Alçada d'un arbre X16827

Statement

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Implementeu una funció RECURSIVA que, donat un arbre binari d’enters, retorna la seva alçada. L’alçada d’un arbre és el nombre de nodes que es troben en el camí més llarg des de l’arrel fins a alguna de les fulles. Noteu que, si l’arbre és buit, llavors té alçada 0, i si l’arbre té un únic node (que serà arrel i fulla alhora), llavors té alçada 1. Aquesta és la capcelera:

// Pre:
// Post: Retorna l'alçada de t
int heightOfTree(BinTree<int> t);

Aquí tenim un exemple de paràmetre d’entrada de la funció i la corresponent sortida:

heightOfTree(        3        ) => 4
                     |
              ------- -------
             |               |
             1               3
             |               |
              ----       ----
                  |     |
                  5     2
                        |
                         ----
                             |
                             1

Fixeu-vos que l’enunciat d’aquest exercici ja ofereix uns fitxers que haureu d’utilitzar per a compilar: main.cc, BinTree.hh, heightOfTree.hh. Us falta crear el fitxer heightOfTree.cc amb els corresponents includes i implementar-hi la funció anterior. Només cal que pugeu heightOfTree.cc al jutge.

Entrada

La primera linia de l’entrada descriu el format en el que es descriuen els arbres, o bé INLINEFORMAT o bé VISUALFORMAT. Després venen un nombre arbitrari de casos. Cada cas consisteix en una descripció d’un arbre un arbre binari 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 la corresponent alçada de l’arbre. Fixeu-vos en que el programa que us oferim ja s’encarrega d’escriure aquesta alçada. 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.

Public test cases

Input

VISUALFORMAT
     7
     |
 ---- ----
|         |
2         5

        4
        |
 ------- -------
|               |
4               4
|               |
 ----       ----
     |     |
     3     6

     4
     |
 ---- ----
|         |
2         2
|
 ----
     |
     3

                           6
                           |
                   -------- --------
                  |                 |
                  8                 2
                  |                 |
              ----              ---- ----
             |                 |         |
             7                 5         7
             |                 |
      ------- -------      ---- ----
     |               |    |         |
     3               5    2         3
     |               |
 ---- ----       ---- ----
|         |     |         |
4         2     6         1

3

        4
        |
 ------- -------
|               |
5               3
|               |
 ----       ----
     |     |
     1     2
     |
 ---- ----
|         |
3         4

        5
        |
         ----
             |
             6
             |
      ------- -------
     |               |
     2               2
     |               |
 ---- ----       ---- ----
|         |     |         |
5         2     4         8

     3
     |
 ---- ----
|         |
4         1
          |
           ----
               |
               6
               |
           ---- ----
          |         |
          7         4

4

     4
     |
 ---- ----
|         |
4         2
|
 ----
     |
     5

Output

Input

INLINEFORMAT
0(55(29(-47(-15,98),),-18(86(-59(60(29(,-38),30),-13(-80,-29)),62(-21,2(12(-28,-20),-67(-58,-79)))),-56(-5(-100(-37(7,-70),-18(,-82)),-34(30,94(-46,))),96(,51(63(41,-88),))))),-8)
75(-46(-53(-48,-53),98(,61)),-49)
67(25,-50)
9(-87,25(95,))
15(-92(-47(70,),-87),)
4(-1(27,-35),)
78(86(-5(,68),),46(88(-59,-9(68,83)),79(89(-93,-72),-31(-76,-91))))
-25(93(76(4,-8),-51(-22(-3,21),31(-34,32))),-95(-40(,53),93(,-81(16(-61,13(89,)),-7(-20,37)))))
94(37(,6),72(-90(,24(,-38(55(-65,22),46))),38(69(22(-65,-12),-54(49(78,-10),-3)),52(56,39(80(,24(-48,)),8(68(-38(,85),27(76,-13)),33(74,32)))))))
58
-20(82,81(-19,37))
97(-45(53(87(-96(-16(-35,97(,-23)),65(97,52(56,))),59(20(55(77,-30),),61)),),-26(98(,15),48(,-71(-22,)))),90(-99(88(,-4(-79(52(-16,),-27(,-80)),-36(-94,83))),),57(25(66(42(-49(-6,26),),57(-96,-75)),96(-15(,-46(,27)),1(91,44))),40(,-44))))
-6(-10(,25(80,6(57,47))),-60(80,87))
40(-71(4(-17(90(,-4(,-57)),-67(,-87)),100),20(14(-28,80),-11(-30,-2))),70(80,))
-14(-95(-31(41(-30(59(-71(27,-4),-75(,-92)),),59),-42),13(31(,-79),-24(62(52(80,-94(,-60)),26(,39)),8(45(,53),-73(11,26))))),60(-2(-2(-73,78(-82,10(-71(,-45(-19,-16)),-28))),-96(-12(88(83(-6,-52(7,-29)),-80),-39(33(11(,35),12),36(11(,13(53(-94,),-67)),30(-4,57)))),41(,66(91,97)))),-64(,93(49,))))
8(54(11(-99(67(7,),),-47(-10,-18)),82(9,-9)),43(16,-56))
-69(-15(25(57(38(-54,-13),80),-5),39(,-5(-28(-34,),74(-30,)))),67(41(4,),-19(72,)))
-53(19,35(9(29(-5,87),-60(21(-7,-16),)),62(-37(90(47,28),-35(91,40)),60)))
40(-49(-36,-47(51(-22(-7(-67(74(33,-100),18),-91(13,)),-69(73(-3,53(5,-65)),)),74(-100,-88)),42(-69(-100,),-35(27(28(-70(40(48,),-46(-26(-40,),)),14(,13)),-51(7,-40)),40(-53(0(57,83),7(-47(18,55),18(-58,))),-48))))),97(88(69(-81(,-9(49(21(33(67(61,-38),),-74),77(22(28,-43(-93,88)),-43(55(-73,-25),))),)),55(-52,)),-38(100(79(3,42(-63(,41(,-1)),50)),-90(0(-40(-11,-93(99,)),28(-95(-55,),-28)),)),-38(,-61(-71(40(,-71),),-66(12(-33,-73),))))),18(-8(100(-98(,1(-28(70(35(7,-25),-61),),99)),13(83(19(-91,-38),76(27,-79)),55)),49(-86(-58(60,8),-34),17(-27(52(82,),-22(-15,)),-99(31(-28(98,-23),-55(59(93,),)),-65(-15(5(28,-79),95(60,93)),-82(-91(20,),-1(61,))))))),-53(69(82,),4(-50(,-55(90(-86,-51),-72(-97(5(55,),),))),0(-31(57(22(-94,),48(-71(,57),-93(3,))),-63(-79(96,-20),-18(-27,-99))),29(51,38(70,))))))))
-9(-64(16,),49(-79,74))

Output

Input

INLINEFORMAT
0(55(29(-47(-15,98),),-18(86(-59(60(29(,-38),30),-13(-80,-29)),62(-21,2(12(-28,-20),-67(-58,-79)))),-56(-5(-100(-37(7,-70),-18(,-82)),-34(30,94(-46,))),96(,51(63(41,-88),))))),-8)
75(-46(-53(-48,-53),98(,61)),-49)
67(25,-50)
9(-87,25(95,))
15(-92(-47(70,),-87),)
4(-1(27,-35),)
78(86(-5(,68),),46(88(-59,-9(68,83)),79(89(-93,-72),-31(-76,-91))))
-25(93(76(4,-8),-51(-22(-3,21),31(-34,32))),-95(-40(,53),93(,-81(16(-61,13(89,)),-7(-20,37)))))
94(37(,6),72(-90(,24(,-38(55(-65,22),46))),38(69(22(-65,-12),-54(49(78,-10),-3)),52(56,39(80(,24(-48,)),8(68(-38(,85),27(76,-13)),33(74,32)))))))
58
-20(82,81(-19,37))
97(-45(53(87(-96(-16(-35,97(,-23)),65(97,52(56,))),59(20(55(77,-30),),61)),),-26(98(,15),48(,-71(-22,)))),90(-99(88(,-4(-79(52(-16,),-27(,-80)),-36(-94,83))),),57(25(66(42(-49(-6,26),),57(-96,-75)),96(-15(,-46(,27)),1(91,44))),40(,-44))))
-6(-10(,25(80,6(57,47))),-60(80,87))
40(-71(4(-17(90(,-4(,-57)),-67(,-87)),100),20(14(-28,80),-11(-30,-2))),70(80,))
-14(-95(-31(41(-30(59(-71(27,-4),-75(,-92)),),59),-42),13(31(,-79),-24(62(52(80,-94(,-60)),26(,39)),8(45(,53),-73(11,26))))),60(-2(-2(-73,78(-82,10(-71(,-45(-19,-16)),-28))),-96(-12(88(83(-6,-52(7,-29)),-80),-39(33(11(,35),12),36(11(,13(53(-94,),-67)),30(-4,57)))),41(,66(91,97)))),-64(,93(49,))))
8(54(11(-99(67(7,),),-47(-10,-18)),82(9,-9)),43(16,-56))
-69(-15(25(57(38(-54,-13),80),-5),39(,-5(-28(-34,),74(-30,)))),67(41(4,),-19(72,)))
-53(19,35(9(29(-5,87),-60(21(-7,-16),)),62(-37(90(47,28),-35(91,40)),60)))
40(-49(-36,-47(51(-22(-7(-67(74(33,-100),18),-91(13,)),-69(73(-3,53(5,-65)),)),74(-100,-88)),42(-69(-100,),-35(27(28(-70(40(48,),-46(-26(-40,),)),14(,13)),-51(7,-40)),40(-53(0(57,83),7(-47(18,55),18(-58,))),-48))))),97(88(69(-81(,-9(49(21(33(67(61,-38),),-74),77(22(28,-43(-93,88)),-43(55(-73,-25),))),)),55(-52,)),-38(100(79(3,42(-63(,41(,-1)),50)),-90(0(-40(-11,-93(99,)),28(-95(-55,),-28)),)),-38(,-61(-71(40(,-71),),-66(12(-33,-73),))))),18(-8(100(-98(,1(-28(70(35(7,-25),-61),),99)),13(83(19(-91,-38),76(27,-79)),55)),49(-86(-58(60,8),-34),17(-27(52(82,),-22(-15,)),-99(31(-28(98,-23),-55(59(93,),)),-65(-15(5(28,-79),95(60,93)),-82(-91(20,),-1(61,))))))),-53(69(82,),4(-50(,-55(90(-86,-51),-72(-97(5(55,),),))),0(-31(57(22(-94,),48(-71(,57),-93(3,))),-63(-79(96,-20),-18(-27,-99))),29(51,38(70,))))))))
-9(-64(16,),49(-79,74))

Output

Information

Author: PRO1
Language: Catalan
Official solutions: C++
User solutions: C++ Make