Exercises 5.3

 

1. -2 squared = 4

-1 squared = 1

0 squared = 0

1 squared = 1

2 squared = 4

3 squared = 9

 

2.    1
1
2
2
1
3
3
2
1
4
4
3
2
1
5
5
4
3
2
1

 

3.    3
0
1
2
3
4

 

4.    111
121
122
131
132
133
211
221
222
231
232
233
311
321
322
331
332
333

 

5.  

111

121
122

131
132
133


222

232
233



333

6.    000

    112

    228

    18

 

7.    000

    112

    228

    18

 

8.    5123###

    31###

    1***

 

9, 10, 11

(a) limit = 10

                      Pretest loop                                     Posttest loop                           Test-in-the-middle loop

 

number

sum

 

number

sum

 

number

sum

 

0

0

 

0

0

 

0

0

 

1

1

 

1

1

 

1

1

 

2

3

 

2

3

 

2

3

 

3

6

 

3

6

 

3

6

 

4

10

 

4

10

 

4

10

 

5

15

 

5

15

 

5

15

 

 

 

 

 

 

 

6

15

 

 

(b) limit = 1

                      Pretest loop                                     Posttest loop                           Test-in-the-middle loop

 

number

sum

 

number

sum

 

number

sum

 

0

0

 

0

0

 

0

0

 

1

1

 

1

1

 

1

1

 

2

3

 

2

3

 

2

3

 

 

 

 

 

 

 

3

3

 

 

(c) limit = 0

                      Pretest loop                                     Posttest loop                           Test-in-the-middle loop

 

number

sum

 

number

sum

 

number

sum

 

0

0

 

0

0

 

0

0

 

1

1

 

1

1

 

1

1

 

 

 

 

 

 

 

2

1

 

 

12.

/* sumToN(n) computes the sum 1 + 2 + … + n.

 *

 * Receive: n, an integer value

 * Return:  the value of the sum 1 + 2 + … + n

 */

 

public static int sumToN(int n)

{

  int sum = 0;

 

  for (int i = 1; i <= n; i++)

    sum += i;

 

  return sum;

}

 

 

13.

/* sumMToN(m, n) computes the sum of the integers from m to n.

 *

 * Receive: m and n, two integers

 * Return:  the value of the sum of m to n

 */

 

 public static int sumMToN (int m, int n)

 {

   if (m > n) return 0;   // no integers between m and n

 

   int sum = 0;           // compute sum = m + (m + 1) + ... + n

 

   for (int i = m; i <= n; i++)

     sum += i;

 

   return sum;

 }

 

 

14.

  for (int n = 1; n <= 100; n++)

    theScreen.println((n * n));

 

15.

  for (int n = 50; n > 0; n--)

    theScreen.println((n * n * n));

 

16.

  for (int i = 1; i <= 49; i += 2)

    theScreen.println(Math.sqrt((double)(i)));

 

17.

  for (double x = -2.0; x <= 2.0; x += 0.1)

    theScreen.println("(" + x + ","

                      + (x * x * x - 3 * x + 1) + ")");

 

18.

  for (;;)

  {

    theScreen.println(x);

    x -= 0.5;

    if (x <= 0) break;

  }

 

19.

  for (;;)

  {

    a = theKeyboard.readInt();

    b = theKeyboard.readInt();

    c = theKeyboard.readInt();

    theScreen.println((a + b + c));

    if ( (a < 0) || (b < 0) || (c < 0) ) break;

  }

 

20.

  i = 1;

  for (;;)

  {

    theScreen.println((i * i));

    if ( i * i - (i-1)*(i-1) > 50) break;

    i++;

  }