Returns the coefficient for the term of order k. For example, the term of order 3 in the previous polynomial equals 5, whereas the term of order 0 equals 42. This method should work correctly even when k is negative or greater than the actual degree of the polynomial, and simply return zero for such nonexistent terms.

Calculate the decision parameter of Bresenham's circle drawing method, p. The algorithm for drawing circles by Bresenham is given in stages.

Write a procedure sum-range (from to) for finding the sum of integers in the range from to to, inclusive. Make sure that (sum-range 4 18), (sum-range 18 4), and (sum-range 7 7) all give the expected result. Note that this function should be able to count up or count down depending on the order of the paramaters. So, (sum-range 4 18) and (sum-range 18 4) should give the same result. (sum-range 7 7) should return 7. (Dr.Racket)

Solve the following recurrences using iteration methods and Master's Theorem (if possible) a. T(n) = 2T (n/3) +3 b. T(n) = 3T (n/6) + n

Consider the following version of Horner's method which computes a polynomial with coefficients a1, a2, ..., an and variable k. Example:     acc = 1   for i = 1 to n     acc *= k     acc += a[ i ]   return acc Determine precisely what polynomial is being computed and answer the following questions about it.What is the degree (ie, k's exponent) of the lowest-degree term? A. N+1 B. N-1 C. N D. 0 E. 1

Consider the following version of Horner's method which computes a polynomial with coefficients a1, a2, ..., an and variable k. Example:     acc = 1   for i = 1 to n     acc *= k     acc += a[ i ]   return acc Determine precisely what polynomial is being computed and answer the following questions about it. What is the coefficient of the highest-degree term? A.A[0] B. 0 C. A[1] D. 1

Prove that: The sum of an even integer and an odd integer is odd, where both numbers are > 0. Write out all steps of your proof.

An evil king has n bottles of wine, and a spy has just poisoned one of them. Unfortunately, they do not know which one it is. The poison is very deadly; just one drop diluted even a billion to one will still kill. Even so, it takes a full month for the poison to take effect. Design a scheme for determining exactly which one of the wine bottles was poisoned in just one month’s time while expending O(log n) taste testers.

Expand the following recurrence to help you find a closed-form solution, and then use induction to prove your answer is correct. T(n) = √nT(√n) + n, for n>2; T(2) = 1.