![](\"https://assets.leetcode.com/uploads/2024/08/01/chess_knight.jpg\")
There is a 50 x 50 chessboard with one knight and some pawns on it. You are given two integers kx and ky where (kx, ky) denotes the position of the knight, and a 2D array positions where positions[i] = [xi, yi] denotes the position of the pawns on the chessboard.
Alice and Bob play a turn-based game, where Alice goes first. In each player's turn:
\n\nAlice is trying to maximize the sum of the number of moves made by both players until there are no more pawns on the board, whereas Bob tries to minimize them.
\n\nReturn the maximum total number of moves made during the game that Alice can achieve, assuming both players play optimally.
\n\nNote that in one move, a chess knight has eight possible positions it can move to, as illustrated below. Each move is two cells in a cardinal direction, then one cell in an orthogonal direction.
\n\n
\n
Example 1:
\n\nInput: kx = 1, ky = 1, positions = [[0,0]]
\n\nOutput: 4
\n\nExplanation:
\n\n![\"\"](\"https://assets.leetcode.com/uploads/2024/08/16/gif3.gif\")
The knight takes 4 moves to reach the pawn at (0, 0).
Example 2:
\n\nInput: kx = 0, ky = 2, positions = [[1,1],[2,2],[3,3]]
\n\nOutput: 8
\n\nExplanation:
\n\n![\"\"](\"https://assets.leetcode.com/uploads/2024/08/16/gif4.gif\")
(2, 2) and captures it in two moves: (0, 2) -> (1, 4) -> (2, 2).(3, 3) and captures it in two moves: (2, 2) -> (4, 1) -> (3, 3).(1, 1) and captures it in four moves: (3, 3) -> (4, 1) -> (2, 2) -> (0, 3) -> (1, 1).Example 3:
\n\nInput: kx = 0, ky = 0, positions = [[1,2],[2,4]]
\n\nOutput: 3
\n\nExplanation:
\n\n(2, 4) and captures it in two moves: (0, 0) -> (1, 2) -> (2, 4). Note that the pawn at (1, 2) is not captured.(1, 2) and captures it in one move: (2, 4) -> (1, 2).\n
Constraints:
\n\n0 <= kx, ky <= 491 <= positions.length <= 15positions[i].length == 20 <= positions[i][0], positions[i][1] <= 49positions[i] are unique.positions[i] != [kx, ky] for all 0 <= i < positions.length.Compiled with clang 17 using the latest C++ 23 standard, and libstdc++ provided by GCC 13.
Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
Most standard library headers are already included automatically for your convenience.
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