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public class PrintSquares { public static void main(String [] args ) {

public class PrintSquares { public static void main(String [] args ) { System.out.println ("****"); System.out.println ("* *"); System.out.println ("* *"); System.out.println ("****"); System.out.println (); System.out.println ("****"); System.out.println ("* *");

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public class PrintSquares { public static void main(String [] args ) {

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  1. public class PrintSquares { public static void main(String [] args) { System.out.println("****"); System.out.println("* *"); System.out.println("* *"); System.out.println("****"); System.out.println(); System.out.println("****"); System.out.println("* *"); System.out.println("* *"); System.out.println("****"); } } public class PrintSteps { public static void main(String [] args) { System.out.println("-----"); System.out.println(" |"); System.out.println(" |"); System.out.println(" -----"); System.out.println(" |"); System.out.println(" |"); } }

  2. public static void pos(int n, String str){ for(inti=0;i<n;i++)System.out.print(str); } public static void square(intlen){ pos(len, “*”); System.out.println(); for(inti=0;i<len-2;i++){ pos(1, “*”); pos(len-2, “*”); pos(1, “*”); System.out.println(); } pos(len, “*”); System.out.println(); } public static void squares (int n, int length){ square(length); for(inti=1;i<n;i++){ System.out.print square(length); } }

  3. public static void pos(int n, String str){ for(inti=0;i<n;i++)System.out.print(str); } public static void step(int start, int width, int depth){ space(start, “ “); pos(width, “-”); System.out.println(); for(inti=0;i<depth;i++){ pos(start+width, “ “); pos(1, “|”); System.out.println(); } } public static void steps (int n, int width, int depth){ for(inti=0;i<n;i++){ step((width+1)*i, width, depth); } }

  4. Calculate the result 1+3+5+7+9+11+13+…+99 when f1(99) is called. job division: 1+3+5+…+97+99 => 1+…+97 f1(99) => f1(97) results collection: f1(97)+99 result reporting: return

  5. job division: 1+3+5+…+97 => 1+…+95 f1(97) => f1(95) results collection: f1(95)+97 result reporting: return General format:: job division: f1(x) => f1(x-2) results collection: f1(x-2)+x result reporting: return

  6. job division: f1(x) => f1(x-2) f1(3) => f1(1) => none! Terminating condition: x <=1 Why x<=2 ok? 7, 5, 3 go false!

  7. job division: f1(x) => f1(x-2) results collection: f1(x-2)+x result reporting: return Terminating condition: x <=1 public static int f1 ( ) int x { if (x <=1) return 1; else return f1(x-2)+x; }

  8. Calculate the result 1+2+4+8+16+32+…+4096 when f2(4096) is called. job division: 1+2+…+2048+4096 => 1+…+2048 f2(4096) => f2(2048) results collection: f2(2048)+4096 result reporting: return

  9. job division: f2(x) => f2(x/2) results collection: f2(x/2)+x result reporting: return

  10. f2(x) => f2(x/2) f2(2) => f2(1) => none! Terminating condition: x <=1

  11. job division: f2(x) => f2(x/2) results collection: f2(x/2)+x result reporting: return Terminating condition: x <=1 public static int f2 ( ) int x { if (x <=1) return 1; else return f2(x/2)+x; }

  12. Calculate the result 1/i+2/(i-1)+3/(i-2)+…+(i-1)/2+i/1 when f3(1, i). job division: 1/i+2/(i-1)+…+i/1 => 2/(i-1)+…+i/1 => f3(2,i-1) results collection: f3(2, i-1) + (double)1/i result reporting: return f3(1,i) f3(1,i)

  13. job division: f3(x, y) => f3(x+1, y-1) results collection: f3(x+1, y-1)+(double)x/y result reporting: return

  14. f3(x, y) => f3(x+1, y-1) f3(i-1, 2) => f3(i, 1) => none! Terminating condition: x >=i Terminating condition: y <=1 Where is “I” in “f3”?

