Elements
           of
           Programming
           Interviews in C++
           TheInsiders’ Guide
           AdnanAziz
           Tsung-HsienLee
           AmitPrakash
            This document is a sampling of our book, Elements of Program-
            ming Interviews in C++ (EPI). Its purpose is to provide examples
            of EPI’s organization, content, style, topics, and quality. The sam-
            pler focuses solely on problems; in particular, it does not include
            three chapters on the nontechnical aspects of interviewing. We’d
            love to hear from you—we’re especially interested in your sugges-
            tions as to where the exposition can be improved, as well as any
            insights into interviewing trends you may have.
              You can buy EPI at Amazon.com (paperback) and Google Play
            (Ebook).
           http://ElementsOfProgrammingInterviews.com
       AdnanAzizisaResearchScientist at Facebook. Previously, he was a professor at the Department
       of Electrical and Computer Engineering at The University of Texas at Austin, where he conducted
       research and taught classes in applied algorithms. He received his Ph.D. from The University of
       California at Berkeley; his undergraduate degree is from Indian Institutes of Technology Kanpur.
       He has worked at Google, Qualcomm, IBM, and several software startups. When not designing
       algorithms, he plays with his children, Laila, Imran, and Omar.
       Tsung-Hsien Lee is a Senior Software Engineer at Uber. Previously, he worked as a Software
       Engineer at Google and as Software Engineer Intern at Facebook. He received both his M.S. and
       undergraduate degrees from National Tsing Hua University. He has a passion for designing and
       implementingalgorithms. Helikes to apply algorithms to every aspect of his life. He takes special
       pride in helping to organize Google Code Jam 2014 and 2015.
       AmitPrakashisaco-founderandCTOofThoughtSpot,aSiliconValleystartup. Previously,hewasa
       MemberoftheTechnicalStaffatGoogle,whereheworkedprimarilyonmachinelearningproblems
       that arise in the context of online advertising. Before that he worked at Microsoft in the web search
       team. He received his Ph.D. from The University of Texas at Austin; his undergraduate degree is
       from Indian Institutes of Technology Kanpur. When he is not improving business intelligence, he
       indulges in his passion for puzzles, movies, travel, and adventures with Nidhi and Aanya.
       ElementsofProgrammingInterviews: TheInsiders’Guide
       byAdnanAziz,Tsung-HsienLee,andAmitPrakash
       Copyright©2017AdnanAziz,Tsung-HsienLee,andAmitPrakash. Allrightsreserved.
       Nopartofthispublication may be reproduced, stored in a retrieval system, or transmitted, in any
       form, or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the
       prior consent of the authors.
       The views and opinions expressed in this work are those of the authors and do not necessarily
       reflect the official policy or position of their employers.
                               A
       Wetypesetthis book using LT X and the Memoir class. We used TikZ to draw figures. Allan Ytac
                                E
       created the cover, based on a design brief we provided.
       The companion website for the book includes contact information and a list of known errors for
       eachversionofthebook. Ifyoucomeacrossanerrororanimprovement,pleaseletusknow.
       Website: http://elementsofprogramminginterviews.com
       Distributed under the Attribution-NonCommercial-NoDerivs 3.0 License
                               TableofContents
               I        DataStructuresandAlgorithms                                                                                                                                        1
               1     Primitive Types                                                                                                                                                       2
                     1.1         Computingtheparityofaword . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                       3
               2     Arrays                                                                                                                                                                7
                     2.1         TheDutchnationalflagproblem . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                        9
               3     Strings                                                                                                                                                             13
                     3.1         Interconvert strings and integers . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                               14
                     3.2         Baseconversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                              15
               4     LinkedLists                                                                                                                                                         17
                     4.1         Test for cyclicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                          19
               5     Stacks and Queues                                                                                                                                                   22
                     5.1         ImplementastackwithmaxAPI . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                       23
                     5.2         Computebinarytreenodesinorderofincreasingdepth . . . . . . . . . . . . . . .                                                                            27
               6     BinaryTrees                                                                                                                                                         30
                     6.1         Test if a binary tree is height-balanced . . . . . . . . . . . . . . . . . . . . . . . . .                                                              32
               7     Heaps                                                                                                                                                               35
                     7.1         Mergesortedfiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                               37
               8     Searching                                                                                                                                                           39
                     8.1         Search a sorted array for first occurrence of k . . . . . . . . . . . . . . . . . . . . .                                                                42
               9     HashTables                                                                                                                                                          44
                     9.1         Is an anonymousletter constructible?                                  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . . . .            48
               10 Sorting                                                                                                                                                                50
                     10.1        Computetheintersectionoftwosortedarrays . . . . . . . . . . . . . . . . . . . .                                                                         52
                     10.2        Renderacalendar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                               53
               11 BinarySearchTrees                                                                                                                                                      56
                                                                                                     i
                     11.1        Test if a binary tree satisfies the BST property . . . . . . . . . . . . . . . . . . . . .                                                               58
               12 Recursion                                                                                                                                                              61
                     12.1        Generatethepowerset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                 62
               13 DynamicProgramming                                                                                                                                                     65
                     13.1        Countthenumberofwaystotraversea2Darray . . . . . . . . . . . . . . . . . . .                                                                            67
               14 GreedyAlgorithmsandInvariants                                                                                                                                          71
                     14.1        The3-sumproblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                 73
               15 Graphs                                                                                                                                                                 75
                     15.1        Paint a Boolean matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                              79
               16 Parallel Computing                                                                                                                                                     80
                     16.1        ImplementaTimerclass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                  81
               II DomainSpecificProblems                                                                                                                                                  83
               17 DesignProblems                                                                                                                                                         84
                     17.1        Designasystemfordetectingcopyrightinfringement . . . . . . . . . . . . . . . .                                                                          85
               18 LanguageQuestions                                                                                                                                                      87
                     18.1        References and pointers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                               87
               19 Object-Oriented Design                                                                                                                                                 88
                     19.1        Creational Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                             88
               20 CommonTools                                                                                                                                                            90
                     20.1        Merginginaversioncontrolsystem . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                      90
               III The Honors Class                                                                                                                                                      94
               21 HonorsClass                                                                                                                                                            95
                     21.1        Computethegreatestcommondivisor                                             .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   .  .        96
                     21.2        Computethemaximumproductofallentriesbutone                                                             .  .  .  .  .  .  .  .  .  .  .  .   .  .        97
               IV NotationandIndex                                                                                                                                                    100
               Notation                                                                                                                                                                101
               IndexofTerms                                                                                                                                                            103