Suma i mida de molts arbres X68237


Statement
 

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En aquest exercici, heu d’implementar un programa que llegeix comandes que manipulen variables que guarden àrbres binaris d’enters. La primera comanda numvars= n ; indica el nombre total n de variables. Els noms d’aquestes variables son t0,…,t(n-1), i se suposa que inicialment cadascuna guarda un àrbre buit. Després venen comandes que construeixen nous àrbres a partir de variables i els assignen a variables (com per exemple t2 =BinTree( 3 , t0 , t1 );, i comandes que accedeixen als fills d’un arbre existent i els assignen a variables (com per exemple t3 = t2 .left(); o t3 = t2 .right();). També hi ha comandes per a escriure per la sortida un àrbre en INLINEFORMAT (com per exemple cout<< t2 <<endl;), i instruccions per a escriure la mida o la suma dels valors d’un arbre guardat en una variable, com per exemple (cout<<size( t2 )<<endl; o cout<<sum( t2 )<<endl;).

Aquest és un exemple d’entrada del programa:

numvars= 4 ;
t1 =BinTree( 1 , t2 , t3 );
t2 =BinTree( 2 , t1 , t3 );
t3 =BinTree( 3 , t2 , t1 );
cout<< t0 <<endl;
cout<< t1 <<endl;
cout<< t2 <<endl;
cout<< t3 <<endl;
cout<<size( t0 )<<endl;
cout<<size( t1 )<<endl;
cout<<size( t2 )<<endl;
cout<<size( t3 )<<endl;
cout<<sum( t0 )<<endl;
cout<<sum( t1 )<<endl;
cout<<sum( t2 )<<endl;
cout<<sum( t3 )<<endl;
t1 =BinTree( 1 , t2 , t3 );
t2 =BinTree( 2 , t1 , t3 );
t3 =BinTree( 3 , t2 , t1 );
cout<< t0 <<endl;
cout<< t1 <<endl;
cout<< t2 <<endl;
cout<< t3 <<endl;
cout<<size( t0 )<<endl;
cout<<size( t1 )<<endl;
cout<<size( t2 )<<endl;
cout<<size( t3 )<<endl;
cout<<sum( t0 )<<endl;
cout<<sum( t1 )<<endl;
cout<<sum( t2 )<<endl;
cout<<sum( t3 )<<endl;
t1 = t3 .left();
t2 = t1 .right();
t3 = t2 .left();
cout<< t0 <<endl;
cout<< t1 <<endl;
cout<< t2 <<endl;
cout<< t3 <<endl;
cout<<size( t0 )<<endl;
cout<<size( t1 )<<endl;
cout<<size( t2 )<<endl;
cout<<size( t3 )<<endl;
cout<<sum( t0 )<<endl;
cout<<sum( t1 )<<endl;
cout<<sum( t2 )<<endl;
cout<<sum( t3 )<<endl;

La sortida del programa amb la seqüència de comandes d’entrada anterior hauria de ser:

()
1
2(1,)
3(2(1,),1)
0
1
2
4
0
1
3
7
()
1(2(1,),3(2(1,),1))
2(1(2(1,),3(2(1,),1)),3(2(1,),1))
3(2(1(2(1,),3(2(1,),1)),3(2(1,),1)),1(2(1,),3(2(1,),1)))
0
7
12
20
0
11
20
34
()
2(1(2(1,),3(2(1,),1)),3(2(1,),1))
3(2(1,),1)
2(1,)
0
12
4
2
0
20
7
3

Com podeu observar a l’exemple d’entrada anterior, hi han espais en blanc per a facilitar la lectura. Podeu llegir i tractar les comandes així:

#include <iostream>
#include <string>
#include <cstdlib>
//...

using namespace std;

#include "BinTree.hh"

int getIdVar(string s)
{
 return atoi(s.substr(1).c_str());
}

//...

int main()
{
 //...
 string s1, s2, s3, s4, s5, s6, s7;
 int numvars;
 cin >> s1 >> numvars >> s2;
 // ...
 while (cin >> s1 >> s2) {
  if (s1[0] == 't') {
   int idvar = getIdVar(s1);
   if (s2 == "=BinTree(") {
    int value;
    cin >> value >> s3 >> s4 >> s5 >> s6 >> s7;
    int idvar1 = getIdVar(s4);
    int idvar2 = getIdVar(s6);
    //...
   } else if (s2 == "=") {
    cin >> s3 >> s4;
    int idvar1 = getIdVar(s3);
    if (s4 == ".left();") {
     //...
    } else {
     //...
    }
   }
  } else if (s1 == "cout<<") {
   int idvar = getIdVar(s2);
   cin >> s3;
   //...
   //....setOutputFormat(BinTree<int>::INLINEFORMAT);
   //cout << ... << endl;
  } else if (s1 == "cout<<size(") {
   int idvar = getIdVar(s2);
   cin >> s3;
   //...
  } else if (s1 == "cout<<sum(") {
   int idvar = getIdVar(s2);
   cin >> s3;
   //...
  }
 }
}

Fixeu-vos que l’enunciat d’aquest exercici us ofereix el fitxer BinTree.hh. Us falta crear el fitxer main.cc, que haurieu de construïr a partir de la plantilla que us hem oferit abans, fent un ús convenient del tipus BinTree. Només cal que pugeu main.cc al jutge.

Observació: Us recomanem que comenceu implementant una solució bàsica per tal de superar els jocs de proves públics i obtenir així la meitat de la nota. Ja la optimitzareu més endavant si teniu temps.

Entrada

La primera linia de l’entrada és de la forma numvars= LIMIT ;, a on LIMIT és un nombre natural positiu. Després venen instruccions d’aquestes menes: 

tNUM =BinTree( VALUE , tNUM1 , tNUM2 );
tNUM1 = tNUM2 .left();
tNUM1 = tNUM2 .right();
cout<< tNUM <<endl;
cout<<size( tNUM )<<endl;
cout<<sum( tNUM )<<endl;

On VALUE es un enter i NUM, NUM1, NUM2 son naturals en el rang {0,…,LIMIT-1}.

Se suposa que les entrades son correctes: sempre es demana accedir a left o right d’arbres no buits, i no es produeixen errors d’overflow.

Sortida

Per a cada instrucció dels següents tres tipus, el vostre programa ha d’escriure el resultat esperat (l’arbre contingut en la variable en INLINEFORMAT, o la mida de l’arbre contingut en la variable, o la suma de l’arbre contingut en la variable, segons el cas). 

cout<< tNUM <<endl;
cout<<size( tNUM )<<endl;
cout<<sum( tNUM )<<endl;

Observació

La solució d’aquest exercici s’ha de basar en un ús raonable del tipus BinTree. Qualsevol solució que ignori això i faci servir enfocaments o estructures de dades alternatives que no formen part de l’assignatura serà invalidada.

Avaluació sobre 10 punts:

  • Solució lenta: 5 punts.
  • solució ràpida: 10 punts.

Entenem com a solució ràpida una que és correcta, on cada operació té cost CONSTANT (excepte per a la d’escriptura d’arbres, que s’espera cost proporcional a la mida de l’arbre involucrat), i capaç de superar els jocs de proves públics i privats. Entenem com a solució lenta una que no és ràpida, però és correcta i capaç de superar els jocs de proves públics.

