1. Give ef?cient algorithms (along with running time analyses) to
a. Find the minimum subsequence sum.
b. Find the minimum positive subsequence sum.
c. Find the maximum subsequence product.
2. An important problem in numerical analysis is to ?nd a solution to the equation f (X) = 0 for some arbitrary f . If the function is continuous and has two points low and high such that f (low) and f (high) have opposite signs, then a root must exist between low and high and can be found by a binary search. Write a function that takes as parameters f , low, and high and solves for a zero. What must you do to ensure termination?