Exercises 8.5

1. 10 cubed = 1000

9 cubed = 729

8 cubed = 512

7 cubed = 343

6 cubed = 216

5 cubed = 125

4 cubed = 64

3 cubed = 27

2 cubed = 8

1 cubed = 1

2. 10 squared = 100

8 squared = 64

6 squared = 36

4 squared = 16

2 squared = 4

3.

1

1

2

2

3

3

1

4

4

2

5

5

3

1

4.

3

1

3

5

5.

3 1 3

3 1 2

3 1 1

3 2 3

3 2 2

3 3 3

2 1 2

2 1 1

2 2 2

1 1 1

6.

1 1 1

1 2 1

1 2 2

1 3 1

1 3 2

1 3 3

2 2 2

2 3 2

2 3 3

3 3 3

7.

1 1 1

1 1 2

1 2 1

1 2 2

1 2 3

1 3 1

1 3 2

1 3 3

1 3 4

2 1 1

2 1 2

2 1 3

2 2 1

2 2 2

2 2 3

2 2 4

2 3 1

2 3 2

2 3 3

2 3 4

1 1 1

1 1 2

1 1 3

1 1 4

1 2 1

1 2 2

1 2 3

1 2 4

1 3 1

1 3 2

1 3 3

1 3 4

2 1 1

2 1 2

2 1 3

2 1 4

2 2 1

2 2 2

2 2 3

2 2 4

2 3 1

2 3 2

2 3 3

2 3 4

8.

1 1 1

1 1 2

1 1 3

1 1 4

1 2 1

1 2 2

1 2 3

1 2 4

1 3 1

1 3 2

1 3 3

1 3 4

2 1 1

2 1 2

2 1 3

2 1 4

2 2 1

2 2 2

2 2 3

2 2 4

2 3 1

2 3 2

2 3 3

2 3 4

9.

1 1 1

1 1 2

1 1 3

1 1 4

1 2 1

1 2 2

1 2 3

1 2 4

1 3 1

1 3 2

1 3 3

1 3 4

2 2 1

2 2 2

2 2 3

2 2 4

2 3 1

2 3 2

2 3 3

2 3 4

10.

2 1 1

11.

1 1 1

1 1 2

1 1 3

1 1 4

1 2 1

1 2 2

1 2 3

1 2 4

1 3 1

1 3 2

1 3 3

1 3 4

2 1 1

2 1 2

2 1 3

2 1 4

2 2 1

2 2 2

2 2 3

2 2 4

2 3 1

2 3 2

2 3 3

2 3 4

12.

5 1 9

4 2 6

3 3 3

2 4 0

1 5 -3

13.

0 10 10

1 9 11

2 8 12

3 7 13

4 6 14

5 5 15

6 4 16

14.

0 10 10

1 9 11

2 8 12

3 7 13

4 6 14

5 5 15

6 4 16

7 3 17

8 2 18

9 1 19

10 0 20

11 -1 21

15.

5

1

2

3

###

3

1

###

1

***

16.

base-2 log of 32 = 5

base-2 log of 16 = 4

base-2 log of 8 = 3

base-2 log of 4 = 2

base-2 log of 2 = 1

base-2 log of 1 = 0

17.

2

3

5

9

4

6

10

6

9

*****

18.

0 1

1 -1

2 3

19.

0002448612*****

20. While loop Do-while loop Forever loop

number	product	number	product	number	product
0	1	0	1	0	1
1	1	1	1	1	1
2	2	2	2	2	2
3	6	3	6	3	6
4	24	4	24	4	24
				5	24

21. While loop Do-while loop Forever loop

number	product	number	product	number	product
0	1	0	1	0	1
1	1	1	1	1	1
2	2	2	2	2	2
				3	2

22. While loop Do-while loop Forever loop

number	product	number	product	number	product
0	1	0	1	0	1
		1	1	1	1
				2	2
				3	2

23.

do

{

theScreen.println(x);

x -= 0.5;

}

while (x > 0);

24.

for (int i = 1; i <= 50 ; i++)

theScreen.println( (2*i) * (2*i) );

25.

for (double x = 1.0; x <= 5.0; x += 0.25)

theScreen.println( Math.sqrt(x) );

26.

int fib1 = 1, fib2 = 1, fib3;

theScreen.println(1);

theScreen.println(1);

for (;;)

{

fib3 = fib1 + fib2;

if (fib3 >= 500) break;

theScreen.println(fib3);

fib1 = fib2;

fib2 = fib3;

}

27.

for(;;)

{

theScreen.print("Enter a real number: ");

x = theKeyboard.readDouble();

if (x > 0) break;

theScreen.println("Sorry, you entered: " + x

+ "\nThe number must be POSITIVE");

}

28.

public static int summation (int first, int last)

{

int runningTotal = 0;

for (int count = first; count <= last; count++)

runningTotal += count;

return runningTotal;

}

29.

public static BigInteger summation (BigInteger n)

{

BigInteger runningTotal = BigInteger.ZERO,

count = BigInteger.ONE;

while ( count.compareTo(n) <= 0)

{

runningTotal = runningTotal.add(count) ;

count = count.add( BigInteger.ONE );

}

return runningTotal;

}

30.

public static BigInteger summation (BigInteger first,

BigInteger last)

{

BigInteger runningTotal = BigInteger.ZERO,

count = first;

while ( count.compareTo(last) <= 0)

{

runningTotal = runningTotal.add(count) ;

count = count.add( BigInteger.ONE );

}

return runningTotal;

}

31.

public static double Power(double x, int n)

{

double product = 1.0;

for (int i = 0; i < n; i++)

product *= x;

return product;

}

32.

public static double power(double x, int n)

{

double product = 1.0;

for (int i = 0; i < Math.abs(n); i++)

product *= x;

if (n >= 0)

return product;

else if (x != 0)

return 1.0 / product;

else

{

System.err.println("0 to a negative power is undefined – "

+ "returning 0\n");

return 0;

}

}

33.

public static int divisorSum (int n)

{

int sum = 0;

for (int i = 1; i <= n/2; i++)

if (n % i == 0) sum += i;

return sum;

}

34.

public static boolean isPrime(int n)

{

if (n < 2)

return false; // 0 & 1 are not primes

if (n == 2)

return true; // 2 is prime

if (n % 2 == 0)

return false; // evens > 2 are not prime

for (int d = 3; d*d <= n; d++) // check if any odd integer // in the range 3 through

// square root of n divides n

if (n % d == 0)

return false; // d divides n; n not prime

return true; // otherwise, n is prime

}

35.

public static int intLog2(int n)

{

int count = 0;

while (n > 1)

{

count++;

n /= 2;

}

return count;

}