In the game of Connect-K, red and blue pieces are dropped into an N-by-N table. The table stands up vertically so that pieces drop down to the bottom-most empty slots in their column. For example, consider the following two configurations:
In these pictures, each '.' represents an empty slot, each 'R' represents a slot filled with a red piece, and each 'B' represents a slot filled with a blue piece. The left configuration is legal, but the right one is not. This is because one of the pieces in the third column (marked with the arrow) has not fallen down to the empty slot below it.
A player wins if they can place at least K pieces of their colour in a row, either horizontally, vertically, or diagonally. The four possible orientations are shown below:
In the "Legal Position" diagram at the beginning of the problem statement, both players had lined up two pieces in a row, but not three. You have a tricky plan to ensure victory with Connect-K! When your opponent is not looking, you are going to rotate the board 90 degrees clockwise onto its side. Gravity will then cause the pieces to fall down into a new position as shown below:
Unfortunately, you only have time to rotate once before your opponent will notice. All that remains is picking the right time to make your move. Given a board position, you should determine which player (or players!) will have K pieces in a row after you rotate the board clockwise and gravity takes effect in the new direction.
In these pictures, each '.' represents an empty slot, each 'R' represents a slot filled with a red piece, and each 'B' represents a slot filled with a blue piece. The left configuration is legal, but the right one is not. This is because one of the pieces in the third column (marked with the arrow) has not fallen down to the empty slot below it.
A player wins if they can place at least K pieces of their colour in a row, either horizontally, vertically, or diagonally. The four possible orientations are shown below:
In the "Legal Position" diagram at the beginning of the problem statement, both players had lined up two pieces in a row, but not three. You have a tricky plan to ensure victory with Connect-K! When your opponent is not looking, you are going to rotate the board 90 degrees clockwise onto its side. Gravity will then cause the pieces to fall down into a new position as shown below:
Unfortunately, you only have time to rotate once before your opponent will notice. All that remains is picking the right time to make your move. Given a board position, you should determine which player (or players!) will have K pieces in a row after you rotate the board clockwise and gravity takes effect in the new direction.
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