chapter 13: recursion j ava p rogramming: from problem analysis to program design, from problem...
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Chapter 13: RecursionChapter 13: Recursion
JJavaava PProgramming:rogramming:
From Problem Analysis to Program From Problem Analysis to Program Design, Design,
Fourth EditionFourth Edition
Java Programming: From Problem Analysis to Program Design, Second Edition 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: From Problem Analysis to Program Design, Second Edition 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: From Problem Analysis to Program Design, Second Edition 4
Recursive Definitions 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, Second Edition 5
Recursive Definitions 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, Second Edition 6
Tracing a Recursive Method
Recursive method:
Has 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, Second Edition 7
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: From Problem Analysis to Program Design, Second Edition 8
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, Second Edition 9
Designing Recursive Methods
Understand problem requirements.
Determine limiting conditions.
Identify base cases.
Java Programming: From Problem Analysis to Program Design, Second Edition 10
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: From Problem Analysis to Program Design, Second Edition 11
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, Second Edition 12
Recursive Factorial Method
Java Programming: From Problem Analysis to Program Design, Second Edition 13
Largest Value in Arraypublic 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, Second Edition 14
Largest Value in Array
Java Programming: From Problem Analysis to Program Design, Second Edition 15
Recursive Fibonacci
Java Programming: From Problem Analysis to Program Design, Second Edition 16
Recursive Fibonacci
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, Second Edition 17
Recursive Fibonacci
Java Programming: From Problem Analysis to Program Design, Second Edition 18
Towers of Hanoi: Three Disk Problem
Java Programming: From Problem Analysis to Program Design, Second Edition 19
Towers of Hanoi: Three Disk Solution
Java Programming: From Problem Analysis to Program Design, Second Edition 20
Towers of Hanoi: Three Disk Solution
Java Programming: From Problem Analysis to Program Design, Second Edition 21
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, Second Edition 22
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, Second Edition 23
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: From Problem Analysis to Program Design, Second Edition 24
Programming Example: Decimal to Binary
Java Programming: From Problem Analysis to Program Design, Second Edition 25
Programming Example: Sierpinski Gasket
Java Programming: From Problem Analysis to Program Design, Second Edition 26
Programming Example:Sierpinski Gasket
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: From Problem Analysis to Program Design, Second Edition 27
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); }}
Programming Example: Sierpinski Gasket
Java Programming: From Problem Analysis to Program Design, Second Edition 28
Programming Example: Sierpinski Gasket
Java Programming: From Problem Analysis to Program Design, Second Edition 29
Chapter Summary
Recursive definitions
Recursive algorithms
Recursive methods
Base cases
General cases
Java Programming: From Problem Analysis to Program Design, Second Edition 30
Chapter Summary
Tracing recursive methods
Designing recursive methods
Varieties of recursive methods
Recursion vs. iteration
Various recursive functions
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