that i x¡ . Note that an element x; can be part of up to n - 1 exchanged pairs, and that the maximal possible number of exchanged pairs in X is n(n − 1)/2, which is achieved if the array is sorted in descending order. Give a divide-and-conquer algorithm that counts the number of exchanged pairs in X in O(nlogn) time.arrow_forward
- Let B = {a + bi|a, b ∈ N}. Prove that B is countable.arrow_forwardLet A be a random permutation of [1,2,3,4,5,6,7,8]. Determine the probability that exactly 12 comparisons are required by Merge Sort to sort the input array A. Clearly and carefully justify your answer.arrow_forwardQuestion: use magic-pivot to obtain a deterministic quick-sort algorithim with the worst-case running time of O(n log n).arrow_forward
- Algorithm A excecutes an O(logn) time compuation for each entry of an n-element array. What is the worst case running time of Algorithm A?arrow_forwardmake algorithm for MatrixMultiplication (A1, A2, ... , An) pre-cond: An instance is a sequence of n matrices. post-cond: optSol is a bracketing that requires the fewest multiplications, and optCost is the resulting number of multiplications.arrow_forwardUse the Transform-and-Conquer algorithm design technique with Instance Simplification variant to design an O(nlogn) algorithm for the problem below. Show the pseudocode. Given a set S of n integers and another integer x, determine whether or not there exist two elements in S whose sum is exactly x.arrow_forward
- Suppose arrays A and B are both sorted in increasing order and both contain n elements. What is the time complexity to find the median of A U B, i.e., the set of elements in A or B?arrow_forwardConsider the problem of sorting an array A[1, ..., n] of integers. We presented an O(n log n)- time algorithm in class and, also, proved a lower bound of (nlogn) for any comparison-based algorithm.arrow_forwardWe apply the binary search on a 17-element ordered array. Assume that a givenkey appears in the array, and it is between the 5th element and the 13th element(inclusive). How many comparisons do we need for the average-case efficiency?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill Education
Starting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSON
Digital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSON
Database Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage Learning
Programmable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education