Behind 2048 Behind 2048
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Maybe you’ve already heard about the simple and addictive game, 2048 (read more about it here). In this task we will look behind the scenes and try to recreate its basic movement functionality.

2048 is played on a simple 4×4 grid with tiles. Player can move tiles left, right, up, and down. If two tiles of the same number collide while moving, they will merge into a tile with the sum value of the two tiles. The resulting tile cannot merge with another tile again in the same move. If we have three tiles of the same number, then first collide tiles which closer to edge in the moving direction (right move - closer to the right edge). Every turn, a new tile will appear in the last empty spot (value 0) on the board with a value of 2. The last empty slot is determined by indexes that are defined in the following order:
[[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]]
[[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]]
At the beginning, there's already two numbers on the board.

You are given a game state represented as a 4x4 matrix with numbers that are powers of 2. Players move in a direction (up, down, left, right). You should return the game state after this move.

If the game is won, i.e. 2048 appears on the board, then return the winning matrix:
[['U','W','I','N'], ['U','W','I','N'], ['U','W','I','N'], ['U','W','I','N']]
[['U','W','I','N'], ['U','W','I','N'], ['U','W','I','N'], ['U','W','I','N']]
If the game is lose, i.e. nothing change after the player move and there is not a empty spot, then return the losing matrix:
[['G','A','M','E'], ['O','V','E','R'], ['G','A','M','E'], ['O','V','E','R']]
[['G','A','M','E'], ['O','V','E','R'], ['G','A','M','E'], ['O','V','E','R']]

Input: A game state as a list of lists with integers and player's move as a string ('up', 'down', 'left' or 'right').

Output: The game state after player's move as a list of lists with integers or letters.

How it is used: This can be used as a bases for further adding GUI to the python version of the 2048 game.

Example:

move2048([[0, 2, 0, 0],
          [0, 0, 0, 0],
          [0, 0, 0, 0],
          [0, 2, 0, 0]], 'up') == [[0, 4, 0, 0],
                                   [0, 0, 0, 0],
                                   [0, 0, 0, 0],
                                   [0, 0, 0, 2]]
move2048([[4, 0, 0, 0],
          [0, 4, 0, 0],
          [0, 0, 0, 0],
          [0, 0, 8, 8]], 'right') == [[0, 0, 0, 4],
                                      [0, 0, 0, 4],
                                      [0, 0, 0, 0],
                                      [0, 0, 2, 16]]
move2048([[2, 0, 2, 2],
          [0, 4, 4, 4],
          [8, 8, 8, 16],
          [0, 0, 0, 0]], 'right') == [[0, 0, 2, 4],
                                      [0, 0, 4, 8],
                                      [0, 8, 16, 16],
                                      [0, 0, 0, 2]]
move2048([[256, 0, 256, 4],
          [16, 8, 8, 0],
          [32, 32, 32, 32],
          [4, 4, 2, 2]], 'right') == [[0, 0, 512, 4],
                                      [0, 0, 16, 16],
                                      [0, 0, 64, 64],
                                      [0, 2, 8, 4]]
move2048([[4, 4, 0, 0],
          [0, 4, 1024, 0],
          [0, 256, 0, 256],
          [0, 1024, 1024, 8]], 'down') == [['U', 'W', 'I', 'N'],
                                           ['U', 'W', 'I', 'N'],
                                           ['U', 'W', 'I', 'N'],
                                           ['U', 'W', 'I', 'N']]
move2048([[2, 4, 8, 16],
          [32, 64, 128, 256],
          [512, 1024, 2, 4],
          [8, 16, 32, 64]], 'left') == [['G', 'A', 'M', 'E'],
                                        ['O', 'V', 'E', 'R'],
                                        ['G', 'A', 'M', 'E'],
                                        ['O', 'V', 'E', 'R']]

Preconditions: len(state) == 4
all(len(row) == 4 for row in state)
all(all(x in (0, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024) for x in row) for row in state)