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leetcode/problem/knight-probability-in-chessboard.html

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+<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>
+
+<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>
+<img src="https://assets.leetcode.com/uploads/2018/10/12/knight.png" style="width: 300px; height: 300px;" />
+<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>
+
+<p>The knight continues moving until it has made exactly <code>k</code> moves or has moved off the chessboard.</p>
+
+<p>Return <em>the probability that the knight remains on the board after it has stopped moving</em>.</p>
+
+<p>&nbsp;</p>
+<p><strong>Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 3, k = 2, row = 0, column = 0
+<strong>Output:</strong> 0.06250
+<strong>Explanation:</strong> There are two moves (to (1,2), (2,1)) that will keep the knight on the board.
+From each of those positions, there are also two moves that will keep the knight on the board.
+The total probability the knight stays on the board is 0.0625.
+</pre>
+
+<p><strong>Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 1, k = 0, row = 0, column = 0
+<strong>Output:</strong> 1.00000
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= n &lt;= 25</code></li>
+	<li><code>0 &lt;= k &lt;= 100</code></li>
+	<li><code>0 &lt;= row, column &lt;= n</code></li>
+</ul>