Question

1)List four differences between recursion and iteration. (consider: definition, termination, implementation difficulty and speed)

2)Write a recursive function/method to perform exponentiation

             return xm, assuming m >= 0. [3 marks]

Answer 1

Definition: Iteration in simple words means repeating the same process again and again. In programming terms, an iteration is a set of operation which is to be carried out until a breaking condition is met whereas Recursion means a repeated application of a given procedure, In terms of programming language it a recursive function is a function that calls itself.

Termination: An iteration gets terminated when the breaking condition is triggered. i,e, a variable reaches the breaking condition whereas a recursion gets terminated when a statement called the base case is executed. It makes the function return before the control reaching to the recursive call.

implementation: An iteration needs three conditions to start. Initialization, Condition, increment or decrement whereas A recursive call needs only a base case and recursive call to the function.

Speed: Iteration has faster execution as compared to recursion

Ans2. Since no particular language is mentioned I am writing this code in Java

public static exponentiate (int x, int m)

{

if(m == 0)

return 1;

else

return x* exponentiate(x,m-1)

}