Recursion
- 1. Recursion
- 2. What is recursion • Looping without a loop statement • A function that is part of its own definition • Can only work if there’s a terminating condition, otherwise it goes forever (the base case)
- 3. A recursive function • N Factorial • 1! = 1 2! = 1 x 2 = 2 3! = 1 x 2 x 3 = 2! x 3 = 6 N! = 1 x 2 x 3 x .... (N-2) x (N-1) x N = (N-1)! x N
- 4. How recursion is handled • Every time a function is called, the function values, local variables, parameters and return addresses are pushed onto the stack. • Over and Over again • You might run out!
- 5. Dry-running a recursive call Procedure Printsequence(n) n <- n-1 if n > 1 then Printsequence(n) endif output(n) EndProcedure
- 6. Dry-running a recursive call Procedure Printsequence(n) n <- n-1 if n > 1 then output(n) Printsequence(n) endif EndProcedure
- 7. How to write a recursive procedure • Code the general case Result = n * Factorial(n-1) • Code the base case Result = 1 • Ensure that the base case is reached after a finite number of recursive calls