Lai Ah Fur

1. 遞迴 Lai Ah Fur

2. Recursion • Recursive program: call by itself • 會無窮迴圈,故需設定終止條件(ground case) • Solve the complex problems • 費耗用System Stack

3. 0 if n=0 (anchor or ground base) n+S(n-1) if n>0 (inductive) S(n)= result=sum(n); System.out.println("1+2+3+...+"+n+"="+result); static int sum(int n) { if (n==0) return 0; else return (n+sum(n-1)); } //sum

4. GCD輾轉相減法 • static int gcd_loop1(int m, int n)   • {   • while (m!=n)   • {   • while (m>n) m=m-n;   • while (m<n) n=n-m;   • }   • return (m);   • }  

5. GCD輾轉相除法 static int gcd_loop2(int m, int n)   {   int t;   if (m<n)   { t=m;m=n;n=t; }   while (n!=0)   {   t=m%n; m=n; n=t;   }   return (m);   }  

6. Recursive GCD static int gcd(int m, int n)   {   int temp;   if (m<n) {temp=m;m=n;n=temp;}   if (m%n==0) return (n);   else return (gcd(n,m%n));   }//gcd  

7. 費式系列 static void fib_nonarray(int n) { int first=1,second=1,next=0; first=second=1; System.out.print(first +" "+second+" "); for(int i=3;i<=n;i++) { next=first+second; System.out.print(next+" "); second=first; first=next; }//for System.out.println("\n"); }

8. static void fib_nonrecursive(int n) { fib[1]=fib[2]=1; for(int i=3;i<=n;i++) fib[i]=fib[i-1]+fib[i-2]; }

9. static int fib_recursive(int n) { if (n<=2) return 1; else return (fib_recursive(n-1)+fib_recursive(n-2)); }

10. f(n)=1………………...n=1,2 f(n)=f(n-1)+f(n-2)….....n>2 Examples: 1,1,2,3,5,8,13,21,34,35,....