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

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{

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(" |");

}

}

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);

}

}

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);

}

}

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

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

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!

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;

}

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

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;

}

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)

job division: f3(x, y) => f3(x+1, y-1)

results collection: f3(x+1, y-1)+(double)x/y

result reporting: return

f3(i-1, 2) => f3(i, 1) => none!

Terminating condition: x >=i

Terminating condition: y <=1

Where is “I” in “f3”?

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;

}

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

job division: f3(x, y) => f3(x+1, y-1)

results collection: f3(x+1, y-1)+(double)y/x

result reporting: return

f3(i-1, 2), i.e., 2/i-1 => f3(i, 1), i.e., 1/i => none!

Terminating condition: y<=1

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;

}

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

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

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);

}

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

job division: f5(x, y) => f5((x-y)*1.01, y)

results collection: f5((x-y)*1.01,y)

result reporting: return

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);

}

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!

job division: f6(x) => f6(x-1)

results collection:

f6(x-1);

System.out.print(x);

result reporting: void

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);

}

}

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!

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

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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