In-Class Examination 2

• Before you answer any questions, write your name and perm number.
• Read each question carefully.  Make sure that you clearly understand each question before answering it.
• Put your answer to each question on its own page.
• Use a pen to write your answer.  You may wish to work out an answer on scratch paper before writing it on your answer page; answers that are difficult to read may lose points for that reason.

1. Let a and b be int variables.  Translate the following nested if/else statement to an equivalent switch statement.   If this cannot be done, explain why.

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        if (a + b < 0)
            c = 1;
        else if (a + b < 1)
            d = 1;
        else if (a + b < 2)
            e = 1;
        else if (a + b < 4)
            f = 1;
        else
            c = 1;


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Solution:
        switch (a + b)
        {
            case 0:
                d = 1;
                break;
            case 1:
                e = 1;
                break;
            case 2: case 3:
                f = 1;
                break;
            default:
                c = 1;
        }

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        for (i = 3; i < n; i++)
        {
            if (i % 2 == 0 )
                continue;
            else if (i % 67 == 0)
                break;
            sum += i;
        }

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Solution:
            i = 3;
        while (i < n && i % 67 != 0)
        {
            if (i % 2 != 0 )
                sum += i;
            i++;
        }

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        c = -1;
    if (a < 0)
        c = 2;
        if (a < 1)
        if (b < 0)
            c = 2;


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Solution:
        if (a < 0 || a < 1 && b < 0)
            c = 2;
        else
            c = -1;

1. (15 points) A prime number is a positive integer such that the only positive integers that evenly divide it are 1 and itself.  The smallest prime is 2.  For example, 3 and 7 are prime numbers; 8 and 9 are not.  Define your own Java method, called prime, that returns true if its int argument, n, is a prime number.   It returns false otherwise.  You may assume that n is positive.  To get full credit, you must make use of the fact that if n is not prime, then there is some integer less than or equal to  the square root of n that evenly divides n.  For example, if n was 121, your method would not check for factors that are greater than 11.
2. (5 points) Using the method called prime whose specification is given above, define your own Java method, called composite,  that returns true if and only if its int argument, n, is not prime.  You may assume that n is positive.

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Solution:
    boolean prime(int n)
    {
        if (n == 2) return true;
        if (n % 2 == 0 || n < 2) return false;
        for (int i = 3; i <= Math.sqrt(n); i += 2)
            if (n % i == 0) return false;
        return true;
    }

    boolean composite(int n) { return !prime(n); }

1. (13 points) Define a method, called elementwiseSum, that has 3 int array parameters, called x, y, and z. The method does not return anything. For every element i of z, it puts the value of the ith element of x plus the value of the ith element of y into the ith element of z.  For a particular ith element of z, if there is no corresponding ith element of x or no ith element of y, then the ith element of z should be set to -1.  Ignore elements of x and/or y for which there is no corresponding element of z.
2. (5 points) Give Java statements to declare an int array, a,  with 100 elements, an int array b with 200 elements, and an int array c with 50 elements.  For every element i of a, set the ith element of a to i.   Set each element of b to a random integer between -10 and 10, inclusive.
3. (1 point) Give a Java statement that invokes method elementwiseSum with arrays a, b, and c.
4. (1 point) Are the values of c changed by invoking elementwiseSum?

Solution:
First part:
   void sum(int a[], int b[], int c[])
   {
       for (int i = 0; i < c.length; i++)
           c[i] = -1;

       for (int i = 0; i < a.length && i < b.length && i < c.length; i++)
           c[i] = a[i] + b[i];
   }
 

Second part:
int a[] = new int[100], b[] = new int[200], c[] = new int[50];

    for (int i = 0; i < a.length; i++)
        a[i] = i;
    for (int i = 0; i < b.length; i++)
        b[i] = (int) (21*Math.random()) - 10;

      Third part:
 sum(a, b, c);
 
      Fourth part:
         The contents of c ARE changed by invoking this method.