Create lexicographically minimal String utilizing given operation

Given a string s of size N consisting of digits from 0 to 9. Discover the lexicographically minimal sequence that may be obtained from given string s by performing the given operations:

• Deciding on any place i within the string and delete the digit ‘d‘ at i^th place,  
• Insert min(d+1, 9) on any place within the string s.

Examples:

Enter: s = ” 5217 “
Output: s = ” 1367 “
Clarification: 
Select 0^th place, d = 5 and insert 6 i.e. min(d+1, 9) between 1 and 7 in string;  s = ” 2167 “
Select 0^th place, d = 2 and insert 3 i.e. min(d+1, 9) between 1 and 6 in string;  s = ” 1367 “

Enter: s = ” 09412 “
Output: s = ” 01259 “
Clarification:
Select 1^st place, d = 9 and insert 9 i.e. min(d+1, 9) eventually of string; s = ” 04129 “
Select 1^st place, d = 4 and insert 5 i.e. min(d+1, 9) between 2 and 9 in string; s = ” 0 1 2 5 9 “

Strategy: Implement the thought under to unravel the issue:

At every place i, we verify if there’s any digit s_j such that s_j < s_i and j > i. As we’d like the lexicographically minimal string, we have to deliver the j^th digit forward of i^th digit. So delete the i^th digit and insert min(s_i+1, 9) behind the j^th digit. In any other case, if no lesser digits are current forward of i^th digit, maintain the digit as it’s and don’t carry out the operation.

Comply with the under steps to implement the above thought:

• Create a suffix vector to retailer the minimal digit in the proper a part of i^th place within the string.
• Run a loop from N-2 to 0 and retailer the minimal digit discovered until index i from the top. [This can be done by storing suf[i] = min( suf[i+1], s[i] ) ].
• Create a end result vector that can retailer the digits that will likely be current within the remaining lexicographically minimal string.
• Traverse for every place from i = 0 to N-1 within the string and verify if there’s any digit lower than the present digit (d = s[i]-‘0’) on the proper facet:
  • If sure then push min(d+1, 9) in end result.
  • Else push (d) within the end result.
• Kind the vector end result and print the values [Because we can easily arrange them in that way as there is no constraint on how many times we can perform the operation].

Under is the implementation of the above method:

Time Complexity: O(N * log N)
Auxiliary House: O(N)

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