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Java Programming: From Problem Analysis to Program Design, Second Edition 1
Chapter 14: Recursion
Recursive definitions.
Base case and general case.
Recursive algorithms.
Recursive methods.
Direct and indirect recursion.
Recursion Vs Iteration
Java Programming: From Problem Analysis to Program Design, Second Edition 2
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 3
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 4
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 7
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 8
Designing Recursive Methods
Understand problem requirements.
Determine limiting conditions.
Identify base cases.
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 9
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 10
Recursive Factorial Method
Java Programming: From Problem Analysis to Program Design, Second Edition 13
Recursive Fibonacci
Java Programming: From Problem Analysis to Program Design, Second Edition 14
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 15
Recursive Fibonacci
Java Programming: From Problem Analysis to Program Design, Second Edition 16
Towers of Hanoi: Three Disk Problem
Java Programming: From Problem Analysis to Program Design, Second Edition 19
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 20
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 21
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 22
Programming Example: Decimal to Binary
Java Programming: From Problem Analysis to Program Design, Second Edition 25
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 26
Programming Example: Sierpinski Gasket
Java Programming: From Problem Analysis to Program Design, Second Edition 27
Chapter Summary
Recursive definitions
Recursive algorithms
Recursive methods
Base cases & General cases
Designing recursive methods
Recursion vs. iteration
Various recursive functions
