1370. Increasing Decreasing String

You are given a string s. Reorder the string using the following algorithm:

1. Remove the smallest character from s and append it to the result.
2. Remove the smallest character from s that is greater than the last appended character, and append it to the result.
3. Repeat step 2 until no more characters can be removed.
4. Remove the largest character from s and append it to the result.
5. Remove the largest character from s that is smaller than the last appended character, and append it to the result.
6. Repeat step 5 until no more characters can be removed.
7. Repeat steps 1 through 6 until all characters from s have been removed.

If the smallest or largest character appears more than once, you may choose any occurrence to append to the result.

Return the resulting string after reordering s using this algorithm.

Example 1:

Input: s = "aaaabbbbcccc"
Output: "abccbaabccba"
Explanation: After steps 1, 2 and 3 of the first iteration, result = "abc"
After steps 4, 5 and 6 of the first iteration, result = "abccba"
First iteration is done. Now s = "aabbcc" and we go back to step 1
After steps 1, 2 and 3 of the second iteration, result = "abccbaabc"
After steps 4, 5 and 6 of the second iteration, result = "abccbaabccba"

Example 2:

Input: s = "rat"
Output: "art"
Explanation: The word "rat" becomes "art" after re-ordering it with the mentioned algorithm.

Constraints:

• 1 <= s.length <= 500
• s consists of only lowercase English letters.