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
- Minimum number of moves required to reach the destination by the king in a chess board
- Check if a king can move a valid move or not when N nights are there in a modified chessboard
- Number of blocks in a chessboard a knight can move to in exactly k moves
- Minimum number of moves to reach N starting from (1, 1)
- Minimum moves to reach target on a infinite line | Set 2
- Expected number of moves to reach the end of a board | Matrix Exponentiation
- Expected number of moves to reach the end of a board | Dynamic programming
- Find minimum moves to reach target on an infinite line
- Minimum total cost incurred to reach the last station
- Minimum time to reach a point with +t and -t moves at time t
- Total ways of choosing X men and Y women from a total of M men and W women
- Maximum bishops that can be placed on N*N chessboard
- Check if the given chessboard is valid or not
- Probability of Knight to remain in the chessboard
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