0753. Cracking the Safe

https://leetcode.com/problems/cracking-the-safe

Description

There is a safe protected by a password. The password is a sequence of n digits where each digit can be in the range [0, k - 1].

The safe has a peculiar way of checking the password. When you enter in a sequence, it checks the most recent n digits that were entered each time you type a digit.

• For example, the correct password is "345" and you enter in "012345":

  • After typing 0, the most recent 3 digits is "0", which is incorrect.

  • After typing 1, the most recent 3 digits is "01", which is incorrect.

  • After typing 2, the most recent 3 digits is "012", which is incorrect.

  • After typing 3, the most recent 3 digits is "123", which is incorrect.

  • After typing 4, the most recent 3 digits is "234", which is incorrect.

  • After typing 5, the most recent 3 digits is "345", which is correct and the safe unlocks.

Return any string of minimum length that will unlock the safe at some point of entering it.

Example 1:

**Input:** n = 1, k = 2
**Output:** "10"
**Explanation:** The password is a single digit, so enter each digit. "01" would also unlock the safe.

Example 2:

**Input:** n = 2, k = 2
**Output:** "01100"
**Explanation:** For each possible password:
- "00" is typed in starting from the 4th digit.
- "01" is typed in starting from the 1st digit.
- "10" is typed in starting from the 3rd digit.
- "11" is typed in starting from the 2nd digit.
Thus "01100" will unlock the safe. "01100", "10011", and "11001" would also unlock the safe.

Constraints:

• 1 <= n <= 4

• 1 <= k <= 10

• 1 <= kn <= 4096

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