Chapter 13 Recursion. Chapter Objectives
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1 Chapter 13 Recursion Chapter Objectives Learn about recursive definitions Explore the base case and the general case of a recursive definition Learn about recursive algorithms Java Programming: From Problem Analysis to Program Design, 5e 2 1
2 Chapter Objectives (continued) Learn about recursive methods Become aware of direct and indirect recursion Explore how to use recursive methods to implement recursive algorithms Java Programming: From Problem Analysis to Program Design, 5e 3 Recursion Recursive Definitions 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: From Problem Analysis to Program Design, 5e 4 2
3 Recursive Definitions (continued) Java Programming: From Problem Analysis to Program Design, 5e 5 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 Recursive method Method that calls itself Base case Case in recursive definition in which the solution is obtained directly Stops the recursion Java Programming: From Problem Analysis to Program Design, 5e 6 3
4 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: From Problem Analysis to Program Design, 5e 7 Tracing a Recursive Method Recursive method Logically, you can think of a recursive method having unlimited copies of itself Every recursive call has its own: Code Set of parameters Set of local variables Java Programming: From Problem Analysis to Program Design, 5e 8 4
5 Tracing a Recursive Method (continued) 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: From Problem Analysis to Program Design, 5e 9 Recursive Definitions Directly recursive: a method that calls itself Indirectly recursive: a 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: the case where every recursive call results in another recursive call Java Programming: From Problem Analysis to Program Design, 5e 10 5
6 Designing Recursive Methods Understand problem requirements Determine limiting conditions Identify base cases Java Programming: From Problem Analysis to Program Design, 5e 11 Designing Recursive Methods (continued) Provide direct solution to each base case Identify general case(s) Provide solutions to general cases in terms of smaller versions of general cases Java Programming: From Problem Analysis to Program Design, 5e 12 6
7 Recursive Factorial Method public static int fact(int num) { if (num = = 0) return 1; else return num * fact(num 1); } Java Programming: From Problem Analysis to Program Design, 5e 13 Recursive Factorial Method (continued) Java Programming: From Problem Analysis to Program Design, 5e 14 7
8 Largest Value in Array Java Programming: From Problem Analysis to Program Design, 5e 15 Largest Value in Array (continued) if the size of the list is 1 the largest element in the list is the only element in the list else to find the largest element in list[a]...list[b] a. find the largest element in list[a + 1]...list[b] and call it max b. compare list[a] and max if (list[a] >= max) the largest element in list[a]...list[b] is list[a] else the largest element in list[a]...list[b] is max Java Programming: From Problem Analysis to Program Design, 5e 16 8
![Largest Value in Array (continued) public static int largest(int[] list, int lowerindex, int upperindex) { int max; if (lowerindex == upperindex) return list[lowerindex]; else { max = largest(list,](/docs-images/73/69063404/images/9-0.jpg "lowerindex + 1, upperindex); if (list[lowerindex] >= max) return list[lowerindex]; else return max; } } Java Programming: From Problem Analysis to Program Design, 5e 17 Execution of largest (list, 0,")
9 Largest Value in Array (continued) 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 list[lowerindex]; else return max; } } Java Programming: From Problem Analysis to Program Design, 5e 17 Execution of largest (list, 0, 3) Java Programming: From Problem Analysis to Program Design, 5e 18 9
10 Execution of largest (list, 0, 3) Java Programming: From Problem Analysis to Program Design, 5e 19 Recursive Fibonacci Java Programming: From Problem Analysis to Program Design, 5e 20 10
11 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: From Problem Analysis to Program Design, 5e 21 Recursive Fibonacci (continued) Java Programming: From Problem Analysis to Program Design, 5e 22 11
12 Towers of Hanoi Problem with Three Disks Java Programming: From Problem Analysis to Program Design, 5e 23 Towers of Hanoi: Three Disk Solution Java Programming: From Problem Analysis to Program Design, 5e 24 12
13 Towers of Hanoi: Three Disk Solution (continued) Java Programming: From Problem Analysis to Program Design, 5e 25 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: From Problem Analysis to Program Design, 5e 26 13
14 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: From Problem Analysis to Program Design, 5e 27 Programming Example: Decimal to Binary Java Programming: From Problem Analysis to Program Design, 5e 28 14
15 Java Programming: From Problem Analysis to Program Design, 5e 29 Sierpinski Gaskets of Various Orders Java Programming: From Problem Analysis to Program Design, 5e 30 15
16 Programming Example: Sierpinski Gasket Input: nonnegative integer indicating level of Sierpinski gasket Output: triangle shape displaying a Sierpinski gasket of the given order Solution includes: Recursive method drawsierpinski Method to find midpoint of two points Java Programming: From Problem Analysis to Program Design, 5e 31 Programming Example: Sierpinski Gasket (continued) 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: From Problem Analysis to Program Design, 5e 32 16
17 Programming Example: Sierpinski Gasket (continued) Java Programming: From Problem Analysis to Program Design, 5e 33 Chapter Summary Recursive definitions Recursive algorithms Recursive methods Base cases General cases Java Programming: From Problem Analysis to Program Design, 5e 34 17
18 Chapter Summary (continued) Tracing recursive methods Designing recursive methods Varieties of recursive methods Recursion vs. iteration Various recursive functions explored Java Programming: From Problem Analysis to Program Design, 5e 35 18
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