TilingBoard.cs

void Solve(int[,] m, int sCol, int eCol, int sRow, int eRow, int br, int bc)
        {
                // determine the direction of the tile based on the mising block
            var direction = GetDirection(sCol, eCol, sRow, eRow, br, bc);
                // solve for size = 1
            if ((eCol - sCol == 1) && (eRow - sRow == 1))
            {
                PlaceOne(m, sCol, eCol, sRow, eRow, direction, cIdx);
                cIdx += 1;
            }   
            else
            {
                    // get the half board 
                var mR = sRow + ((eRow - sRow) >> 1);
                var mC = sCol + ((eCol - sCol) >> 1);

                    // place a tile in the middle of the board 
                PlaceOne(m, mC, mC+1, mR, mR + 1, direction, cIdx);
                cIdx++;
                    // solving for 4 regions recursively
                // top left
                if (br >= sRow && br <= mR && bc >= sCol && bc <= mC)
                { 
                    Solve(m, sCol, mC, sRow, mR, br, bc);
                }
                else
                {   
                    Solve(m, sCol, mC, sRow, mR, mR, mC);
                }

                //top right
                if (br >= sRow && br <= mR && bc >= mC + 1 && bc <= eCol)
                {
                    Solve(m, mC + 1, eCol, sRow, mR, br, bc);
                }
                else
                {   
                    Solve(m, mC + 1, eCol, sRow, mR, mR, mC + 1);
                }
                    
                // bot left
                if (br >= mR+1 && br <= eRow && bc >= sCol && bc <= mC)
                {
                  
                    Solve(m, sCol, mC, mR + 1, eRow, br, bc);
                }
                else
                {   
                    Solve(m, sCol, mC, mR+ 1, eRow, mR+1, mC);
                }

                // bot right
                if (br >= mR + 1 && br <= eRow && bc >= mC + 1 && bc <= eCol)
                {   
                    Solve(m, mC + 1, eCol, mR + 1, eRow, br, bc);
                }
                else
                {   
                    Solve(m, mC + 1, eCol, mR + 1, eRow, mR+1, mC+1);
                }
            }
        }