Problem Statement |
| | There is an N x M board divided into 1 x 1 cells. The rows of the board are numbered from 0 to N-1, and the columns are numbered from 0 to M-1. The cell located in row r and column c has coordinates (r, c).
In a coloring of the board, each cell on the board is colored white or black. A coloring is called rectangle-avoiding if it is impossible to choose 4 distinct cells of the same color so that their centers form a rectangle whose sides are parallel to the sides of the board. In other words, a coloring is rectangle-avoiding if, for each a, b, c, and d with 0 <= a < b < N, 0 <= c < d < M, there is at least one white cell and at least one black cell among the cells (a, c), (a, d), (b, c) and (b, d).
You are given a String[] board representing a board. The j-th character of the i-th element of board represents cell (i, j), and it can be 'W', 'B' or '?'. Here, 'W' indicates a white cell, 'B' indicates a black cell and '?' indicates an uncolored cell. For each uncolored cell, you may choose to color it either white or black. Return the number of different rectangle-avoiding colorings that can be achieved. If it is impossible to achieve a rectangle-avoiding coloring, return 0. |
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Definition |
| | | Class: | RectangleAvoidingColoring | | Method: | count | | Parameters: | String[] | | Returns: | long | | Method signature: | long count(String[] board) | | (be sure your method is public) |
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Notes |
| - | Two colorings are different if there is a cell on the board that is colored white in one coloring and black in the other coloring. |
| - | The answer will always fit into a 64-bit signed integer data type. |
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Constraints |
| - | board will contain between 1 and 50 elements, inclusive. |
| - | Each element of board will contain between 1 and 50 characters, inclusive. |
| - | All elements of board will contain the same number of characters. |
| - | Each character in each element of board will be 'W', 'B' or '?'. |
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Examples |
| 0) | |
| | | Returns: 14 | | Since each cell can be black or white, there are 2^4 = 16 ways to color this board. Of them, only 2 monochromatic colorings are not rectangle-avoiding, so the answer is 16 - 2 = 14. |
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| 1) | |
| | | Returns: 3 | | It is the same board as in previous example, but colors for some cells are already predefined. There are 4 ways to color the remaining cells and in one of them the board becomes completely black. Therefore the answer is 4 - 1 = 3. |
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| 2) | |
| | | Returns: 0 | | This board is already colored and the coloring is not rectangle-avoiding. |
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| 3) | |
| | {"??B??",
"W???W",
"??B??"} |
| Returns: 12 | |
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| 4) | |
| | {"??",
"W?",
"W?",
"?W",
"W?"} |
| Returns: 16 | |
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