Given a sequence of values a1, . . , an give an algorithm that finds the coefficients of the polynomial p(x) of degree n such that p(x) = 0 if and only if x = ai for some i. you can assume the elements ai are distinct. your algorithm should run in time o(n log2 n).

Assume you need to test a function named inorder. the function inorder receives three int arguments and returns true if and only if the arguments are in non-decreasing order: that is, the second argument is not < the first and the third is not < the second. write the definition of driver function testinorder whose job it is to determine whether inorder is correct. so testinorder returns true if inorder is correct and returns false otherwise. for the purposes of this exercise, assume inorder is an expensive function call, so call it as few times as possible!