Write a program that takes a command-line argument n and creates an n-by-n boolean matrix...

Write a program that takes a command-line argument n and creates an n-by-n boolean matrix with the element in row i and column j set to true if i and j are relatively prime, then shows the matrix on the standard drawing (see EXERCISE 1.4.16). Then, write a similar program to draw the Hadamard matrix of order n (see EXERCISE 1.4.29). Finally, write a program to draw the boolean matrix such that the element in row n and column j is set to true if the coefficient of xj in (1 + x)i (binomial coefficient) is odd (see EXERCISE 1.4.41). You may be surprised at the pattern formed by the third example.

EXERCISE 1.4.16

Write a program that takes an integer command-line argument n and creates an n-by-n boolean array a[] [] such that a[i] [j] is true if i and j are relatively prime (have no common factors), and false otherwise. Use your solution to EXERCISE 1.4.6 to print the array. Hint: Use sieving.

EXERCISE 1.4.6

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 indices.

EXERCISE 1.4.41

Binomial coefficients. Write a program that takes an integer command-line argument n and creates a two-dimensional ragged array a[] [] such that a[n] [k] contains the probability that you get exactly k heads when you toss a fair coin n times. These numbers are known as the binomial distribution: if you multiply each element in row i by 2n, you get the binomial coefficients—the coefficients of xk in (x+1)n—arranged in Pascal’s triangle. To compute them, start with a [n] [0] = 0.0 for all n and a[l] [1] = 1.0, then compute values in successive rows, left to right, with a[n][k] = (a[n-l] [k] + a[n-l] [k-1]) / 2.0.