using System.Diagnostics;

namespace Lab_5
{

    public class Program
    {
        //Sequential multiplication of two polynomials

        //O(n^2)
        public static List<int> PolynomialMultiplication(List<int> poly1, List<int> poly2)
        {

            int m = poly1.Count;
            int n = poly2.Count;
            List<int> result = new List<int>(new int[m + n - 1]);

            for (int i = 0; i < m; i++)
            {
                for (int j = 0; j < n; j++)
                {
                    result[i + j] += poly1[i] * poly2[j];
                }
            }

            return result;

        }

        //Karatsuba algorithm for polynomial multiplication

        public static List<int> AddPolynomials(List<int> poly1, List<int> poly2)
        {
            int maxLength = Math.Max(poly1.Count, poly2.Count);
            List<int> result = new List<int>(new int[maxLength]);

            for (int i = 0; i < maxLength; i++)
            {
                int coef1 = i < poly1.Count ? poly1[i] : 0;
                int coef2 = i < poly2.Count ? poly2[i] : 0;
                result[i] = coef1 + coef2;
            }

            return result;
        }

        public static List<int> SubtractPolynomials(List<int> poly1, List<int> poly2)
        {
            int maxLength = Math.Max(poly1.Count, poly2.Count);
            List<int> result = new List<int>(new int[maxLength]);

            for (int i = 0; i < maxLength; i++)
            {
                int coef1 = i < poly1.Count ? poly1[i] : 0;
                int coef2 = i < poly2.Count ? poly2[i] : 0;
                result[i] = coef1 - coef2;
            }

            return result;
        }

        public static List<int> Karatsuba(List<int> poly1, List<int> poly2)
        {
            int n = Math.Max(poly1.Count, poly2.Count);

            if (n == 1)
            {
                return new List<int> { poly1[0] * poly2[0] };
            }

            while (poly1.Count < n) poly1.Add(0);
            while (poly2.Count < n) poly2.Add(0);

            int half = n / 2;

            List<int> low1 = poly1.GetRange(0, half);
            List<int> high1 = poly1.GetRange(half, n - half);
            List<int> low2 = poly2.GetRange(0, half);
            List<int> high2 = poly2.GetRange(half, n - half);

            List<int> z0 = Karatsuba(low1, low2);
            List<int> z1 = Karatsuba(AddPolynomials(low1, high1), AddPolynomials(low2, high2));
            List<int> z2 = Karatsuba(high1, high2);

            List<int> result = new List<int>(new int[2 * n - 1]);

            for (int i = 0; i < z0.Count; i++) result[i] += z0[i];

            List<int> middle = SubtractPolynomials(SubtractPolynomials(z1, z0), z2);
            for (int i = 0; i < middle.Count; i++) result[i + half] += middle[i];

            for (int i = 0; i < z2.Count; i++) result[i + 2 * half] += z2[i];

            return result;
        }

        //Parallel multiplication of two polynomials

        //O(n^2)
        public static List<int> ParallelPolynomialMultiplication(List<int> poly1, List<int> poly2)
        {
            int m = poly1.Count;
            int n = poly2.Count;
            List<int> result = new List<int>(new int[m + n - 1]);

            Parallel.For(0, m, i =>
            {
                for (int j = 0; j < n; j++)
                {
                    result[i + j] += poly1[i] * poly2[j];
                }
            });

            return result;
        }

        //Karatsuba algorithm for polynomial multiplication

        public static List<int> ParallelKaratsuba(List<int> poly1, List<int> poly2)
        {
            int n = Math.Max(poly1.Count, poly2.Count);

            if (n == 1)
            {
                return new List<int> { poly1[0] * poly2[0] };
            }

            while (poly1.Count < n) poly1.Add(0);
            while (poly2.Count < n) poly2.Add(0);

            int half = n / 2;

            List<int> low1 = poly1.GetRange(0, half);
            List<int> high1 = poly1.GetRange(half, n - half);
            List<int> low2 = poly2.GetRange(0, half);
            List<int> high2 = poly2.GetRange(half, n - half);

            List<int> z0 = [], z1 = [], z2 = [];

            Parallel.Invoke(
               () => z0 = ParallelKaratsuba(low1, low2),
               () => z1 = ParallelKaratsuba(AddPolynomials(low1, high1), AddPolynomials(low2, high2)),
               () => z2 = ParallelKaratsuba(high1, high2)
            );

            List<int> result = new List<int>(new int[2 * n - 1]);

            for (int i = 0; i < z0.Count; i++) result[i] += z0[i];

            List<int> middle = SubtractPolynomials(SubtractPolynomials(z1, z0), z2);
            for (int i = 0; i < middle.Count; i++) result[i + half] += middle[i];

            for (int i = 0; i < z2.Count; i++) result[i + 2 * half] += z2[i];

            return result;
        }


        public static void Main(string[] args)
        {
            int degree = 999;
            Random random = new Random();

            // Generate Polynomial 1
            List<int> poly1 = new List<int>();
            for (int i = 0; i <= degree; i++)
            {
                poly1.Add(random.Next(-100, 101));
            }

            // Generate Polynomial 2
            List<int> poly2 = new List<int>();
            for (int i = 0; i <= degree; i++)
            {
                poly2.Add(random.Next(-100, 101));
            }
            //Console.WriteLine("Polynomial 1: " + string.Join(" ", poly1));
            //Console.WriteLine("Polynomial 2: " + string.Join(" ", poly2));
            Stopwatch timer = new Stopwatch();
            timer.Start();
            List<int> result = PolynomialMultiplication(poly1, poly2);
            timer.Stop();
            //Console.WriteLine("Result O(n) sequencial: " + string.Join(" ", result));
            Console.WriteLine("Time: " + timer.ElapsedMilliseconds + "ms");
            timer.Start();
            result = Karatsuba(poly1, poly2);
            timer.Stop();
            //Console.WriteLine("Result Karatsuba sequencial: " + string.Join(" ", result));
            Console.WriteLine("Time: " + timer.ElapsedMilliseconds + "ms");
            timer.Start();
            result = ParallelPolynomialMultiplication(poly1, poly2);
            timer.Stop();
            //Console.WriteLine("Result O(n) parallel: " + string.Join(" ", result));
            Console.WriteLine("Time: " + timer.ElapsedMilliseconds + "ms");
            timer.Start();
            result = ParallelKaratsuba(poly1, poly2);
            timer.Stop();
            //Console.WriteLine("Result Karatsuba parallel: " + string.Join(" ", result));
            Console.WriteLine("Time: " + timer.ElapsedMilliseconds + "ms");
        }
    }
}