COSC5313 Program-1 Due: 2/13/2013 Rook Polynomial Computation Task: Write a well-structured and well-documented program that does the following: 1. Read a set of inputs arranged as follows: The size of the Board (Row-size and Column-size) The number of available squares, and All available squares. 2. Compute the Rook Polynomial and 3. Print out the input board and the resulting Rook polynomial. Output Reuirements: 1. Each input board will be printed out with each available square marked with an "X" 2. The resulting Rook Polynomial will be printed as follows: The Degree of the polynomial followed by the coefficients of all the terms in ascending order of powers. Extra Credits: For an extra bonus of up to 10 points, you can use the Complementary Reduction method if the input board has overwhelmingly many available squares like the second input case given below. INPUTS: Use the following two input cases: Case-1: 5 5 6 // The board is 5-by-5 with 6 available squares 1 3 1 4 2 4 3 2 3 5 5 5 Case-2: 5 5 19 // The board is 5-by-5 with 19 available squares 1 1 1 2 1 5 2 1 2 2 2 3 2 5 3 1 3 3 3 4 4 1 4 2 4 3 4 4 4 5 5 1 5 2 5 3 5 4