CS 205 - Programming for the Sciences
Spring 2008 - Practice Exam 2b Answers

Problem 1

Matrix multiplication

private void multiply_Click(object sender, EventArgs e)
{
    double[,] matrixA = ReadMatrix(matA);
    double[,] matrixB = ReadMatrix(matB);

    // declare and create a result matrix
    double[,] matrixR = new double[MATRIX_SIZE, MATRIX_SIZE];
    for (int i = 0; i < MATRIX_SIZE; i++)
        for (int j = 0; j < MATRIX_SIZE; j++)
        {
            // for each element of result matrix, compute a sum
            double sum = 0;
            for (int k = 0; k < MATRIX_SIZE; k++)
                sum = sum + matrixA[i, k] * matrixB[k, j];
            // set result matrix element
            matrixR[i, j] = sum;
        }

    // "copy" result matrix into the matResult grid of textboxes
    for (int row = 0; row < MATRIX_SIZE; row++)
        for (int col = 0; col < MATRIX_SIZE; col++)
            matResult[row, col].Text = matrixR[row, col].ToString();
}

Problem 2

Sieve of Eratosthenes

private void calc_primes_Click(object sender, EventArgs e)
{
    int upper = Convert.ToInt32(upperBound.Text);

    // declare and create an array to indicate if i is a prime number
    // we will ignore primes[0] and primes[1]
    bool [] primes = new bool[upper];

    // initialize the array elements to true starting with 2
    for (int n = 2; n < upper; n++)
        primes[n] = true;

    // start at 2, "cross out" the multiples of prime numbers
    // until the square of i is greater than or equal to upper
    int i = 2;
    while (i*i < upper)
    {
        if (primes[i])  // i is a prime
        {
            // "cross out" the multiples of i
            // start at j at the next multiple of i (i*2)
            // and increment j by i
            for (int j = i * 2; j < upper; j = j + i)
                primes[j] = false;
        }
        i++;  // look at next number
    }
    // print only the true ones
    results.Items.Add("The prime numbers less than " + upper);
    for (i = 2; i < upper; i++)
        if (primes[i])
            results.Items.Add(i);
}