From the book
EXERCISES
From the book
From the book
From the book
EXERCISES
- Give the value of each of the following expressions:
- ( 0 + 15 ) / 2
- 2.0e-6 * 100000000.1
- true && false || true && true
- Give the type and value of each of the following expressions:
- (1 + 2.236)/2
- 1 + 2 + 3 + 4.0
- 4.1 >= 4
- 1 + 2 + "3"
- Write a program that takes three integer command-line arguments and prints equal if all three are equal, and not equal otherwise.
- What (if anything) is wrong with each of the following statements?
- if (a > b) then c = 0;
- if a > b { c = 0; }
- if (a > b) c = 0;
- if (a > b) c = 0 else b = 0;
- Write a code fragment that prints true if the double variables x and y are both strictly between 0 and 1 and false otherwise.
- What does the following program print?
- Give the value printed by each of the following code fragments:
double t = 9.0; while (Math.abs(t - 9.0/t) > .001) t = (9.0/t + t) / 2.0; StdOut.printf("%.5f\n", t);int sum = 0; for (int i = 1; i < 1000; i++) for (int j = 0; j < i; j++) sum++; StdOut.println(sum);int sum = 0; for (int i = 1; i < 1000; i *= 2) for (int j = 0; j < 1000; j++) sum++; StdOut.println(sum);- What do each of the following print?
- System.out.println('b');
- System.out.println('b' + 'c');
- System.out.println((char) ('a' + 4));
- Write a code fragment that puts the binary representation of a positive integer N into a String s.
- What is wrong with the following code fragment?
- Write a code fragment that prints the contents of a two-dimensional boolean array, using * to represent true and a space to represent false. Include row and column numbers.
- What does the following code fragment print?
- Write a code fragment to print the transposition (rows and columns changed) of a two-dimensional array with M rows and N columns.
- Write a static method lg() that takes an int value N as argument and returns the largest int not larger than the base-2 logarithm of N. Do not use Math.
- Write a static method histogram() that takes an array a[] of int values and an integer M as arguments and returns an array of length M whose ith entry is the number of times the integer i appeared in the argument array. If the values in a[] are all between 0 and M–1, the sum of the values in the returned array should be equal to a.length.
- Give the value of exR1(6):
- Criticize the following recursive function:
- Consider the following recursive function:
- Run the following program on your computer:
- Write a recursive static method that computes the value of ln (N !)
- Write a program that reads in lines from standard input with each line containing a name and two integers and then uses printf() to print a table with a column of the names, the integers, and the result of dividing the first by the second, accurate to three decimal places. You could use a program like this to tabulate batting averages for baseball players or grades for students.
- Write a version of BinarySearch that uses the recursive rank() given on page 25 and traces the method calls. Each time the recursive method is called, print the argument values lo and hi, indented by the depth of the recursion. Hint: Add an argument to the recursive method that keeps track of the depth.
- Add to the BinarySearch test client the ability to respond to a second argument: + to print numbers from standard input that are not in the whitelist, - to print numbers that are in the whitelist.
- Give the sequence of values of p and q that are computed when Euclid’s algorithm is used to compute the greatest common divisor of 105 and 24. Extend the code given on page 4 to develop a program Euclid that takes two integers from the command line and computes their greatest common divisor, printing out the two arguments for each call on the recursive method. Use your program to compute the greatest common divisor or 1111111 and 1234567.
- Use mathematical induction to prove that Euclid’s algorithm computes the greatest common divisor of any pair of nonnegative integers p and q.
int f = 0;
int g = 1;
for (int i = 0; i <= 15; i++)
{
StdOut.println(f);
f = f + g;
g = f - g;
}
Explain each outcome.
Solution: Java has a built-in method Integer.toBinaryString(N) for this job, but the point of the exercise is to see how such a method might be implemented. Here is a particularly concise solution:
String s = ""; for (int n = N; n > 0; n /= 2) s = (n % 2) + s;
int[] a; for (int i = 0; i < 10; i++) a[i] = i * i;
Solution: It does not allocate memory for a[] with new. This code results in a variable a might not have been initialized compile-time error.
int[] a = new int[10]; for (int i = 0; i < 10; i++) a[i] = 9 - i; for (int i = 0; i < 10; i++) a[i] = a[a[i]]; for (int i = 0; i < 10; i++) System.out.println(i);
public static String exR1(int n)
{
if (n <= 0) return "";
return exR1(n-3) + n + exR1(n-2) + n;
}
public static String exR2(int n)
{
String s = exR2(n-3) + n + exR2(n-2) + n;
if (n <= 0) return "";
return s;
}
Answer: The base case will never be reached. A call to exR2(3) will result in calls to exR2(0), exR2(-3), exR3(-6), and so forth until a StackOverflowError occurs.
public static int mystery(int a, int b)
{
if (b == 0) return 0;
if (b % 2 == 0) return mystery(a+a, b/2);
return mystery(a+a, b/2) + a;
}
What are the values of mystery(2, 25) and mystery(3, 11)? Given positive integers a and b, describe what value mystery(a, b) computes. Answer the same question, but replace + with * and replace return 0 with return 1.
public class Fibonacci
{
public static long F(int N)
{
if (N == 0) return 0;
if (N == 1) return 1;
return F(N-1) + F(N-2);
}
public static void main(String[] args)
{
for (int N = 0; N < 100; N++)
StdOut.println(N + " " + F(N));
}
}
What is the largest value of N for which this program takes less 1 hour to compute the value of F(N)? Develop a better implementation of F(N) that saves computed values in an array.