using System;
using System.Collections.Generic;
using System.Linq;

namespace magicSquare
{
	internal class SquareMatrix
	{
		public int Size { get; private set; }
		private int SizeSize { get; set; }
		public int MagicSum { get; private set; }

		private int[,] Values { get; set; }

		private int[] ColumnSums { get; set; }
		private int[] RowSums { get; set; }
		public int Diag1Sum { get; private set; }
		public int Diag2Sum { get; private set; }

		private int[] ColumnDeltas { get; set; }
		private int[] RowDeltas { get;  set; }
		public int Diag1Delta { get; private set; }
		public int Diag2Delta { get; private set; }

		public SquareMatrix(int[,] values)
		{
			if (values.GetLength(0) != values.GetLength(1))
				throw new ArgumentException("must be square matrix");

			Values = values;
			Size = values.GetLength(0);
			SizeSize = Size * Size;
			MagicSum = (Size * (SizeSize + 1)) / 2;

			ColumnSums = (from col in Enumerable.Range(0, Size)
						  let sum = (from row in Enumerable.Range(0, Size)
									 select Values[row, col]).Sum()
						  select sum).ToArray();
			RowSums = (from row in Enumerable.Range(0, Size)
					   let sum = (from col in Enumerable.Range(0, Size)
								  select Values[row, col]).Sum()
					   select sum).ToArray();
			Diag1Sum = (from i in Enumerable.Range(0, Size)
						select Values[i, i]).Sum();
			Diag2Sum = (from i in Enumerable.Range(0, Size)
						select Values[Size - 1 - i, i]).Sum();

			ColumnDeltas = (from col in Enumerable.Range(0, Size)
							select ColumnSums[col] - MagicSum).ToArray();
			RowDeltas = (from row in Enumerable.Range(0, Size)
						 select RowSums[row] - MagicSum).ToArray();
			Diag1Delta = Diag1Sum - MagicSum;
			Diag2Delta = Diag2Sum - MagicSum;
		}

		public IEnumerable<Tuple<int, int>> MaxColumnDeltaPairs()
		{
			return MaxDeltaPairs(ColumnDeltas, Size);
		}

		public IEnumerable<Tuple<int, int>> MaxRowDeltaPairs()
		{
			return MaxDeltaPairs(RowDeltas, Size);
		}

		public Tuple<int, int> FindValueCoord(int values)
		{
			return (
				       from row in Enumerable.Range(0, Size)
				       from col in Enumerable.Range(0, Size)
				       where Values[row, col] == values
				       let coord = new Tuple<int, int>(row, col)
				       select coord).First();
		}

		public void SolveDiags()
		{
			var middleNumber = (SizeSize + 1)/2;
			var diag1Values = Enumerable.Range(middleNumber - (Size - 1)/2, Size);

		}

		private static IEnumerable<Tuple<int, int>> MaxDeltaPairs(int[] deltas, int size)
		{
			const int limit = 4;
			var deltaIs = (from i in Enumerable.Range(0, size)
			                  select new Tuple<int, int>(i, deltas[i])).ToList();

			var lows = deltaIs.OrderBy(tuple => tuple.Item2).Take(limit);
			var highs = deltaIs.OrderByDescending(tuple => tuple.Item2).Take(limit);

			var pairs =
				from lo in lows
				from hi in highs
				 where lo.Item1 != hi.Item1
				 let pair = new Tuple<Tuple<int, int>, Tuple<int, int>>(lo, hi)
				 select pair;
			return
				pairs
				.OrderBy(pair => Math.Abs(pair.Item1.Item2 + pair.Item2.Item2))
				.Select(pair => new Tuple<int,int>(pair.Item1.Item1, pair.Item2.Item1));
		}

		public static bool IsDiagonal(int i, int j, int size)
		{
			return i == j || size - 1 - j == i;
		}

		public bool IsDiagonal(int i, int j)
		{
			return i == j || Size - 1 - j == i;
		}

		public bool IsDiagonal(Tuple<int,int> tpl)
		{
			return IsDiagonal(tpl.Item1, tpl.Item2);
		}

		public bool IsFeasible()
		{
			return Diag1Sum == MagicSum &&
			       Diag2Sum == MagicSum &&
			       ColumnSums.All(s => s == MagicSum) &&
			       RowSums.All(s => s == MagicSum);
		}

		public int GetValue(int row, int col)
		{
			return Values[row,col];
		}

		public int ColumnSum(int col)
		{
			return ColumnSums[col];
		}

		public int RowSum(int row)
		{
			return RowSums[row];
		}

		public int ColumnDelta(int col)
		{
			return ColumnDeltas[col];
		}

		public int RowDelta(int row)
		{
			return RowDeltas[row];
		}

		private void UpdateValue(int row, int col, int value)
		{
			// update sums
			var delta = value - Values[row, col];
			Values[row, col] = value;
			if (row == col)
			{
				Diag1Sum += delta;
				Diag1Delta += delta;
			}
			if (col == Size - 1 - row)
			{
				Diag2Sum += delta;
				Diag2Delta += delta;;
			}
			ColumnSums[col] += delta;
			ColumnDeltas[col] += delta;
			RowSums[row] += delta;
			RowDeltas[row] += delta;
		}

		private int AbsDelta(int row, int col)
		{
			return Math.Abs(RowDeltas[row]) + Math.Abs(ColumnDeltas[col]);
		}

		public int AbsDeltaDiff(int row1, int col1, int row2, int col2)
		{
			var v1 = Values[row1, col1];
			var v2 = Values[row2, col2];

			return Math.Abs(v1 - v2);
		}

		public int AbsDeltaDiff(Tuple<int, int> coord1, Tuple<int, int> coord2)
		{
			return AbsDeltaDiff(coord1.Item1, coord1.Item2, coord2.Item1, coord2.Item2);
		}

		public void Swap(Tuple<int, int> coord1, Tuple<int, int> coord2)
		{
			Swap(coord1.Item1, coord1.Item2, coord2.Item1, coord2.Item2);
		}

		public void Swap(int row1, int col1, int row2, int col2)
		{
			var v1 = Values[row1, col1];
			var v2 = Values[row2, col2];

			UpdateValue(row1,col1,v2);
			UpdateValue(row2,col2,v1);
		}
	}
}