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void shuffle(Object[] a) { Random random = new Random(); int n = a.length; for (int i = 0; i < n; i++) { ch02.pr10.TestReverse.swap(a,i,random.nextInt(a.length)); } } int[] tally(String s) { int[] frequency = new int[26]; for (int i = 0; i < s.length(); i++) { char ch = Character.toUpperCase(s.charAt(i)); if (Character.isLetter(ch)) { ++frequency[(int)ch - (int)'A']; // count ch } return frequency; } double innerProduct(double[] x, double[] y) { double sum = 0.0; for (int i = 0; i < x.length && i < y.length; i++) sum += x[i]*y[i]; return sum; } double[][] outerProduct(double[] x, double[] y) { double[][] z = new double[x.length][y.length]; for (double xi : x) { for (double yj : y) { z[i][j] = xi*yj; } } return z; } double[][] product(double[][] x, double[][] y) { double[][] z = new double[x.length][y[0].length]; for (int i = 0; i < x.length; i++) { for (int j = 0; j < y[0].length; j++) { double sum = 0.0; for (int k = 0; k < x[0].length; k++) { sum += x[i][k]*y[k][j]; } z[i][j] = sum; } } return z; } double[][] transpose(double[][] x) { double[][] y = new double[x[0].length][x.length]; for (int i = 0; i < x[0].length; i++) { for (int j = 0; j < x.length; j++) { y[i][j] = x[j][i]; } } return y; }

CHAP. 2]

int[][] pascal(int n) { int[][] p = new int[n][n]; for (int j = 0; j < n; j++) { p[j][0] = p[j][j] = 1; } for (int i = 2; i < n; i++) { for (int j = 1; j < i; j++) { p[i][j] = p[i-1][j-1] + p[i-1][j]; } } return p; } public class TestSieve { private static final int SIZE=1000; private static boolean[] isPrime = new boolean[SIZE]; public static void main(String[] args) { initializeSieve(); printSieve(); } private static void initializeSieve() { for (int i = 2; i < SIZE; i++) { isPrime[i] = true; } for (int n = 2; 2*n < SIZE; n++) { if (isPrime[n]) { for (int m = n; m*n <SIZE; m++) { isPrime[m*n] = false; } } } } private static void printSieve() int n=0; for (int i = 0; i < SIZE; i++) if (isPrime[i]) { System.out.printf("%5d%s", } } System.out.printf("%n%d primes } } { { i, ++n%16==0 "\n":"");

Since a monopoly produces output where MR = MC and P > MR, the monopolist produces less and charges a higher price than a perfect competitor with the same cost curves. For example, if Figure 14-1 was for a perfectly competitive industry, output would be 3 units and price $5 (given where P = MC), rather than Q = 2.5 and P = $5.50 for the monopolist. Thus, monopoly leads to a misallocation of resources. For ef ciency considerations, government (federal, state, or local) often allows natural monopolies (such as public utilities) to operate but subjects them to regulation. This usually takes the form of setting a price that allows the monopolist to earn the normal or fair return of about 8 10 percent on its investment. However, such regulation only partly corrects the more serious problem of misallocation of resources.

less than %d%n", n, SIZE);

public class TestSieve { private static final int SIZE=1000; private static Vector<Boolean> isPrime = new Vector<Boolean>(SIZE); public static void main(String[] args) { initializeSieve(); printSieve(); } private static void initializeSieve() { isPrime.add(false); // 0 is not prime isPrime.add(false); // 1 is not prime for (int i = 2; i < SIZE; i++) { isPrime.add(true); }