Programming Task 1: Hello Polynomial World

• You are working in teams of four (two sets of partners). This will require workplace-style maturity.
• These tasks will test your ability to put notions into practice within a team setting.
• Submit your teams' working code to andy at novocin.com prior to your scheduled review.
• I will run the code on real inputs using ideone.com with the C++11 environment.
• Presentation day will consist of a scheduled 45 minute meeting.
• At that meeting I will run the code.
• I will select one person from your team using a random integer, that person will explain the code and answer my questions.
• I will assign a grade that day for all of you based on the randomly selected team member's explanation.
• It is your responsibility to make sure that everyone on your team understands the concepts behind your solution.
• Coding in C++ is a soft requirement of the course, this method allows the coding aspects of the project to be spread while ensuring some practical awareness.

The Programming tasks for this assignment:

1. Input: Two polynomials, one per line, each with format:

   
         n  c1 c2 ... cn
         

   The input will come from stdin. Here n is the length of the polynomial and it is followed by n integers which are the coefficients of the polynomial. Note that c1 is the constant coefficient (i.e. coefficient of \(x^0\) ).
   
   Output: The product of the two input polynomials, displayed to stdout, in the format:
   

   c1*x^0 + c2*x^1 + c3*x^2 + \( \cdots \) + cm*x^m

   Here m is the integer degree of the output polynomial. While ci is the \( i^{\textrm{th}} \) coefficient of the product (i.e. the coefficient of \( x^{i-1} \) ).

   
   
   Constraints: Each input polynomial will have length at least 1 and at most 100. All coefficients will be between -100 and 100, inclusive. Your algorithm must have \( \mathcal{O}(n^2) \) arithmetic operations, where \( n \) is the maximum input length. You may assume that all coefficients of the output will fit into an int.
   
   Sample instance:
   Input:

   
         4  -1 0 0 1
         4  1 0 0 1
         

   Output:

   
         -1*x^0 + 0*x^1 + 0*x^2 + 0*x^3 + 0*x^4 + 0*x^5 + 1*x^6
         

2. Input: The same as above, two polynomials given as an integer length and a space followed by that many space-separated coefficients, one polynomial per line.
   
   Output: The product of the two polynomials, evaluated at 1, i.e. let \( P(x) = f(x) g(x) \) where \(f, g\) are your input polynomials then your goal is to display \( P(1) \). This will be an integer which should be displayed to stdout.
   
   Constraints: Each input polynomial will have length at least 1 and at most 100. All coefficients will be between -100 and 100, inclusive. Your algorithm must have only \( \mathcal{O}(n) \) arithmetic operations, where \( n \) is the maximum input length.
   
   Sample instance:
   Input:

   
         4  -100 2 3 99
         2  1 -2
         

   
   
   Output:

   
         -4
         

3. Input: The length of two special polynomials, on one line, separated by a space, i.e.

   
         n1 n2
         

   Here the special polynomials are of the form   \( f_n (x) = 1 + 2x + 3x^2 + \cdots + nx^{n-1} \). So if the input was 5 2 then the two polynomials would be \( 1 + 2x + 3x^2 + 4x^3 + 5x^4 \) and \( 1 + 2x \).
   
   Output: The product of the two polynomials, evaluated at 1, i.e. \(P(1)\) where \(P(x) = f_{n1}(x) \cdot f_{n2}(x) \). This will be an integer which should be displayed to stdout.
   
   Constraints: The inputs will be two numbers between 1 and 10000, inclusive. Your algorithms must use only \(\mathcal{O}(1) \) arithmetic operations, regardless of the input size.
   
   Sample instance:
   Input:

   
         5 8
         

   
   
   Output:

   
         540
         

Help

A sample environment is available at this IDEONE snippet. It happens to return the correct result for one input. A real algorithm will actually compute something.