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Recursion

Recursion. Recursive method Calls itself (directly or indirectly) through another method Method knows how to solve only a base case Method divides problem Base case Simpler problem Method now divides simpler problem until solvable Recursive call Recursive step. 5!. 1. 5!. 1.

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Recursion

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  1. Recursion • Recursive method • Calls itself (directly or indirectly) through another method • Method knows how to solve only a base case • Method divides problem • Base case • Simpler problem • Method now divides simpler problem until solvable • Recursive call • Recursive step

  2. 5! 1 5! 1 Final value = 120 5! = 5 * 24 = 120 is returned 5 * 4! 5 * 4! 4! = 4 * 6 = 24 is returned 4 * 3! 4 * 3! 3! = 3 * 2 = 6 is returned 3 * 2! 3 * 2! 2! = 2 * 1 = 2 is returned 2 * 1! 2 * 1! 1 returned (b) Values returned from each recursive call. (a) Sequence of recursive calls. Recursive evaluation of 5!.

  3. Example Using Recursion: The Fibonacci Series • Fibonacci series • Each number in the series is sum of two previous numbers • e.g., 0, 1, 1, 2, 3, 5, 8, 13, 21…fibonacci(0) = 0 fibonacci(1) = 1fibonacci(n) = fibonacci(n - 1) + fibonacci( n – 2 ) • fibonacci(0) and fibonacci(1) are base cases • Golden ratio (golden mean)

  4. fibonacci( 3 ) return fibonacci( 2 ) fibonacci( 1 ) + + return fibonacci( 1 ) fibonacci( 0 ) return 1 return 0 return 1 Set of recursive calls for fibonacci(3).

  5. Example Using Recursion: The Hanoi Tower

  6. Example Using Recursion: The Hanoi Tower

  7. Example Using Recursion: The Hanoi Tower

  8. Recursion vs. Iteration • Iteration • Uses repetition structures (for, while or do…while) • Repetition through explicitly use of repetition structure • Terminates when loop-continuation condition fails • Controls repetition by using a counter • Recursion • Uses selection structures (if, if…else or switch) • Repetition through repeated method calls • Terminates when base case is satisfied • Controls repetition by dividing problem into simpler one

  9. Recursion vs. Iteration (cont.) • Recursion • More overhead than iteration • More memory intensive than iteration • Can also be solved iteratively • Often can be implemented with only a few lines of code

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