Problem 3: Sparse polynomials (Problem H in Mooshak POO 2015/2016)

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1 Programação Oretada por Objectos Problem 3: Sparse polyomals (Problem H Mooshak POO 215/216) Submt: Your source code to mooshak ad Your report (wth a zp fle) to Up to November 23, 215, 1H I ths problem you are gog to develop a program for mapulatg polyomals wth umerc coeffcets (ad expoets).. Read the problem descrpto gve the appedx. Make sure you fully uderstad the problem. Should you have ay doubt about t, do ot hestate to ask. 1. Notce that we are dealg wth sparse polyomals, that s, polyomals whose umber of terms wth ull coeffcets s approxmately equal to the polyomal degree. 2. For effcecy reasos t s completely out of questo to use the aïf approach of employg a array to save all the polyomals coeffcets (cludg the ull coeffcets). That would smplfy the mplemetato of operatos, but would be also extremely expesve terms of the requred storage space. 3. What we are gog to do s that save oly the terms wth o-ull coeffcets. For stace, for the polyomal A(x) = 2x wll be save oly two terms, that are roughly llustrated the followg fgure: coeffcet expoet Term 1 Term 2 4. Develop a class that mplemets a sgle-lk lst ad defes ts terator. 5. Use the developed class to mplemet aother class that mplemets sparse polyomals as descrbed above. I these classes, restrct the methods oly to those strctly ecessary,.e., do ot code ay method that s ot deemed ecessary for the curret problem. 6. NB: Ay other approach to ths problem, depedetly of ts mert, wll be marked wth (zero) values. POO Problem 3-1

2 Programação Oretada por Objectos 7. Employ the prcples ad techques of Object-Oreted Programmg, specally, use ested classes ad terfaces. 8. Use test-drve developmet. 9. Documet your report both the UML dagram(s) ad the ut tests developed, as well as all the desg optos take. POO Problem 3-2

3 Programação Oretada por Objectos Appedx: Sparse Polyomals // Lea abaxo a versão Portuguesa Wrte a program that a. sum 2 polyomals b. multply 2 polyomals c. compute the value of a polyomal at a gve teger pot. A polyomal s a sum of terms of the form ax e, where: x s the varable a s the coeffcet, ad e s the expoet I ths problem, the umber of terms wll ever be bgger tha 7 (seve). However, these terms ca have very hgh expoets. Furthermore, varable, coeffcets, ad expoets are guarateed to be tegers. Gve the polyomals P( x) = p x ad Q( x) = q x = the ( ) P x + Q(x) = = (p + q ) x = j q jx ) = j= ad P ( x).q(x) = (p x Recall also the Horer s rule whch allows computg A(x) at x usg a mmum of operatos. Ths rule s based o the followg observato: A(x) = a x + a -1 x a 1 x + a o = (... (a x + a -1 ) x + + a 1 ) x + a o ) Iput The put has three rows. The frst row represets a polyomal wth teger varable, coeffcets ad expoets. Furthermore, the terms of the polyomals are gve by descedet order. The secod row has oe (ad oly oe) of the followg possble characters: + (meag that a sum of polyomals should be computed) * (meag that a product of polyomals should be (meag that the polyomal represeted the frst le should be evaluated at the teger pot provded the put ext le) The thrd row represets a polyomal (f the character the prevous le s ether + or *) or a teger (f the character the prevous le s POO Problem 3-3

4 Programação Oretada por Objectos Polyomals are represeted by a space separated sequece of tegers. The frst teger represets the coeffcet of the term wth the hghest expoet. The secod teger represets the expoet of the terms. The ext tegers have smlar meag. Terms wth ull coeffcets are ot represeted. A x = 2x s represeted by the followg teger sequece: For stace, the polyomal ( ) Output The output has always oe row oly. Ths row s ether oe teger (wheever the requred operato or oe polyomal (f the requred operato s + or *). I ths last case, the polyomal should be represeted wth the same format descrbed for the put. Sample put Sample output Sample put Sample output POO Problem 3-4

5 Programação Oretada por Objectos Appedx: Polómos esparsos // Read above the Eglsh verso Escreva um programa em Java que a. some 2 polómos b. multplque 2 polómos c. determe o valor do polómo um poto dado tero. Um polómo é uma soma de termos, em que cada termo é da forma ax e, ode: x é a varável a é o coefcete e e é o expoete. Neste problema o úmero de termos uca será superor a 7 (sete), o etato, esses termos podem ter expoetes elevados. Quer a varável quer os coefcetes dos polómos são garatdamete teros. Dados os polómos P( x) = p x e Q( x) = q x P x + Q(x) = = etão ( ) = (p + q ) x = j q jx ) = j= e P ( x).q(x) = (p x Lembre-se ada da regra de Horer que possblta calcular o valor de um polómo A(x) em x usado o meor úmero possível de operações. Esta regra basea-se a segute observação: A(x) = a x + a -1 x a 1 x + a o = (... (a x + a -1 ) x + + a 1 ) x + a o ) Iput A etrada terá sempre três lhas. A prmera lha represetará sempre um polómo de varável, coefcetes e expoete teros. A seguda lha terá um e só um dos segutes caracteres: + (Idcado que se pretede efectuar a soma de polómos) * (Idcado que se pretede efectuar o produto de (Idcado que se pretede calcular o valor do polómo um poto) A tercera lha represetará um polómo (caso o caracter da lha ateror seja + ou *) ou um tero (o caso desse caracter ser Os polómos são represetados por uma sequêca de teros separados por espaços. O prmero tero represeta o coefcete do termo de maor expoete, o segudo tero represeta o expoete, e assm sucessvamete até ao últmo termo, de meor expoete. Não se represetam POO Problem 3-5

6 Programação Oretada por Objectos termos com coefcete ulos. Por exemplo, o polómo A( x) 2x segute sequêca de teros: = é represetado pela Output Um tero, se a operação seleccoado Um polómo o formato descrto acma, se a operação for + ou * Sample put Sample output Sample put Sample output POO Problem 3-6