You are most likely familiar with the game 2048.
2048 is played on a gray 4 × 4 grid with numbered tiles that slide smoothly when a player moves them using one of the four arrow keys - Up , Down , Left or Right . On every turn, a new tile with a value of either
4randomly appears on an empty spot of the board. After one of the keys is pressed, the tiles slide as far as possible in the chosen direction until they are stopped either by another tile or by the edge of the grid. If two tiles with the same number collide while moving, they merge into a tile with this number doubled. You can't merge an already merged tile in the same turn. If there are more than
2tiles in the same row (column) that can merge, the farthest (closest to an edge) pair will be merged first (see the second example).
In this problem you are not going to solve the 2048 puzzle, but you are going to find the final state of the board from the given one after a defined set of n arrow key presses, assuming that no new random tiles will appear on the empty spots.
The following example shows the next state of the board after pressing Right.
You are given a matrix 4 × 4 which corresponds to the 2048 game grid.
gridcorresponds to the upper left tile of the grid. Each element of the grid is equal to some power of
2if there is a tile with that value in the corresponding position, and
0if it corresponds to the empty spot. You are also given a sequence of key presses as a string path. Each character of the string equals
Dcorresponding to Left , Right , Up or Down respectively.
Please note that in some cases after pressing an arrow key nothing will be changed.
grid = [[0, 0, 0, 0], [0, 0, 2, 2], [0, 0, 2, 4], [2, 2, 4, 8]]
path = "RR"
the output should be
game2048(grid, path) = [[0, 0, 0, 0], [0, 0, 0, 4], [0, 0, 2, 4], [0, 0, 8, 8]]
def merge(row, left_or_down): i, new_row = 0,  transposed = [e for e in row if e] if not left_or_down: transposed = transposed[::-1] while i < len(transposed): if i == len(transposed) - 1: new_row += [transposed[i]] break if transposed[i] == transposed[i + 1]: new_row += [2 * transposed[i]] i += 2 else: new_row += [transposed[i]] i += 1 if not left_or_down: new_row = *(4 - len(new_row)) + new_row[::-1] return new_row + *(4 - len(new_row)) def game2048(grid, path): for direc in path: if direc in 'LR': grid = [merge(row, direc == 'L') for row in grid] if direc in 'UD': grid = [merge(row[::-1], direc == 'D') for row in zip(*grid)] grid = [row for row in zip(*grid)][::-1] return grid