Create lexicographically minimum String using given operation

Given a string s of length N consisting of digits from 0 to 9. Find the lexicographically minimum sequence that can be obtained from given string s by performing the given operations:

• Selecting any position i in the string and delete the digit 'd' at i^th position,  
• Insert min(d+1, 9) on any position in the string s.

Examples:

Input: s = " 5217 "
Output: s = " 1367 "
Explanation: 
Choose 0^th position, d = 5 and insert 6 i.e. min(d+1, 9) between 1 and 7 in string;  s = " 2167 "
Choose 0^th position, d = 2 and insert 3 i.e. min(d+1, 9) between 1 and 6 in string;  s = " 1367 "

Input: s = " 09412 "
Output: s = " 01259 "
Explanation:
Choose 1^st position, d = 9 and insert 9 i.e. min(d+1, 9) at last of string; s = " 04129 "
Choose 1^st position, d = 4 and insert 5 i.e. min(d+1, 9) between 2 and 9 in string; s = " 0 1 2 5 9 "

Approach: Implement the idea below to solve the problem:

At each position i, we check if there is any digit s_j such that s_j < s_i and j > i. As we need the lexicographically minimum string, we need to bring the j^th digit ahead of i^th digit. So delete the i^th digit and insert min(s_i+1, 9) behind the j^th digit. Otherwise, if no lesser digits are present ahead of i^th digit, keep the digit as it is and don't perform the operation.

Follow the below steps to implement the above idea:

• Create a suffix vector to store the minimum digit in the right part of i^th position in the string.
• Run a loop from N-2 to 0 and store the minimal digit found till index i from the end. [This can be done by storing suf[i] = min( suf[i+1], s[i] ) ].
• Create a result vector that will store the digits that will be present in the final lexicographically minimum string.
• Traverse for each position from i = 0 to N-1 in the string and check if there is any digit less than the current digit (d = s[i]-'0') on the right side:
  • If yes then push min(d+1, 9) in result.
  • Else push (d) in the result.
• Sort the vector 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].

Below is the implementation of the above approach:

// C++ code to implement the approach

#include <bits/stdc++.h>
using namespace std;

// Function to print the minimum
// string after operation
string minimumSequence(string& s)
{
    int n = s.size();
    vector<int> suf(n);
    string sol = "";

    // Storing values in suf
    suf[n - 1] = s[n - 1] - '0';
    for (int i = n - 2; i >= 0; i--)
        suf[i] = min(suf[i + 1], s[i] - '0');

    // Storing values of final sequence
    // after performing given operation
    vector<int> res;
    for (int i = 0; i < n; i++) {

        // If smaller element is present
        // beyond index i
        if (suf[i] < s[i] - '0')
            res.push_back(min(9, s[i] - '0' + 1));
        else
            res.push_back(s[i] - '0');
    }

    // Sort the res in increasing order
    sort(res.begin(), res.end());
    for (int x : res)
        sol += char(x + '0');

    return sol;
}

// Driver code
int main()
{
    string s = "09412";

    // Function call
    cout << minimumSequence(s);

    return 0;
}

// Java code to implement the approach
import java.io.*;
import java.util.*;

class GFG {

  static String MinimumSequence(String s)
  {
    int n = s.length();
    int[] suf = new int[n];
    String sol = "";

    // Storing values in suf
    suf[n - 1] = s.charAt(n - 1) - '0';
    for (int i = n - 2; i >= 0; i--)
      suf[i]
      = Math.min(suf[i + 1], s.charAt(i) - '0');

    // Storing values of final sequence
    // after performing given operation
    int[] res = new int[n];
    for (int i = 0; i < n; i++) {
      // If smaller element is present
      // beyond index i
      if (suf[i] < s.charAt(i) - '0')
        res[i] = Math.min(9, s.charAt(i) - '0' + 1);
      else
        res[i] = s.charAt(i) - '0';
    }

    // Sort the res in increasing order
    Arrays.sort(res);
    for (int i = 0; i < res.length; i++) {
      sol += res[i];
    }
    return sol;
  }

  public static void main(String[] args)
  {
    String s = "09412";

    // Function call
    System.out.println(MinimumSequence(s));
  }
}

// This code is contributed by lokesh.

# python3 code to implement the approach

# Function to print the minimum
# string after operation


def minimumSequence(s):

    n = len(s)
    suf = [0 for _ in range(n)]
    sol = ""

    # Storing values in suf
    suf[n - 1] = ord(s[n - 1]) - ord('0')
    for i in range(n-2, -1, -1):
        suf[i] = min(suf[i + 1], ord(s[i]) - ord('0'))

    # Storing values of final sequence
    # after performing given operation
    res = []
    for i in range(0, n):

        # If smaller element is present
        # beyond index i
        if (suf[i] < ord(s[i]) - ord('0')):
            res.append(min(9, ord(s[i]) - ord('0') + 1))
        else:
            res.append(ord(s[i]) - ord('0'))

    # Sort the res in increasing order
    res.sort()
    for x in res:
        sol += str(x)

    return sol


# Driver code
if __name__ == "__main__":

    s = "09412"

    # Function call
    print(minimumSequence(s))

    # This code is contributed by rakeshsahni

//c# code implementation

using System;
using System.Linq;

public class GFG {
    static string MinimumSequence(string s)
    {
        int n = s.Length;
        int[] suf = new int[n];
        string sol = "";
        // Storing values in suf
        suf[n - 1] = s[n - 1] - '0';
        for (int i = n - 2; i >= 0; i--)
            suf[i] = Math.Min(suf[i + 1], s[i] - '0');

        // Storing values of final sequence
        // after performing given operation
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            // If smaller element is present
            // beyond index i
            if (suf[i] < s[i] - '0')
                res[i] = Math.Min(9, s[i] - '0' + 1);
            else
                res[i] = s[i] - '0';
        }

        // Sort the res in increasing order
        Array.Sort(res);
        for (int i=0;i<res.Length;i++){
            sol += res[i].ToString();
        }

        return sol;
    }

    static void Main(string[] args)
    {
        string s = "09412";

        // Function call
        Console.WriteLine(MinimumSequence(s));
    }
}
// code by ksam24000

// Javascript code to implement the approach

// Function to print the minimum
// string after operation
function minimumSequence(s)
{
    let n = s.length;
    let suf =new Array(n);
    let sol = "";

    // Storing values in suf
    suf[n - 1] = parseInt(s[n - 1]);
    for (let i = n - 2; i >= 0; i--)
        suf[i] = Math.min(suf[i + 1], parseInt(s[i]));

    // Storing values of final sequence
    // after performing given operation
    let res= [];
    for (let i = 0; i < n; i++) {

        // If smaller element is present
        // beyond index i
        if (suf[i] < parseInt(s[i]))
            res.push(Math.min(9, parseInt(s[i]) + 1));
        else
            res.push(parseInt(s[i]));
        
    }

    // Sort the res in increasing order
    res.sort();
    for (let x=0 ; x<res.length; x++)
        sol+=res[x];

    return sol;
}

// Driver code
    let s = "09412";

    // Function call
    document.write(minimumSequence(s));

01259

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

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• Introduction to String - Data Structure and Algorithm Tutorials
• Introduction to Greedy Algorithm - Data Structures and Algorithm Tutorials