Public test cases

  • Input

    numvars= 4 ;
t1 =BinTree( 1 , t2 , t3 );
t2 =BinTree( 2 , t1 , t3 );
t3 =BinTree( 3 , t2 , t1 );
cout<< t0 <<endl;
cout<< t1 <<endl;
cout<< t2 <<endl;
cout<< t3 <<endl;
cout<<size( t0 )<<endl;
cout<<size( t1 )<<endl;
cout<<size( t2 )<<endl;
cout<<size( t3 )<<endl;
cout<<sum( t0 )<<endl;
cout<<sum( t1 )<<endl;
cout<<sum( t2 )<<endl;
cout<<sum( t3 )<<endl;
t1 =BinTree( 1 , t2 , t3 );
t2 =BinTree( 2 , t1 , t3 );
t3 =BinTree( 3 , t2 , t1 );
cout<< t0 <<endl;
cout<< t1 <<endl;
cout<< t2 <<endl;
cout<< t3 <<endl;
cout<<size( t0 )<<endl;
cout<<size( t1 )<<endl;
cout<<size( t2 )<<endl;
cout<<size( t3 )<<endl;
cout<<sum( t0 )<<endl;
cout<<sum( t1 )<<endl;
cout<<sum( t2 )<<endl;
cout<<sum( t3 )<<endl;
t1 = t3 .left();
t2 = t1 .right();
t3 = t2 .left();
cout<< t0 <<endl;
cout<< t1 <<endl;
cout<< t2 <<endl;
cout<< t3 <<endl;
cout<<size( t0 )<<endl;
cout<<size( t1 )<<endl;
cout<<size( t2 )<<endl;
cout<<size( t3 )<<endl;
cout<<sum( t0 )<<endl;
cout<<sum( t1 )<<endl;
cout<<sum( t2 )<<endl;
cout<<sum( t3 )<<endl;

    Output

    ()
1
2(1,)
3(2(1,),1)
0
1
2
4
0
1
3
7
()
1(2(1,),3(2(1,),1))
2(1(2(1,),3(2(1,),1)),3(2(1,),1))
3(2(1(2(1,),3(2(1,),1)),3(2(1,),1)),1(2(1,),3(2(1,),1)))
0
7
12
20
0
11
20
34
()
2(1(2(1,),3(2(1,),1)),3(2(1,),1))
3(2(1,),1)
2(1,)
0
12
4
2
0
20
7
3

  • Input

    numvars= 3 ;
cout<< t1 <<endl;
cout<< t1 <<endl;
t1 =BinTree( 1 , t0 , t0 );
t1 =BinTree( 2 , t2 , t1 );
cout<<size( t1 )<<endl;
t0 = t1 .left();
t2 =BinTree( 5 , t0 , t0 );
t2 =BinTree( 2 , t1 , t1 );
t0 = t2 .right();
t1 = t1 .left();
t0 =BinTree( 4 , t0 , t0 );
t1 =BinTree( 2 , t2 , t2 );
cout<<size( t0 )<<endl;
cout<<sum( t1 )<<endl;
t2 =BinTree( 2 , t0 , t2 );
cout<< t1 <<endl;
cout<<size( t0 )<<endl;
t0 = t1 .right();
t0 =BinTree( 0 , t0 , t0 );
t1 = t0 .left();
t2 = t1 .right();
cout<< t0 <<endl;
t0 = t1 .left();
t0 =BinTree( 4 , t0 , t2 );
cout<<sum( t1 )<<endl;
cout<<sum( t1 )<<endl;
cout<< t0 <<endl;
t0 =BinTree( 2 , t0 , t1 );
t2 =BinTree( 1 , t2 , t1 );
cout<< t2 <<endl;
cout<<sum( t2 )<<endl;
t1 = t2 .right();
cout<< t0 <<endl;
cout<< t1 <<endl;
cout<< t2 <<endl;
t2 = t0 .right();
cout<< t1 <<endl;
cout<<size( t1 )<<endl;
cout<<sum( t0 )<<endl;
cout<<size( t2 )<<endl;
t1 = t2 .right();
cout<<sum( t1 )<<endl;
cout<<size( t1 )<<endl;
t2 = t1 .left();
cout<< t1 <<endl;
t1 =BinTree( 3 , t1 , t2 );
cout<<sum( t2 )<<endl;
t1 =BinTree( 2 , t1 , t1 );
cout<< t2 <<endl;
cout<<sum( t0 )<<endl;
cout<<size( t2 )<<endl;
t1 =BinTree( 5 , t2 , t1 );
cout<< t2 <<endl;
t2 = t1 .right();
cout<<sum( t0 )<<endl;
t2 = t1 .left();
t2 =BinTree( 1 , t2 , t1 );
cout<< t2 <<endl;
cout<< t2 <<endl;
cout<<size( t1 )<<endl;
cout<<sum( t1 )<<endl;
cout<< t1 <<endl;
t1 = t2 .left();
t1 = t0 .right();
cout<<sum( t1 )<<endl;
t2 = t1 .right();
cout<< t1 <<endl;
t1 =BinTree( 2 , t1 , t2 );
cout<< t2 <<endl;
t2 = t0 .right();
t2 = t0 .right();
cout<<size( t1 )<<endl;
cout<< t1 <<endl;
cout<< t1 <<endl;
cout<< t1 <<endl;
cout<<sum( t1 )<<endl;
t1 = t1 .left();
cout<<size( t2 )<<endl;
cout<< t1 <<endl;
cout<< t0 <<endl;
cout<< t0 <<endl;
cout<< t1 <<endl;
cout<< t2 <<endl;

