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Java Programming: From Problem Analysis to Program Design, 3e Chapter 14 Recursion
Chapter Objectives ,[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Chapter Objectives (continued) ,[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Recursive Definitions ,[object Object],[object Object],[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Recursive Definitions (continued) Java Programming: From Problem Analysis to Program Design, 3e
Recursive Definitions (continued) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Recursive Definitions (continued) ,[object Object],[object Object],[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Tracing a Recursive Method ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Tracing a Recursive Method (continued) ,[object Object],[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Recursive Definitions ,[object Object],[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Designing Recursive Methods ,[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Designing Recursive Methods (continued) ,[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Recursive Factorial Method Java Programming: From Problem Analysis to Program Design, 3e public static int  fact( int  num) {   if  (num = = 0)   return  1;   else   return  num * fact(num – 1); }
Recursive Factorial Method (continued) Java Programming: From Problem Analysis to Program Design, 3e
Largest Value in Array Java Programming: From Problem Analysis to Program Design, 3e
Largest Value in Array (continued) Java Programming: From Problem Analysis to Program Design, 3e ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Largest Value in Array (continued) Java Programming: From Problem Analysis to Program Design, 3e 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; } }
Execution of  largest (list, 0, 3) Java Programming: From Problem Analysis to Program Design, 3e
Execution of  largest (list, 0, 3) Java Programming: From Problem Analysis to Program Design, 3e
Recursive Fibonacci Java Programming: From Problem Analysis to Program Design, 3e
Recursive Fibonacci (continued) Java Programming: From Problem Analysis to Program Design, 3e 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); }
Recursive Fibonacci (continued) Java Programming: From Problem Analysis to Program Design, 3e
Towers of Hanoi Problem with Three Disks Java Programming: From Problem Analysis to Program Design, 3e
Towers of Hanoi: Three Disk Solution Java Programming: From Problem Analysis to Program Design, 3e
Towers of Hanoi: Three Disk Solution (continued) Java Programming: From Problem Analysis to Program Design, 3e
Towers of Hanoi: Recursive Algorithm Java Programming: From Problem Analysis to Program Design, 3e 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); } }
Recursion or Iteration? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Programming Example:  Decimal to Binary Java Programming: From Problem Analysis to Program Design, 3e public static void  decToBin( int  num,  int  base) { if   (num > 0) { decToBin(num / base, base); System.out.print(num % base); } }
Execution of  decToBin(13, 2) Java Programming: From Problem Analysis to Program Design, 3e
Sierpinski Gaskets of Various Orders  Java Programming: From Problem Analysis to Program Design, 3e
Programming Example: Sierpinski Gasket ,[object Object],[object Object],[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Programming Example: Sierpinski Gasket (continued) Java Programming: From Problem Analysis to Program Design, 3e 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 Input Java Programming: From Problem Analysis to Program Design, 3e
Chapter Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e
Chapter Summary (continued) ,[object Object],[object Object],[object Object],[object Object],[object Object],Java Programming: From Problem Analysis to Program Design, 3e

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Chap14

  • 1. Java Programming: From Problem Analysis to Program Design, 3e Chapter 14 Recursion
  • 2.
  • 3.
  • 4.
  • 5. Recursive Definitions (continued) Java Programming: From Problem Analysis to Program Design, 3e
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13. Recursive Factorial Method Java Programming: From Problem Analysis to Program Design, 3e public static int fact( int num) { if (num = = 0) return 1; else return num * fact(num – 1); }
  • 14. Recursive Factorial Method (continued) Java Programming: From Problem Analysis to Program Design, 3e
  • 15. Largest Value in Array Java Programming: From Problem Analysis to Program Design, 3e
  • 16.
  • 17. Largest Value in Array (continued) Java Programming: From Problem Analysis to Program Design, 3e 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; } }
  • 18. Execution of largest (list, 0, 3) Java Programming: From Problem Analysis to Program Design, 3e
  • 19. Execution of largest (list, 0, 3) Java Programming: From Problem Analysis to Program Design, 3e
  • 20. Recursive Fibonacci Java Programming: From Problem Analysis to Program Design, 3e
  • 21. Recursive Fibonacci (continued) Java Programming: From Problem Analysis to Program Design, 3e 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); }
  • 22. Recursive Fibonacci (continued) Java Programming: From Problem Analysis to Program Design, 3e
  • 23. Towers of Hanoi Problem with Three Disks Java Programming: From Problem Analysis to Program Design, 3e
  • 24. Towers of Hanoi: Three Disk Solution Java Programming: From Problem Analysis to Program Design, 3e
  • 25. Towers of Hanoi: Three Disk Solution (continued) Java Programming: From Problem Analysis to Program Design, 3e
  • 26. Towers of Hanoi: Recursive Algorithm Java Programming: From Problem Analysis to Program Design, 3e 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); } }
  • 27.
  • 28. Programming Example: Decimal to Binary Java Programming: From Problem Analysis to Program Design, 3e public static void decToBin( int num, int base) { if (num > 0) { decToBin(num / base, base); System.out.print(num % base); } }
  • 29. Execution of decToBin(13, 2) Java Programming: From Problem Analysis to Program Design, 3e
  • 30. Sierpinski Gaskets of Various Orders Java Programming: From Problem Analysis to Program Design, 3e
  • 31.
  • 32. Programming Example: Sierpinski Gasket (continued) Java Programming: From Problem Analysis to Program Design, 3e 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); } }
  • 33. Programming Example: Sierpinski Gasket Input Java Programming: From Problem Analysis to Program Design, 3e
  • 34.
  • 35.