1. You can enhance polynomial evaluation algorithm by avoiding computing x^k repeatedly. For instance, x^3 is again computed when it finds x^4. Horner's polynomial algorithm is one example which avoids that. Write another polynomial estimation algorithm which avoids such inefficiency.
2. (a) Write the algorithm which adds the sequence of integers from 1 to n. For instance, for n = 5, an algorithm will do: 1 + 2 + 3 + 4 + 5 = 15. Utilize a_k for k-th integer. You may utilize while ... endwhile statement.
(b) Determine complexity of the algorithm.
(c) Compute the constant C and the function f(n) such that complexity function you found in (b) is less than or equal to Cf(n). Therefore, the algorithm has order no more than f(n).