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Rekursive Funktionen (Fakultät). Rekursive Funktionen (ggT). ggT Rekursionsbaum. Rekursive Funktionen (Fibonacci). Fibonacci Rekursionsbaum. Rekursive Funktionen (Ulam). Rekursive Funktionen (McCarthy). McCarthy Rekursionsbaum. Rekursive Funktionen (Potenz). Rekursive Funktionen (Summe). - PowerPoint PPT Presentation
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Rekursive Funktionen (Fakultät)
class Fakultaet {
static long fak(long n) {
if (n <= 0)
return 1;
else
return n * fak(n-1);
}
public static void main(String[] args) {
System.out.println(20 + "! = " + fak(20));
}
}
>>>def fakt (n):
if n==0:
return 1
else:
return fakt(n-1)*n
>>> print fak(20)
2432902008176640000
% fakt
fakt(0,1).
fakt(N,F):- N1 is N-1, fakt(N1,L), F is N*L.
% Nach Konsultation der obigen WB antwortet das System auf die Anfrage:
?- fakt(20,F).
F = 2432902008176640000
Rekursive Funktionen (ggT)
class Teiler {
static int ggT(int m,n) {
if (m==n)
return m;
else if (m>n) return ggT(m-n,n);
else return ggT(m,n-m);
}
public static void main(String[] args) {
System.out.println( „ggT(24,3) = "+ggT(24,3);
}
}
>>>def ggT(m,n):
if m==n:
print m
elif m > n:
return ggT(m-n,n)
else:
return ggT (m,n-m)
>>>print ggT(24,3)
8
% ggT
ggT(M,M,M).
ggT(M,N,G):-M>N, H is M-N,ggT(H,N,G).
ggT(M,N,G):-H1 is N-M, ggT(M,H1,G).
?- ggT(24,3,G).
G = 8
ggT Rekursionsbaum
Rekursive Funktionen (Fibonacci)
class Fibonacci {
static int fibo(int n) {
if (n <2)
return 1;
else
return fibo(n-2)+fibo(n-1);
}
public static void main(String[] args) {
System.out.println(„fibo(6) = " + fibo(6));
}
}
>>>def fibo (n):
if n < 2:
return 1
else:
return fibo(n-1) + fibo(n-2)
>>>print fibo(6)
13
% fibo
fibo(0,1).
fibo(1,1).
fibo(N,M):-N1 is N-1, N2 is N-2,fibo(N1,M1),fibo(N2,M2),M is M1+M2.
? Fibo(6,M).
M = 13
Fibonacci Rekursionsbaum
Rekursive Funktionen (Ulam)
int n=17;
void ulam() {
if (n>1){
if (n%2==0) n=n/2;
else n=3*n+1;
ulam();
}
}
ulam(X):- X==1.
ulam(X):- X1 is (X mod 2), X1==0,
Z is X/2,write(Z),write(' '),ulam(Z).
ulam(X):- Z1 is 3*X+1,write(Z1),
write(' '),ulam(Z1).
def ulam(n):
while n>1:
if n%2 == 0:
n=n/2
return n
else:
n=3*n+1
return n
return ulam(n)
Rekursive Funktionen (McCarthy)
class macCarthy {
static int mcCarthy (int n) {
if (n < 100) return n-10;
else return
mcCarthy(mcCarthy(n+11));
}
public static void main (String[] args) {
System.out.println („mcCarthy(7)=“
+mcCarthy(7));
}
}
>>>def mcCarthy (n):
if n>100:
return n-10
else:
return mcCarthy(mcCarthy
(n+11))
>>>print mcCarthy(88)
91
mcCarthy(X,Y):- X>100, Y is X-10.
mcCarthy(X,Y):- X1 is X+11,
mcCarthy(X1,Y1),
mcCarthy(Y1,Y).
McCarthy Rekursionsbaum
Rekursive Funktionen (Potenz)
class potenz {
static int pot (int x, int n) {
if (n==0) return 1;
else return x*(pot(x,n-1));
}
public static void main(String[] args) {
System.out.println(„7³=“ + pot(7,3));
}
}
>>> def pot (x,n):
if n == 0:
return 1
else:
return x* (pot (x,n-1))
>>>print pot(7,3)
343
pot(X,0,1).
Pot(X,N,P):- N>0, N1 is N-1, pot(X,N1,P1),
P is X * P1.
Rekursive Funktionen (Summe)
public class rekursion
{
int summe(int n){
if (n==1) return 1;
else return summe(n -1) + n;
}
public static void main(String[] args) {
System.out.println(„sum(4)=„summe(4));
}
}
>>> summe(n, s=0):
if n == 1:
return 1
return summe(n-1,s+n)
>>> print summe(4)
10
summe(1,1).
summe(N,S):- N1 is N-1, summe(N1,S1), S is S1 + N.
?- summe(4,S)
S = 10
Rekursive Funktionen (Quadratsumme)
public class rekursion
{
int qsumme(int n){
if (n==1) return 1;
else return (n*n) + qsumme(n-1);
}
public static void main(String[] args) {
System.out.println(„qsum(4)=„qsumme(4));
}
}
>>>def quadr_sum(n,qs=0):
if n == 1:
return 1
qs += n**2 + quadr_sum(n-1,qs)
return qs
>>> print quadr_sum(4)
30
qsumme(1,1).
qsumme(N,Q):- N1 is N - 1, qsumme(N1,Q1), Q is Q1 + (N*N).
?- qsumme(4,Q).
Q = 30
Rekursive Funktionen (Binomialkoeffizient)
public class Binomi {
static long binomi(int n, int k) {
if (k == 0 || n == k) return 1;
else return binomi(n-1, k-1) + binomi(n-1,k);}
public static void main(String[] args) {
System.out.println("Binomialkoeffizient von 5 über 2 =" + binomi(5,2)); }
}
>>>def binomi(n,k):
if k == 0 or n == k:
return 1
else:
return binomi(n-1,k-1)+ binomi(n-1,k)
>>> print binomi(5,2)
10
% Binomialkoeffizient
binomi(_,0,1).
binomi(N,N,1).
binomi(N,K,B):- N1 is N-1, K1 is K-1, binomi(N1,K1,B1),
binomi(N1,K,B2), B is B1+B2.
? binomi(5,2,B).
B = 10
