Cracking_the_Safe.md

753. Cracking the Safe

There is a box protected by a password. The password is n digits, where each letter can be one of the first k digits 0, 1, ..., k-1.

You can keep inputting the password, the password will automatically be matched against the last n digits entered.

For example, assuming the password is "345", I can open it when I type "012345", but I enter a total of 6 digits.

Please return any string of minimum length that is guaranteed to open the box after the entire string is inputted.

Example 1:

Input: n = 1, k = 2
Output: "01"
Note: "10" will be accepted too.

Example 2:

Input: n = 2, k = 2
Output: "00110"
Note: "01100", "10011", "11001" will be accepted too.

Note:

• n will be in the range [1, 4].
• k will be in the range [1, 10].
• k^n will be at most 4096.

Method:

dfs going through all occurrence:

class Solution(object):
    def crackSafe(self, n, k):
        """
        :type n: int
        :type k: int
        :rtype: str
        """
        
        def dfs(res, visited):
            if len(visited)==pow(k, n):
                return True
            prev=''.join(res[len(res)-n+1:])
            for i in range(k):
                new=prev+str(i)
                if new not in visited:
                    res.append(str(i))
                    visited.add(new)
                    if dfs(res, visited):
                        return True
                    res.pop()
                    visited.remove(new)
            return False
        
        res=['0']*n
        dfs(res, set([''.join(res)]))
        return ''.join(res)