    Output

    ()
()
2
5
18
2(2(2(,1),2(,1)),2(2(,1),2(,1)))
5
0(2(2(,1),2(,1)),2(2(,1),2(,1)))
8
8
4(2(,1),2(,1))
1(2(,1),2(2(,1),2(,1)))
12
2(4(2(,1),2(,1)),2(2(,1),2(,1)))
2(2(,1),2(,1))
1(2(,1),2(2(,1),2(,1)))
2(2(,1),2(,1))
5
20
5
3
2
2(,1)
0
()
20
0
()
20
1(,5(,2(3(2(,1),),3(2(,1),))))
1(,5(,2(3(2(,1),),3(2(,1),))))
8
19
5(,2(3(2(,1),),3(2(,1),)))
8
2(2(,1),2(,1))
2(,1)
8
2(2(2(,1),2(,1)),2(,1))
2(2(2(,1),2(,1)),2(,1))
2(2(2(,1),2(,1)),2(,1))
13
5
2(2(,1),2(,1))
2(4(2(,1),2(,1)),2(2(,1),2(,1)))
2(4(2(,1),2(,1)),2(2(,1),2(,1)))
2(2(,1),2(,1))
2(2(,1),2(,1))

  • Input

    numvars= 10 ;
cout<< t6 <<endl;
cout<< t5 <<endl;
t6 =BinTree( -1 , t2 , t9 );
t7 =BinTree( 7 , t0 , t9 );
cout<<size( t6 )<<endl;
t8 =BinTree( 6 , t7 , t9 );
t2 =BinTree( -15 , t3 , t7 );
t9 = t2 .right();
t8 = t9 .right();
t3 = t6 .left();
t9 =BinTree( -1 , t3 , t1 );
t7 =BinTree( 4 , t8 , t4 );
cout<<size( t0 )<<endl;
cout<<sum( t6 )<<endl;
t6 =BinTree( 13 , t3 , t2 );
cout<< t6 <<endl;
cout<<size( t5 )<<endl;
t7 =BinTree( 6 , t6 , t5 );
t5 =BinTree( 9 , t2 , t5 );
t4 =BinTree( -2 , t4 , t3 );
t8 =BinTree( 6 , t4 , t3 );
t4 = t9 .right();
cout<< t0 <<endl;
t8 = t9 .left();
t6 =BinTree( -10 , t4 , t9 );
cout<<sum( t0 )<<endl;
cout<<sum( t8 )<<endl;
cout<< t1 <<endl;
t7 =BinTree( 18 , t2 , t2 );
t0 =BinTree( -7 , t6 , t1 );
cout<< t9 <<endl;
cout<<sum( t9 )<<endl;
t1 =BinTree( 20 , t7 , t7 );
t5 =BinTree( 0 , t9 , t7 );
t6 = t7 .right();
cout<< t6 <<endl;
cout<< t6 <<endl;
t4 =BinTree( 6 , t8 , t1 );
cout<< t9 <<endl;
t9 = t0 .right();
cout<< t8 <<endl;
cout<<size( t0 )<<endl;
cout<<sum( t6 )<<endl;
t5 =BinTree( 18 , t6 , t1 );
cout<<size( t5 )<<endl;
t8 = t4 .right();
cout<<sum( t1 )<<endl;
cout<<size( t3 )<<endl;
t4 = t4 .left();
cout<< t4 <<endl;
t3 =BinTree( 5 , t1 , t7 );
t6 =BinTree( 8 , t2 , t1 );
t5 =BinTree( -11 , t7 , t4 );
