CS 211 Object Oriented Programming Tail Recursion

Tail Recursion A method is tail recursive if the last action of the recursive method is the recursive call Recursion puts frame on the stack the additional overhead required by non-tail recursion could be costly for large inputs http://www.cs.cornell.edu/courses/cs211/2006fa/Sections/S2/recursion.txt

Non Tail Recursion //Factorial public static int recurciveFact(int n) { if(n == 0) return 1; } else return n*recurciveFact(n-1);

Simulation recurciveFact(4) = 4*recurciveFact(3) =1*1 =1 = 2*1 = 2 = 3*2 = 6 = 4*6 = 24

Recursion in Stack Factorial :

Tail Recursion – Factorial public static int tailrecurciveFact(int n) { return factorial(n,1); } private static int factorial(int n,int accum) if(n==0) return accum; else{ return factorial(n-1,n*accum);

Simulation tailrecurciveFact(4) = factorial(4,1) factorial(4,1) = factorial(3,4*1) factorial(3,4*1) = factorial(2,4*1*3) factorial(2,4*1*3) = factorial(1,4*1*3*2) factorial(1,4*1*3*2) = factorial(0,4*1*3*2*1) = 24 factorial(2,4*1*3) = 24 factorial(3,4*1) = 24 factorial(4,1) = 24 tailrecurciveFact(4) = 24;

Tail Recursion - Fibonacci public int fibonacci(int n) { if(n == 0) return 0; else if(n == 1) return 1; else return fibonacci(n - 1) + fibonacci(n - 2); }

Simulation //Fibonacci fibonacci(5) = fibonacci(4) + fibonacci(3)

Non-Tail Recursion public String rev(String w) { if(w == null || w.equals("")) return w; else return rev(w.substring(1, w.length())) + w.substring(0,1); }

Tail Recursion //”hook” public String rev(String w) { return tailRev(w, ""); } //tail recursion public String tRev(String w, String res) { if(w==null || w.equals("")) return res; else return tRev(w.substring(1, w.length()), w.charAt(0) + res);

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