Problem #1 

  Shown below is an algorithm to evaluate the value of a polynomial p(x). 
  Evaluate the running time of this algorithm, using the "direct evaluation" 
  techniques shown in class. (We used these on insertion sort, merge sort, and 
  quicksort.) Show your work. Justify your answer. 

Let p(x) denote a polynomial of degree n-1, i.e.,  

              n-1
	p(x) = Sum (a_i * x^1), a_(n-1) != 0
              i=1 

Input: A[0..n-1], the array of coefficients, and x the point at which to
evaluate.  The size of the input is the size of the array A (note that some
lower degree coefficients may be 0.) 
Output: The value p(x).



The procedure:

PolyEval(A,x)
  value = a0
  for i=1 to n-1
     term = A[i]
     for j=1 to i
	term = term * x
     value = value + term
  return value