cout<<sum( t8 )<<endl;
t7 =BinTree( 19 , t5 , t3 );
t3 =BinTree( 12 , t1 , t8 );
t4 =BinTree( 19 , t3 , t3 );
cout<< t8 <<endl;
t4 =BinTree( -9 , t8 , t8 );
t7 =BinTree( 2 , t7 , t6 );
cout<<sum( t3 )<<endl;
cout<<size( t3 )<<endl;
t2 =BinTree( -9 , t5 , t4 );
cout<< t5 <<endl;
t6 =BinTree( -20 , t9 , t2 );
t4 = t7 .right();
t4 =BinTree( -6 , t8 , t1 );
t9 =BinTree( 8 , t3 , t6 );
t2 =BinTree( -18 , t1 , t0 );
t1 =BinTree( 9 , t0 , t8 );
t6 =BinTree( 15 , t4 , t6 );
t8 =BinTree( -13 , t6 , t2 );
t7 =BinTree( 7 , t2 , t4 );
cout<<sum( t6 )<<endl;
t9 =BinTree( 18 , t0 , t8 );
t1 =BinTree( -4 , t1 , t0 );
t4 = t0 .left();
t1 =BinTree( -12 , t9 , t6 );
t3 =BinTree( -15 , t8 , t0 );
cout<< t6 <<endl;
cout<< t4 <<endl;
t4 =BinTree( 0 , t6 , t2 );
cout<<size( t7 )<<endl;
t9 =BinTree( -7 , t8 , t7 );
t2 =BinTree( -2 , t9 , t9 );
t2 =BinTree( 9 , t7 , t6 );
cout<<sum( t3 )<<endl;
cout<< t1 <<endl;
t9 =BinTree( -6 , t1 , t4 );
t1 = t0 .left();
t8 =BinTree( -7 , t7 , t0 );
t8 = t0 .right();
cout<<sum( t2 )<<endl;
t6 = t1 .right();
t2 =BinTree( -4 , t2 , t2 );
cout<< t5 <<endl;
t9 =BinTree( 9 , t0 , t2 );
cout<< t3 <<endl;
t0 = t4 .right();
t9 = t1 .right();
cout<<size( t6 )<<endl;
cout<< t5 <<endl;
cout<< t4 <<endl;
t3 =BinTree( -18 , t6 , t0 );
t2 =BinTree( 1 , t9 , t4 );
cout<< t5 <<endl;
cout<<sum( t7 )<<endl;
t1 =BinTree( -10 , t4 , t6 );
t4 = t2 .left();
cout<<size( t6 )<<endl;
cout<< t1 <<endl;
cout<< t8 <<endl;
cout<< t9 <<endl;
t8 = t3 .right();
t3 = t8 .right();
t7 =BinTree( 6 , t6 , t8 );
t6 =BinTree( 20 , t8 , t7 );
t3 =BinTree( 9 , t3 , t3 );
t2 =BinTree( 18 , t6 , t5 );
cout<<sum( t6 )<<endl;
t7 =BinTree( 16 , t9 , t6 );
t1 =BinTree( 9 , t0 , t4 );
t0 =BinTree( -19 , t8 , t6 );
t4 = t7 .left();
t9 =BinTree( 20 , t2 , t8 );
t0 = t1 .left();
t8 = t9 .right();
cout<< t5 <<endl;
t2 =BinTree( 11 , t5 , t7 );
t9 =BinTree( -7 , t4 , t5 );
cout<< t3 <<endl;
t7 = t0 .right();
t1 = t9 .left();
cout<<sum( t7 )<<endl;
cout<<size( t2 )<<endl;
cout<< t3 <<endl;
t9 = t0 .right();
t1 =BinTree( 13 , t9 , t6 );
cout<< t1 <<endl;
cout<<sum( t0 )<<endl;
cout<<sum( t3 )<<endl;
t1 = t9 .left();
t6 =BinTree( 14 , t7 , t7 );
cout<<size( t0 )<<endl;
t7 =BinTree( 6 , t4 , t8 );
t2 =BinTree( -14 , t6 , t0 );
t6 = t4 .right();
t8 =BinTree( 7 , t9 , t6 );
cout<< t7 <<endl;
t0 =BinTree( -15 , t1 , t3 );
t7 = t2 .right();
cout<< t4 <<endl;
t0 =BinTree( 16 , t2 , t9 );
cout<<sum( t9 )<<endl;
t4 = t5 .right();
t3 =BinTree( 19 , t7 , t8 );
cout<<size( t6 )<<endl;
t6 =BinTree( -7 , t7 , t6 );
t7 =BinTree( 0 , t5 , t9 );
cout<<size( t8 )<<endl;
t3 =BinTree( -7 , t8 , t3 );
t3 =BinTree( -7 , t7 , t8 );
t1 =BinTree( 1 , t9 , t0 );
cout<< t8 <<endl;
cout<<sum( t5 )<<endl;
t4 = t3 .right();
cout<< t1 <<endl;
t0 =BinTree( -18 , t9 , t7 );
cout<<size( t9 )<<endl;
cout<< t2 <<endl;
cout<<sum( t3 )<<endl;
t2 =BinTree( -2 , t2 , t0 );
cout<<size( t1 )<<endl;
cout<< t5 <<endl;
t4 =BinTree( 9 , t1 , t7 );
t1 = t1 .right();
t4 =BinTree( -3 , t0 , t8 );
t1 = t6 .left();
t1 =BinTree( 3 , t9 , t6 );
t8 = t0 .left();
t1 = t0 .left();
t9 =BinTree( 12 , t7 , t5 );
t4 = t6 .right();
t9 =BinTree( -9 , t7 , t4 );
cout<<size( t1 )<<endl;
cout<< t0 <<endl;
t8 =BinTree( 19 , t5 , t3 );
cout<<sum( t4 )<<endl;
t5 =BinTree( -12 , t4 , t9 );
cout<<sum( t3 )<<endl;
t2 =BinTree( -16 , t2 , t2 );
t3 =BinTree( 13 , t4 , t6 );
t3 =BinTree( 20 , t3 , t4 );
t3 = t9 .right();
cout<< t2 <<endl;
t8 = t9 .left();
t4 =BinTree( -10 , t7 , t6 );
cout<<size( t7 )<<endl;
cout<<sum( t3 )<<endl;
t3 = t8 .left();
cout<< t0 <<endl;
cout<< t1 <<endl;
cout<< t2 <<endl;
cout<< t3 <<endl;
cout<< t4 <<endl;
cout<< t5 <<endl;
cout<< t6 <<endl;
cout<< t7 <<endl;
cout<< t8 <<endl;
cout<< t9 <<endl;

    Output

    ()
()
1
0
-1
13(,-15(,7))
0
()
0
0
()
-1
-1
-15(,7)
-15(,7)
-1
()
3
-8
14
24
0
()
24
20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7)))
60
23
-11(18(-15(,7),-15(,7)),)
58
15(-6(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7)))),-20(,-9(-11(18(-15(,7),-15(,7)),),-9(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7)))))))
-10(,-1)
39
0
-12(18(-7(-10(,-1),),-13(15(-6(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7)))),-20(,-9(-11(18(-15(,7),-15(,7)),),-9(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))))))),-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),)))),15(-6(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7)))),-20(,-9(-11(18(-15(,7),-15(,7)),),-9(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))))))))
104
-11(18(-15(,7),-15(,7)),)
-15(-13(15(-6(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7)))),-20(,-9(-11(18(-15(,7),-15(,7)),),-9(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))))))),-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),))),-7(-10(,-1),))
1
-11(18(-15(,7),-15(,7)),)
0(15(-6(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7)))),-20(,-9(-11(18(-15(,7),-15(,7)),),-9(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))))))),-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),)))
-11(18(-15(,7),-15(,7)),)
37
1
-10(0(15(-6(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7)))),-20(,-9(-11(18(-15(,7),-15(,7)),),-9(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))))))),-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),))),-1)
()
-1
1
-11(18(-15(,7),-15(,7)),)
9(-7(-10(,-1),),-7(-10(,-1),))
-18
42
9(-7(-10(,-1),),-7(-10(,-1),))
13(-7(-10(,-1),),20(-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),)),6(-1,-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),)))))
-12
-27
15
6(-1,-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),)))
-1
-18
0
4
7(-7(-10(,-1),),)
-9
1(-7(-10(,-1),),16(-14(14(-7(-10(,-1),),-7(-10(,-1),)),-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),))),-7(-10(,-1),)))
3
-14(14(-7(-10(,-1),),-7(-10(,-1),)),-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),)))
-45
31
-11(18(-15(,7),-15(,7)),)
3
-18(-7(-10(,-1),),0(-11(18(-15(,7),-15(,7)),),-7(-10(,-1),)))
0
-45
-16(-2(-14(14(-7(-10(,-1),),-7(-10(,-1),)),-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),))),-18(-7(-10(,-1),),0(-11(18(-15(,7),-15(,7)),),-7(-10(,-1),)))),-2(-14(14(-7(-10(,-1),),-7(-10(,-1),)),-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),))),-18(-7(-10(,-1),),0(-11(18(-15(,7),-15(,7)),),-7(-10(,-1),)))))
10
0
-18(-7(-10(,-1),),0(-11(18(-15(,7),-15(,7)),),-7(-10(,-1),)))
-7(-10(,-1),)
-16(-2(-14(14(-7(-10(,-1),),-7(-10(,-1),)),-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),))),-18(-7(-10(,-1),),0(-11(18(-15(,7),-15(,7)),),-7(-10(,-1),)))),-2(-14(14(-7(-10(,-1),),-7(-10(,-1),)),-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),))),-18(-7(-10(,-1),),0(-11(18(-15(,7),-15(,7)),),-7(-10(,-1),)))))
-11(18(-15(,7),-15(,7)),)
-10(0(-11(18(-15(,7),-15(,7)),),-7(-10(,-1),)),-7(-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),)),))
-12(,-9(0(-11(18(-15(,7),-15(,7)),),-7(-10(,-1),)),))
-7(-18(20(18(-15(,7),-15(,7)),18(-15(,7),-15(,7))),-7(-10(,-1),)),)
0(-11(18(-15(,7),-15(,7)),),-7(-10(,-1),))
0(-11(18(-15(,7),-15(,7)),),-7(-10(,-1),))
-9(0(-11(18(-15(,7),-15(,7)),),-7(-10(,-1),)),)
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    PRO2
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    C++
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