1830 - Minimum Number of Operations to Make String Sorted.

Hard

You are given a string s ( 0-indexed ). You are asked to perform the following operation on s until you get a sorted string:

• Find the largest index i such that 1 <= i < s.length and s[i] < s[i - 1].

• Find the largest index j such that i <= j < s.length and s[k] < s[i - 1] for all the possible values of k in the range [i, j] inclusive.

• Swap the two characters at indices i - 1 and j.

• Reverse the suffix starting at index i.

Return the number of operations needed to make the string sorted. Since the answer can be too large, return it modulo <code>10⁹ + 7</code>.

Example 1:

Input: s = "cba"

Output: 5

Explanation: The simulation goes as follows: Operation 1: i=2, j=2. Swap s1 and s2 to get s="cab", then reverse the suffix starting at 2. Now, s="cab".

Operation 2: i=1, j=2. Swap s0 and s2 to get s="bac", then reverse the suffix starting at 1. Now, s="bca".

Operation 3: i=2, j=2. Swap s1 and s2 to get s="bac", then reverse the suffix starting at 2. Now, s="bac".

Operation 4: i=1, j=1. Swap s0 and s1 to get s="abc", then reverse the suffix starting at 1. Now, s="acb".

Operation 5: i=2, j=2. Swap s1 and s2 to get s="abc", then reverse the suffix starting at 2. Now, s="abc".

Example 2:

Input: s = "aabaa"

Output: 2

Explanation: The simulation goes as follows:

Operation 1: i=3, j=4. Swap s2 and s4 to get s="aaaab", then reverse the substring starting at 3. Now, s="aaaba".

Operation 2: i=4, j=4. Swap s3 and s4 to get s="aaaab", then reverse the substring starting at 4. Now, s="aaaab".

Constraints:

• 1 <= s.length <= 3000

• s consists only of lowercase English letters.