Recursive Algorithms in Java: ForestItem Grid and Maze Solver

1. CPSC 233 Tutorial Xin Mar 7, 2011

2. A trap in Asgn 4 • Each element of the grid is a reference to ForestItem, not a character • Different from the example program • Define class ForestItem, and used it in the grid!!!

3. Recursion • The concept • Call itself inside a function • Components • A method definition • Call itself inside the method with a smaller-scaled argument • An ending condition int sum (intarg) { if (arg > 0) return sum (arg – 1) + arg; else return 0; }

4. What’s good? • Logically simple program (for certain problems) • What’s bad? • Hard to understand for new learners • Spend some time to feel comfortable with it • Believe the function works • Don’t confuse yourself by expanding the recursion • memory consuming

5. Example 1 -- SUM public class sum { intsumup(intn) { if (n > 0) return sumup (n - 1) + n; else return 0; } } public class sum_driver { public static void main (String args []) { sum aSum = new sum(); intn = 10; System.out.println("the sum from 0 to " + n + " is " + aSum.sumup(n)); } }

6. Example 2 – Fibonacci number • Definition • F (n) = F (n - 1) + F (n – 2) • F (0) = 0; F(1) = 1;

7. Example 2 -- code public class fibonacci { int fib (intn) { if (n < 0) { System.out.println ("n must be non-negative"); return 0; } else if (n == 0) return 0; else if (n == 1) return 1; else return fib ( n - 1) + fib (n - 2); } } public class fibonacci_driver { public static void main (String args []) { fibonacciaFib = new fibonacci(); intn = 10; System.out.println ("fibonacci(" + n + ") is " + aFib.fib(n)); } }

8. Maze Solver • The idea: • Try an immediate neighbor • Accessible in one step • Is there a way from that neighbor to the EXIT? • Call recursively

9. Improve grid programMove the party n = (dy + 1) * 3 + (dx + 1) dx = (n – 1) % 3 - 1 dy = (n – 1) / 3 - 1