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## Exercises

• 2.1.1 Write a static method max3() that takes three int arguments and returns the value of the largest one. Add an overloaded function that does the same thing with three double values.

• 2.1.2 Write a static method odd() that takes three boolean arguments and returns true if an odd number of the argument values are true, and false otherwise.

• 2.1.3 Write a static method majority() that takes three boolean arguments and returns true if at least two of the argument values are true, and false otherwise. Do not use an if statement.

• 2.1.4 Write a static method eq() that takes two int arrays as arguments and returns true if the arrays have the same length and all corresponding pairs of of elements are equal, and false otherwise.

• 2.1.5 Write a static method areTriangular() that takes three double arguments and returns true if they could be the sides of a triangle (none of them is greater than or equal to the sum of the other two). See EXERCISE 1.2.15.

• 2.1.6 Write a static method sigmoid() that takes a double argument x and returns the double value obtained from the formula 1 / (1 + ex).

• 2.1.7 Write a static method sqrt() that takes a double argument and returns the square root of that number. Use Newton’s method (see PROGRAM 1.3.6) to compute the result.

• 2.1.8 Give the function-call trace for java Harmonic 3 5

• 2.1.9 Write a static method lg() that takes a double argument n and returns the base-2 logarithm of n. You may use Java’s Math library.

• 2.1.10 Write a static method lg() that takes an int argument n and returns the largest integer not larger than the base-2 logarithm of n. Do not use the Math library.

• 2.1.11 Write a static method signum() that takes an int argument n and returns -1 if n is less than 0, 0 if n is equal to 0, and +1 if n is greater than 0.

• 2.1.12 Consider the static method duplicate() below.

`public static String duplicate(String s){   String t = s + s;   return t;}`

What does the following code fragment do?

`String s = "Hello";s = duplicate(s);String t = "Bye";t = duplicate(duplicate(duplicate(t)));StdOut.println(s + t);`
• 2.1.13 Consider the static method cube() below.

`public static void cube(int i){   i = i * i * i;}`

How many times is the following for loop iterated?

`for (int i = 0; i < 1000; i++)   cube(i);`

Answer: Just 1,000 times. A call to cube() has no effect on the client code. It changes the value of its local parameter variable i, but that change has no effect on the i in the for loop, which is a different variable. If you replace the call to cube(i) with the statement i = i * i * i; (maybe that was what you were thinking), then the loop is iterated five times, with i taking on the values 0, 1, 2, 9, and 730 at the beginning of the five iterations.

• 2.1.14 The following checksum formula is widely used by banks and credit card companies to validate legal account numbers:

d0 + f (d1) + d2 + f (d3) + d4 + f (d5) + ... = 0 (mod 10)

The di are the decimal digits of the account number and f (d) is the sum of the decimal digits of 2d (for example, f (7) = 5 because 2 × 7 = 14 and 1 + 4 = 5). For example, 17,327 is valid because 1 + 5 + 3 + 4 + 7 = 20, which is a multiple of 10. Implement the function f and write a program to take a 10-digit integer as a command-line argument and print a valid 11-digit number with the given integer as its first 10 digits and the checksum as the last digit.

• 2.1.15 Given two stars with angles of declination and right ascension (d1, a1) and (d2, a2), the angle they subtend is given by the formula

2 arcsin((sin2(d/2) + cos (d1)cos(d2)sin2(a/2))1/2)

where a1 and a2 are angles between –180 and 180 degrees, d1 and d2 are angles between –90 and 90 degrees, a = a2a1, and d = d2d1. Write a program to take the declination and right ascension of two stars as command-line arguments and print the angle they subtend. Hint: Be careful about converting from degrees to radians.

• 2.1.16 Write a static method scale() that takes a double array as its argument and has the side effect of scaling the array so that each element is between 0 and 1 (by subtracting the minimum value from each element and then dividing each element by the difference between the minimum and maximum values). Use the max() method defined in the table in the text, and write and use a matching min() method.

• 2.1.17 Write a static method reverse() that takes an array of strings as its argument and returns a new array with the strings in reverse order. (Do not change the order of the strings in the argument array.) Write a static method reverseInplace() that takes an array of strings as its argument and produces the side effect of reversing the order of the strings in the argument array.

• 2.1.18 Write a static method readBoolean2D() that reads a two-dimensional boolean matrix (with dimensions) from standard input and returns the resulting two-dimensional array.

• 2.1.19 Write a static method histogram() that takes an int array a[] and an integer m as arguments and returns an array of length m whose ith element is the number of times the integer i appeared in a[]. Assuming the values in a[] are all between 0 and m-1, the sum of the values in the returned array should equal a.length.

• 2.1.20 Assemble code fragments in this section and in SECTION 1.4 to develop a program that takes an integer command-line argument n and prints n five-card hands, separated by blank lines, drawn from a randomly shuffled card deck, one card per line using card names like Ace of Clubs.

• 2.1.21 Write a static method multiply() that takes two square matrices of the same dimension as arguments and produces their product (another square matrix of that same dimension). Extra credit: Make your program work whenever the number of columns in the first matrix is equal to the number of rows in the second matrix.

• 2.1.22 Write a static method any() that takes a boolean array as its argument and returns true if any of the elements in the array is true, and false otherwise. Write a static method all() that takes an array of boolean values as its argument and returns true if all of the elements in the array are true, and false otherwise.

• 2.1.23 Develop a version of getCoupon() that better models the situation when one of the coupons is rare: choose one of the n values at random, return that value with probability 1 /(1,000n), and return all other values with equal probability. Extra credit: How does this change affect the expected number of coupons that need to be collected in the coupon collector problem?

• 2.1.24 Modify PlayThatTune to add harmonics two octaves away from each note, with half the weight of the one-octave harmonics.