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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Recursive Fibonacci Java Programming: Program Design Including Data Structures

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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