Implementeu una funció RECURSIVA que, donat un arbre binari no buit d’enters, retorna el màxim dels seus valors. Aquesta és la capcelera:
// Pre: t és no buit // Post: Retorna el màxim dels valors de t BinaryTree<int> maxOfTree(BinaryTree<int> t);
Aquí tenim un exemple de paràmetre d’entrada de la funció i la corresponent sortida:
3(1(,5),4(1,)) => 5
Fixeu-vos que l’enunciat d’aquest exercici ja ofereix uns fitxers que haureu d’utilitzar per a compilar: Makefile, program.cpp, BinaryTree.hpp, maxOfTree.hpp. Us falta crear el fitxer maxOfTree.cpp and els corresponents includes i implementar-hi la funció anterior. Quan pugeu la vostra solució al jutge, només cal que pugeu un tar construït així:
tar cf solution.tar maxOfTree.cpp
Punts examen: 2.5 Part automàtica: 100%
Entrada
L’entrada té un nombre arbitrari de casos. Cada cas consisteix en una línia amb un string describint un arbre binari no buit d’enters. Fixeu-vos en que el programa que us oferim ja s’encarrega de llegir aquestes entrades. Només cal que implementeu la funció abans esmentada.
Sortida
Per a cada cas, la sortida conté el corresponent màxim de l’arbre. Fixeu-vos en que el programa que us oferim ja s’encarrega d’escriure aquest màxim. Només cal que implementeu la funció abans esmentada.
Observació
La vostra funció i subfuncions que creeu han de treballar només amb arbres. Heu de trobar una solució RECURSIVA del problema. En les crides recursives, incloeu la hipòtesi d’inducció, és a dir una explicació del que es cumpleix després de la crida, i també la funció de fita/decreixement o una justificació de perquè la funció recursiva acaba.
Molt possiblement, una solució directa serà lenta, i necessitareu crear alguna funció recursiva auxiliar per a produïr una solució més eficient capaç de superar tots els jocs de proves.
Input
7(2(5,3(4,5)),1) 6(7(8,7),8(4,6)) 2(4(7(5,3),),2(8,7(2(7,),))) 3(7(5,1),3(5,4)) 7(3,4) 6(,5(7,2)) 2 4(6(1,3),) 4(,8(8(1,5),4(7,))) 4
Output
7 8 8 7 7 7 2 6 8 4
Input
-2(-7(-4,-6(-5,-4)),-8) -3(-2(-1,-2),-1(-5,-3)) -7(-5(-2(-4,-6),),-7(-1,-2(-7(-2,),))) -6(-2(-4,-8),-6(-4,-5)) -2(-6,-5) -3(,-4(-2,-7)) -7 -5(-3(-8,-6),) -5(,-1(-1(-8,-4),-5(-2,))) -5
Output
-2 -1 -1 -2 -2 -2 -7 -3 -1 -5
Input
0(55(29,-47(-15,98)),-18) -94(82(-21,80),-16(63,-85)) -27(-50(6(13,-56),),23(2,36(-2(-37,),))) -56(-5(-100,-37),7(-70,-18)) 5(-3,-32) 50(,-23(-17,91)) 41 91(59(75,-46),) 55(,62(-31(-10,69),-74(67,))) -56 12(96(-22(88,),31(15,-92)),-47(70,)) -58(4,-1(27,-35)) 78 -91(89(35(-95,-24),-50(,77)),-95) -69 89(-93(,-72),-31(-76,-91)) -25(93,76) 32(-71,73(-68(,-12(,-70)),-86(-61(-68,58),-39))) 68(-10(22,60),91) 89(-7(-20,37),)
Output
98 82 36 7 5 91 41 91 69 -56 96 27 78 89 -69 89 93 73 91 89
Input
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99967499 99966476 99971526 99983489 99986895 99958849 99960731 99970982 99999917 99979776