  15. job division: f3(x, y) => f3(x+1, y-1) results collection: f3(x+1, y-1)+(double)x/y result reporting: return Terminating condition: y <=1 public static double f3 ( ) int X, int y { if (y<=1) return (double)x/y; else return f3(x+1, y-1)+(double)x/y; }

  16. Calculate the result 1/i+2/(i-1)+3/(i-2)+…+(i-1)/2+i/1. job division: 1/i+…+(i-1)/2+i/1 => 1/i+…. (i-1)/2 f3(1,i) => f3(2,i-1) results collection: f3(2, i-1) + (double)i/1 result reporting: return

  17. job division: f3(x, y) => f3(x+1, y-1) results collection: f3(x+1, y-1)+(double)y/x result reporting: return

  18. f3(x, y) => f3(x+1, y-1) f3(i-1, 2), i.e., 2/i-1 => f3(i, 1), i.e., 1/i => none! Terminating condition: y<=1

  19. job division: f3(x, y) => f3(x+1, y-1) results collection: f3(x+1, y-1)+(double)y/x result reporting: return Terminating condition: y<=1 public static double f3 ( ) int X, int y { if (y<=1) return (double)y/x; else return f3(x+1, y-1)+(double)y/x; }

  20. The world population reached 6 billion people in 1999 and was growing at the rate of 1.4 percent each year. Write a recursive function f to return/determine when the population will exceed 10 Billion when f4(6, 10, 1999) is called. job division: from 1999 (p=6) to target year (p>10)  from 2000 (p=6*1.014) to target year results collection: f4(6*1.014, 10, 2000) result reporting: return

  21. job division: f4(cp, tp, y) => f4(cp *1.014, tp, y+1) results collection: f4(cp *1.014, tp, y+1) result reporting: return

  22. General Format: => f4(cp, tp, yr) … => f4(>tp, tp, yr) => none! Terminating condition: cp>tp

  23. job division: f4(cp, tp, y) => f4(cp *1.014, tp, y+1) results collection: f4(cp *1.014, tp, y+1) result reporting: return Terminating condition: cp>tp public static int f4 ( ) double cp, double tp, int x { if (cp >tp) return x; else return f4(cp*1.014, tp, x+1); }

  24. A TV set is purchased with a loan of $563 to be paid off with monthly payment (no more than $116). The interest rate is 1 percent per month. Write a recursive function f to return the amount of last bill when f5(563, 116) is called. job division: from 563 until <=116  from (563-116 )*1.01 (i.e., next month) until <=116 results collection: f5((563-116)*1.01, 116) result reporting: return

  25. job division: f5(x, y) => f5((x-y)*1.01, y) results collection: f5((x-y)*1.01,y) result reporting: return

  26. f5(x, y) => f5((x-y)*1.01, y) … => f5(<=116, 116) => none! Terminating condition: x <=116, i.e., y

  27. job division: f5(x, y) => f5((x-y)*1.01, y) results collection: f5((x-y)*1.01,y) result reporting: return Terminating condition: x <=y public static double f5 ( ) double X, int y { if (x<=y) return x; else return f5((x-y)*1.01, y); }

  28. Develop a recursive function f6 to display the sequence 1 2 3 4 5 … i in a text field when f6(i) is called. job division: display 1, 2, …, i-1, i  display 1, 2, …, i-1 results collection: f6(i-1) on the screen, and System.out.print(i) result reporting: results are on the screen, nothing to report!

  29. job division: f6(x) => f6(x-1) results collection: f6(x-1); System.out.print(x); result reporting: void

  30. f6(x) => f6(x-1) … => f6(1) => none! Terminating condition: x <=1

  31. job division: f6(x) => f6(x-1) results collection: f6(x-1); System.out.print(x); result reporting: none Terminating condition: x <=y public static void f6 ( ) int x { if (x <=1) System.out.print(x); else { f6(x-1); System.out.print(x); } }

  32. Develop a recursive function f7 to display the sequence 1 2 3 4 5 … i (i-1) (i-2) … 2 1 in a text field when f7(1,i) is called. job division: display 1, 2, …, i-1, i, i-1, …, 2, 1  display 2, …, i-1, i, i-1, …, 2 results collection: f7(2,i) on the screen, and System.out.print(1) twice! result reporting: results are on the screen, nothing to report!

  33. job division: f7(x, y) => f7(x+1, y) results collection: System.out.print(x) f7(x+1,y); System.out.print(x); result reporting: void

  34. f7(x,y) => f7(x+1,y) … => f7(i-1, i) //two 8’s => none! Terminating condition: x >=y

  35. job division: f7(x,y) => f7(x+1,y) results collection: System.out.print(x); f7(x+1,y); System.out.print(x); result reporting: none Terminating condition: x >=y public static void f7 ( ) int X, int y { if (x>=y) System.out.print(x); else { System.out.print(x); f7(x+1,y); System.out.print(x); } }

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