1. Java Programming: Program Design Including Data Structures
Chapter 14: Recursion
Java Programming:
Program Design Including Data Structures

2. Chapter Objectives Learn about recursive definitions
Explore the base case and the general case of a recursive definition
Learn about recursive algorithms
Learn about recursive methods
Become aware of direct and indirect recursion
Explore how to use recursive methods to implement recursive algorithms
Java Programming: Program Design Including Data Structures

3. Recursive Definitions
Recursion:
Process of solving a problem by reducing it to smaller versions of itself
Recursive definition:
Definition in which a problem is expressed in terms of a smaller version of itself
Has one or more base cases
Java Programming: Program Design Including Data Structures

4. Recursive Definitions (continued)
Recursive algorithm:
Algorithm that finds the solution to a given problem by reducing the problem to smaller versions of itself
Has one or more base cases
Implemented using recursive methods
Java Programming: Program Design Including Data Structures

5. Recursive Definitions (continued)
Recursive method:
Method that calls itself
Base case:
Case in recursive definition in which the solution is obtained directly
Stops the recursion
Java Programming: Program Design Including Data Structures

6. Recursive Definitions (continued)
General solution:
Breaks problem into smaller versions of itself
General case:
Case in recursive definition in which a smaller version of itself is called
Must eventually be reduced to a base case
Java Programming: Program Design Including Data Structures

7. Tracing a Recursive Method
Has unlimited copies of itself
Every recursive call has its own:
Code
Set of parameters
Set of local variables
Java Programming: Program Design Including Data Structures

8. Tracing a Recursive Method
After completing a recursive call:
Control goes back to the calling environment
Recursive call must execute completely before control goes back to previous call
Execution in previous call begins from point immediately following recursive call
Java Programming: Program Design Including Data Structures

9. Recursive Definitions
Directly recursive: method that calls itself
Indirectly recursive: method that calls another method and eventually results in the original method call
Tail recursive method: recursive method in which the last statement executed is the recursive call
Infinite recursion: case where every recursive call results in another recursive call
Java Programming: Program Design Including Data Structures

10. Designing Recursive Methods
Understand problem requirements
Determine limiting conditions
Identify base cases
Java Programming: Program Design Including Data Structures

11. Designing Recursive Methods
Provide direct solution to each base case
Identify general cases
Provide solutions to general cases in terms of smaller versions of general cases
Java Programming: Program Design Including Data Structures

12. Recursive Factorial Method
public static int fact(int num) { if (num = = 0) return 1; else return num * fact(num – 1); }
Java Programming: Program Design Including Data Structures

13. Recursive Factorial Method (continued)
Java Programming: Program Design Including Data Structures

14. Largest Value in Array public static int largest(int[] list,
int lowerIndex,
int upperIndex) {
int max;
if (lowerIndex == upperIndex)
return list[lowerIndex];
else
max = largest(list, lowerIndex + 1,
upperIndex);
if (list[lowerIndex] >= max)
return max; }
Java Programming: Program Design Including Data Structures

15. Largest Value in Array (continued)
Java Programming: Program Design Including Data Structures

16. Recursive Fibonacci
Java Programming: Program Design Including Data Structures

17. Recursive Fibonacci (continued)
public static int rFibNum(int a, int b,
int n) {
if(n = = 1)
return a;
else if (n = = 2)
return b;
else
return rFibNum(a, b, n -1) +
rFibNum(a, b, n - 2); }
Java Programming: Program Design Including Data Structures

18. Recursive Fibonacci (continued)
Java Programming: Program Design Including Data Structures

19. Towers of Hanoi: Three Disk Problem
Java Programming: Program Design Including Data Structures

20. Towers of Hanoi: Three Disk Solution
Java Programming: Program Design Including Data Structures

21. Towers of Hanoi: Three Disk Solution
Java Programming: Program Design Including Data Structures

22. Towers of Hanoi: Recursive Algorithm
public static void moveDisks(int count, int needle1,
int needle3, int needle2) {
if (count > 0)
moveDisks(count - 1, needle1, needle2, needle3);
System.out.println("Move disk " + count
+ " from needle "
+ needle1 + " to needle "
+ needle3 + ". ");
moveDisks(count - 1, needle2, needle3, needle1); }
Java Programming: Program Design Including Data Structures

23. Recursion or Iteration?
Two ways to solve particular problem:
Iteration
Recursion
Iterative control structures use looping to repeat a set of statements
Tradeoffs between two options:
Sometimes recursive solution is easier
Recursive solution is often slower
Java Programming: Program Design Including Data Structures

24. Programming Example: Decimal to Binary
public static void decToBin(int num,
int base) {
if (num > 0)
decToBin(num / base, base);
System.out.print(num % base); }
Java Programming: Program Design Including Data Structures

25. Programming Example: Decimal to Binary
Java Programming: Program Design Including Data Structures

26. Programming Example: Sierpinski Gasket
Java Programming: Program Design Including Data Structures

27. Programming Example: Sierpinski Gasket (continued)
Input: Non-negative integer that indicates level of Sierpinski gasket
Output: Triangle shape that displays a Sierpinski gasket of the given order
Solution includes:
Recursive method drawSierpinski
Method to find midpoint of two points
Java Programming: Program Design Including Data Structures

28. Sierpinski Gasket private void drawSierpinski(Graphics g, int lev,
Point p1, Point p2, Point p3) {
Point midP1P2;
Point midP2P3;
Point midP3P1;
if (lev > 0)
g.drawLine(p1.x, p1.y, p2.x, p2.y);
g.drawLine(p2.x, p2.y, p3.x, p3.y);
g.drawLine(p3.x, p3.y, p1.x, p1.y);
midP1P2 = midPoint(p1, p2);
midP2P3 = midPoint(p2, p3);
midP3P1 = midPoint(p3, p1);
drawSierpinski(g, lev - 1, p1, midP1P2,
midP3P1);
drawSierpinski(g, lev - 1, p2, midP2P3,
midP1P2);
drawSierpinski(g, lev - 1, p3,
midP3P1, midP2P3); }
Java Programming: Program Design Including Data Structures

29. Sierpinski Gasket (continued)
Java Programming: Program Design Including Data Structures

30. Chapter Summary Recursive definitions Recursive algorithms
Recursive methods
Base cases
General cases
Java Programming: Program Design Including Data Structures

31. Chapter Summary (continued)
Tracing recursive methods
Designing recursive methods
Varieties of recursive methods
Recursion vs. iteration
Various recursive functions
Java Programming: Program Design Including Data Structures