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"content": "<p>You have a lock in front of you with 4 circular wheels. Each wheel has 10 slots: <code>'0', '1', '2', '3', '4', '5', '6', '7', '8', '9'</code>. The wheels can rotate freely and wrap around: for example we can turn <code>'9'</code> to be <code>'0'</code>, or <code>'0'</code> to be <code>'9'</code>. Each move consists of turning one wheel one slot.</p>\n\n<p>The lock initially starts at <code>'0000'</code>, a string representing the state of the 4 wheels.</p>\n\n<p>You are given a list of <code>deadends</code> dead ends, meaning if the lock displays any of these codes, the wheels of the lock will stop turning and you will be unable to open it.</p>\n\n<p>Given a <code>target</code> representing the value of the wheels that will unlock the lock, return the minimum total number of turns required to open the lock, or -1 if it is impossible.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> deadends = ["0201","0101","0102","1212","2002"], target = "0202"\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> \nA sequence of valid moves would be "0000" -> "1000" -> "1100" -> "1200" -> "1201" -> "1202" -> "0202".\nNote that a sequence like "0000" -> "0001" -> "0002" -> "0102" -> "0202" would be invalid,\nbecause the wheels of the lock become stuck after the display becomes the dead end "0102".\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> deadends = ["8888"], target = "0009"\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> We can turn the last wheel in reverse to move from "0000" -> "0009".\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> deadends = ["8887","8889","8878","8898","8788","8988","7888","9888"], target = "8888"\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> We cannot reach the target without getting stuck.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= deadends.length <= 500</code></li>\n\t<li><code>deadends[i].length == 4</code></li>\n\t<li><code>target.length == 4</code></li>\n\t<li>target <strong>will not be</strong> in the list <code>deadends</code>.</li>\n\t<li><code>target</code> and <code>deadends[i]</code> consist of digits only.</li>\n</ul>\n",
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"code": "class Solution(object):\n def openLock(self, deadends, target):\n \"\"\"\n :type deadends: List[str]\n :type target: str\n :rtype: int\n \"\"\"\n ",
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"We can think of this problem as a shortest path problem on a graph: there are `10000` nodes (strings `'0000'` to `'9999'`), and there is an edge between two nodes if they differ in one digit, that digit differs by 1 (wrapping around, so `'0'` and `'9'` differ by 1), and if *both* nodes are not in `deadends`."
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