Given an integer M, an 8 * 8 chessboard and the king is placed on one of the square of the chessboard. Let the coordinate of the king be (R, C).
Note that the king can move to a square whose coordinate is (R1, C1) if and only if below condition is satisfied.
The task is to count the number of position where the king can reach (excluding the initial position) from the given square in exactly M moves.
Input: row = 1, column = 3, moves = 1
Output: Total number of position where king can reached = 5
Input: row = 2, column = 5, moves = 2
Output: Total number of position where king can reached = 19
Approach: Calculate the coordinates of the top left square that can be visited by the king (a, b) and the coordinates of the bottom right square (c, d) of the chessboard that the king can visit. Then the total number of cells that the king can visit will be (c – a + 1) * (d – b + 1) – 1.
Below is the implementation of the above approach:
- Total position where king can reach on a chessboard in exactly M moves | Set 2
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- Expected number of moves to reach the end of a board | Dynamic programming
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- Find ways to arrange K green balls among N balls such that exactly i moves is needed to collect all K green balls
- Maximum bishops that can be placed on N*N chessboard
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- Maximum non-attacking Knights that can be placed on an N*M Chessboard
- Maximum non-attacking Rooks that can be placed on an N*N Chessboard
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