/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q14E You are given an array of聽 n聽e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q14E (page 85)

You are given an array of nelements, and you notice that some of the elements are duplicates; that is, they appear more than once in the array. Show how to remove all duplicates from the array in time O(nlogn) .

Short Answer

Expert verified

All duplicates are removed from the array in time: O(nlogn)

Step by step solution

01

Method-I

We may use pre-processing to eliminate duplicates by sorting the array. Its arrays sort consumes Onlogn time, and then we can verify if the last value is like the present value inside one pass; if it is, we don't display that number; otherwise, we do. We'll be able to get rid of the duplicates this way.

So the total amount of time is nLogn+1=OnLogn

02

Method-II

We need to perform nested loops if we haven't done the pre-processing yet. We execute one loop over the whole array (assuming index i and for each index i we check to see if the identical element is in the remaining set; if so, we do not print the element; otherwise, we do. Without pre-processing, the complexity will be ON2.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In justifying our matrix multiplication algorithm (Section 2.5), we claimed the following block wise property: if X and Y are n脳nn matrices, and

X=[ABCD],Y=[EFGH],

where A,B,C,D,E,F,G, and H are n/2脳n/2 sub-matrices, then the product XY can be expressed in terms of these blocks:

XY=[ABCD][EFGH]=[AE+BGAF+BHCE+DGCF+DH]

Prove this property.

In our median-finding algorithm (Section 2.4), a basic primitive is the split operation, which takes as input an array S and a value V and then divides S into three sets: the elements less than V , the elements equal to V , and the elements greater than V . Show how to implement this split operation in place, that is, without allocating new memory.

Practice with the fast Fourier transform.

(a) What is the FFT of (1,0,0,0)? What is the appropriate value of 蝇in this case? And of which sequence is (1,0,0,0)the FFT?

(b)Repeat for (1,0,1,-1).

You are given two sorted lists of size mandn. Give an O(logm+logn)time algorithm for computing the k th smallest element in the union of the two lists.

Thesquare of a matrix A is its product with itself, AA.

(a) Show that five multiplications are sufficient to compute the square of a 2 x 2 matrix.

(b) What is wrong with the following algorithm for computing the square of an n x n matrix?

鈥淯se a divide-and-conquer approach as in Strassen鈥檚 algorithm, except that instead of getting 7 subproblems of size n2, we now get 5 subproblems of size n2 thanks to part (a). Using the same analysis as in Strassen鈥檚 algorithm, we can conclude that the algorithm runs in time O (nc) .鈥�

(c) In fact, squaring matrices is no easier than matrix multiplication. In this part, you will show that if n x n matrices can be squared in time S(n) = O(nc), then any two n x n matrices can be multiplied in time O(nc) .

  1. Given two n x n matrices A and B, show that the matrix AB + BA can be computed in time 3S(n) + O(n2 ) .
  2. Given two n x n matrices X and Y, define the 2n x 2n matrices A and B,L as follows:
    A=X000andB=0Y00
    What is AB + BA, in terms of X and Y?
  3. Using (i) and (ii), argue that the product XY can be computed in time 3S(2n) + O(n2 ). Conclude that matrix multiplication takes time O(nc ).
See all solutions

Recommended explanations on Computer Science Textbooks

Cybersecurity in Computer Science

Read Explanation

Algorithms in Computer Science

Read Explanation

Issues in Computer Science

Read Explanation

Data Representation in Computer Science

Read Explanation

Big Data

Read Explanation

Theory of Computation

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.