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37 lines
1.7 KiB
HTML
<p>On an <code>n x n</code> chessboard, a knight starts at the cell <code>(row, column)</code> and attempts to make exactly <code>k</code> moves. The rows and columns are <strong>0-indexed</strong>, so the top-left cell is <code>(0, 0)</code>, and the bottom-right cell is <code>(n - 1, n - 1)</code>.</p>
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<p>A chess knight has eight possible moves it can make, as illustrated below. Each move is two cells in a cardinal direction, then one cell in an orthogonal direction.</p>
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<img src="https://assets.leetcode.com/uploads/2018/10/12/knight.png" style="width: 300px; height: 300px;" />
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<p>Each time the knight is to move, it chooses one of eight possible moves uniformly at random (even if the piece would go off the chessboard) and moves there.</p>
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<p>The knight continues moving until it has made exactly <code>k</code> moves or has moved off the chessboard.</p>
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<p>Return <em>the probability that the knight remains on the board after it has stopped moving</em>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> n = 3, k = 2, row = 0, column = 0
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<strong>Output:</strong> 0.06250
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<strong>Explanation:</strong> There are two moves (to (1,2), (2,1)) that will keep the knight on the board.
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From each of those positions, there are also two moves that will keep the knight on the board.
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The total probability the knight stays on the board is 0.0625.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> n = 1, k = 0, row = 0, column = 0
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<strong>Output:</strong> 1.00000
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= n <= 25</code></li>
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<li><code>0 <= k <= 100</code></li>
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<li><code>0 <= row, column <= n</code></li>
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</ul>
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