258 Chapter 11 Deques { Double Ended Data Structures Chapter - PDF document

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Chapter 11 Deques { Double Ended Data Structures Chapter Ov erview In this c hapter w e will not only in tro duce the deque data structure from the standard template library , but also use the data t yp e to illustrate t w o imp ortan t general searc h tec hniques, depth and breadth �rst searc h. Next, w e will once again revisit the topic of inheritance, in tro duced in Chapter 9, sho wing ho w inheritance can b e used to construct fr ameworks , whic h are sk eleton applications used as the basis for solving similar problems. Finally , w e conclude the c hapter b y presen ting a simpli�ed deque implemen tation, similar to the standard library data structure. � The deque abstraction � Depth and Breadth �rst searc hing � F ramew orks � A Simpli�ed Implemen tation 11.1 The Deque abstraction The deque data t yp e (pronounced either \dec k" or \DQ") is one of the most in teresting data structures in the standard template library . Of all the STL con tainers, the deque is the least con v en tional. It represen ts a data t yp e that is seldom considered to b e one of the \classic" data abstractions, as are v ectors, lists, sets or trees. Nev ertheless, the deque is a p o w erful and v ersatile abstraction. 259

260 CHAPTER 11. DEQUES { DOUBLE ENDED D A T A STR UCTURES The op erations pro vided b y the deque data t yp e, sho wn in Figure 11.1, are a com bination of those pro vided b y the classes vecto r and list . Lik e a v ector, the deque is a randomly accessible structure. This means that instances of the class deque can b e used in most situations in whic h a v ector migh t b e emplo y ed. Lik e a list , elemen ts can b e inserted in to the middle of a deque, although suc h insertions are not as e�cien t as they are with a list. The term deque is short for Double-Ende d QUEue , and describ es the structure w ell. The deque is a com bination of stac k and queue, allo wing elemen ts to b e inserted at either end. Whereas a vecto r only allo ws e�cien t insertion at one end, the deque can p erform insertion in constan t time at either the fron t or the end of the con tainer. Lik e a v ector, a deque is a v ery space e�cien t structure, using far less memory for a giv en size collection than will, for example, a list . Ho w ev er, again lik e a v ector, insertions in to the middle of the structure are p ermitted, but are not e�cien t. An insertion in to a deque ma y require the mo v emen t of ev ery elemen t in the collection, and is th us ( n ) w orst case. O � - � - One of the most common uses for a deque is as an underlying con tainer for either a stack or a queue . The deque is a preferable con tainer for suc h emplo ymen t if the size of the collection remains relativ ely stable during the course of execution, while if the size v aries widely a list or vecto r is preferable. In man y cases the decision concerning whic h structure is most appropriate can only b e made b y p erforming direct measuremen t of program size or execution time. Because the meaning of the op erations on a deque are similar to those of a v ector or a list w e will not describ e them in detail. Instead, w e will pro ceed to an example program that mak es use of the features pro vided b y a deque . 11.2 Application{Depth and Breadth First Searc h In this section w e will examine a program that will disco v er a path through a maze, suc h as the one sho wn b elo w. W e will assume that the starting p oin t for the searc h is alw a ys in the lo w er righ t corner of the maze, and the goal is the upp er left corner. F S

11.2. APPLICA TION{DEPTH AND BREADTH FIRST SEAR CH 261 Constructors and Assignmen t deque < T > d; default constructor deque < T > d (anInt); construct with initial size deque < T > d (anInt, a T value); construct with initial size and initial v alue deque < T > d (aDeque); cop y constructor d = aDeque; assignmen t of deque from another deque d.sw ap (aDeque); sw ap con ten ts with another deque Elemen t Access and Insertion subscript access, can b e assignmen t target d[i] �rst v alue in collection d.front () �nal v alue in collection d.back () insert v alue b efore iterator d.insert (iterator, value) insert v alue at fron t of con tainer d.push front (value) insert v alue at bac k of con tainer d.push back (value) Remo v al d.pop front () remo v e elemen t from fron t of v ector d.pop back () remo v e elemen t from bac k of v ector d.erase (iterator) remo v e single elemen t d.erase (iterator,iterat or ) remo v e range of elemen ts Size n um b er of elemen ts curren tly held d.size () true if v ector is empt y d.empty () Iterators deque < T > ::iterato r itr declare a new iterator d.b egin () starting iterator d.end () stopping iterator d.rb egin () starting iterator for rev erse access d.rend () stopping iterator for rev erse access T able 11.1: Summary of deque op erations

262 CHAPTER 11. DEQUES { DOUBLE ENDED D A T A STR UCTURES Our purp ose in presen ting this example is not only to con trast t w o di�eren t t yp es of searc h tec hniques, but also to demonstrate the op erations of the deque data t yp e, and �nally to sho w ho w a deque can b e used either in a stac k-lik e or queue-lik e fashion. These t w o broad approac hes to searc hing are kno wn as depth �rst se ar ch and br e adth �rst se ar ch . W e w an t the maze searc hing program to b e general, able to solv e an y t w o dimensional maze and not simply the example maze sho wn ab o v e. W e therefore design a sc heme so that the description of the maze can b e read from an input �le. Di�eren t �les can b e used to test the program on a v ariet y of di�eren t mazes. T o see ho w to do this, note that a maze can b e describ ed as a sequence of squares, or c el ls . The example maze sho wn ab o v e, for example, is a �v e b y �v e square of 25 cells. Eac h cell can b e c haracterized b y a n um b er, whic h describ es the surrounding w alls. Sixteen n um b ers are su�cien t. In this fashion w e ha v e the follo wing v o cabulary for describing cells: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 The pattern of the n umeric v alues b ecomes apparen t if one considers the n um b er not as a decimal v alue, but as a binary pattern. The 1's p osition indicates the presence or absence of a south w all, the 2's p osition the east w all, the 4's p osition the north w all, and the 8's p osition the w est w all. A v alue suc h as 13 is written in binary as 1101. This indicates there are w alls to the north, w est, and south, but not the east. Using this sc heme, the example maze could b e describ ed b y 25 in teger v alues. In the fol- lo wing w e ha v e sup erimp osed these v alues on the maze, to b etter illustrate their relationship to the original structure. 14 12 5 4 6 10 9 4 3 10 9 5 2 13 2 14 14 10 12 2 9 1 1 3 11 This represen tation of the maze m ust b e mapp ed on to an represen- external internal tation. The in ternal represen tation need not matc h the external represen tation, as long as there is a means of con v ersion b et w een the t w o. The in ternal represen tation will again b e a sequence of cells. Eac h cell is an instance of the class cell . Instances of class cell main tain three data �elds: