Lexicographically smallest string formed by reversing Substrings of string S exactly K times

Given a string S and an integer K, the task is to find the lexicographically smallest string possible after reversing any substring of any length exactly K times. 

Examples:

Input: S = "fgazcbdfge", K = 3
Output: abcdgfzfge
Explanation: After 1st operation: S = "agfzcbdfge", in S select S[0 - 2] = "fga" and reverse it
After 2nd operation: S = "abczfgdfge", in S select S[2 - 4] = "fzc" and reverse it
After 3rd operation: S = "abcdgfzfge", in S select S[3 - 6] = "zfgd" and reverse it.

Input: S = "abcdefg", K = 5
Output: abcdefg
Explanation: The string is already lexicographically minimum possible. 
Hence pick any 5 substrings having length 1. So the string will remain unchanged.

Approach: To form the lexicographically smallest string in K steps, in each step select an integer L where S[L] is the character before which all characters are in sorted order and an integer R where S[R] is the character which has to be placed at S[L+1] so that all character till S[L+1] will be in sorted order. Reverse the substring S[L..R] in each step and finally, the required string will be obtained. Follow the below steps to solve the problem:

• Let the given string be S, create another string S1 equal to S then sort S1 in increasing order.
• This algorithm requires three nested loops, the outer loop will run from 0 to K (number of operations)
• In every operation, search for two integers L and R, after they have been found we reverse the substring S[L ... R] and continue the same for subsequent operations.
• Using two nested loops search for characters of S1 in S depending upon the number of operations.
• Since there is the need to only reverse one substring in one operation, just find one character of S1 in S which is S[R] (the character which has to be placed after already sorted characters of S in previous operations) and also find S[L] ( the substring S[0...L-1] is sorted so we don't have to do anything with it, S[R]will be placed at S[L+1]).
• After K operations, the lexicographically smallest possible string is obtained.

Illustration: 

👁 Image

In the above illustration, since the first three characters of the original string were in sorted order we dont have to involve them in any operation Search that character which will appear after them in the sorted order, assume it appears at index R (the character will be S[R]) we select the index of character after the first three character as R (the character will be S[R]) Now we reverse the substring S[L...R] which will result in the   character S[R] to appear at S[L+1] and now the first 4 characters ofthe string S are in sorted order    

Below is the implementation of the above approach.

abcdgfzfge

Time Complexity: O(K * N²) where N  is the length of the string 
Auxiliary Space: O(N)