Largest number not exceeding N that does not contain any of the digits of S

Given a numberic string N (1 ≤ |N| ≤ 10⁵) and another numeric string S (1 ≤ |S| ≤ 10⁵), the task is to find the maximum number ≤ N such that it doesn’t contain digits of string S. Remove leading zeros, if required. 

Note: The string S doesn’t contain ‘0’.

Examples:

Input: N = “2004”, S = “2” 
Output: 1999 
Explanation:
2004 has digit 2 which is in the string S. 
Therefore, keep reducing it by 1 until the number obtained does not contain 2. 
Therefore, the largest number that can be obtained is 1999.

Input: N = “12345”, S = “23” 
Output: 11999

Naive Approach: For every value of N, check if it contains any of the digits of S. Keep reducing N by 1 until any digit that is present in S does not occur in N. 

Time Complexity: O(|N| * log(|N|) * |S|) 
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized using Hashing. Follow the steps below to solve the problem:

• Iterate over the characters of the string S and store the distinct characters of S in a Map.
• Traverse the string N.
• If any digit of N is found to be present in S, say idx^th digit, reduce N[idx] to the largest digit not present in S, say LargestDig.
• Digits in range [idx + 1, |N| – 1] are changed to LargestDig. 
  

Illustration:
Consider N = “2004” and S = “2”. 
To remove 2, it is changed to 1 and the remaining digits are changed to the largest digit which is not present in S, that is digit 9.

• Remove all the leading zeros from the number.

Below is the implementation of the above approach.

C++

// C++ program to implement
// the above approach

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

// Function to obtain the largest number not exceeding
// num which does not contain any digits present in S
string greatestReducedNumber(string num, string s)
{
    // Stores digits of S
    vector<bool> vis_s(10, false);

    // Traverse the string S
    for (int i = 0; i < (int)s.size(); i++) {

        // Set occurrence as true
        vis_s[int(s[i]) - 48] = true;
    }

    int n = num.size();
    int in = -1;

    // Traverse the string n
    for (int i = 0; i < n; i++) {
        if (vis_s[(int)num[i] - '0']) {
            in = i;
            break;
        }
    }

    // All digits of num are not
    // present in string s
    if (in == -1) {
        return num;
    }

    for (char dig = num[in]; dig >= '0'; dig--) {
        if (vis_s[(int)dig - '0'] == 0) {
            num[in] = dig;
            break;
        }
    }

    char LargestDig = '0';

    for (char dig = '9'; dig >= '0'; dig--) {
        if (vis_s[dig - '0'] == false) {

            // Largest Digit not present
            // in the string s
            LargestDig = dig;
            break;
        }
    }

    // Set all digits from positions
    // in + 1 to n - 1 as LargestDig
    for (int i = in + 1; i < n; i++) {
        num[i] = LargestDig;
    }

    // Counting leading zeroes
    int Count = 0;
    for (int i = 0; i < n; i++) {
        if (num[i] == '0')
            Count++;
        else
            break;
    }

    // Removing leading zeroes
    num.erase(0, Count);

    // If the string becomes null
    if ((int)num.size() == 0)
        return "0";

    // Return the largest number
    return num;
}

// Driver Code
int main()
{
    string N = "12345";
    string S = "23";

    cout << greatestReducedNumber(N, S);

    return 0;
}

Java

// Java program to implement
// the above approach

import java.io.*;
import java.util.Arrays;

class GFG {

    // Function to obtain the largest number not exceeding
    // num which does not contain any digits present in S
    static String greatestReducedNumber(String num,
                                        String s)
    {
        // Stores digits of S
        Boolean[] vis_s = new Boolean[10];
        Arrays.fill(vis_s, Boolean.FALSE);

        // Traverse the string S
        for (int i = 0; i < (int)s.length(); i++) {

            // Set occurrence as true
            vis_s[(int)(s.charAt(i)) - 48] = true;
        }

        int n = num.length();
        int in = -1;

        // Traverse the string n
        for (int i = 0; i < n; i++) {
            if (vis_s[(int)num.charAt(i) - '0']) {
                in = i;
                break;
            }
        }

        // All digits of num are not
        // present in string s
        if (in == -1) {
            return num;
        }

    for (char dig = num.charAt(in); dig >= '0'; dig--) {
        if (vis_s[(int)dig - '0'] == false) {
            num = num.substring(0, in) + dig
                  + num.substring(in + 1, n);
            break;
        }
    }

    char LargestDig = '0';

    for (char dig = '9'; dig >= '0'; dig--) {
        if (vis_s[dig - '0'] == false) {

            // Largest Digit not present
            // in the string s
            LargestDig = dig;
            break;
        }
    }

    // Set all digits from positions
    // in + 1 to n - 1 as LargestDig
    for (int i = in + 1; i < n; i++) {
        num = num.substring(0, i) + LargestDig;
    }

    // Counting leading zeroes
    int Count = 0;
    for (int i = 0; i < n; i++) {
        if (num.charAt(i) == '0')
            Count++;
        else
            break;
    }

    // Removing leading zeroes
    num = num.substring(Count, n);

    // If the string becomes null
    if ((int)num.length() == 0)
        return "0";

    // Return the largest number
    return num;
    }

    // Driver Code
    public static void main(String[] args)
    {
        String N = "12345";
        String S = "23";

        System.out.print(greatestReducedNumber(N, S));
    }
}

// This code is contributed by subhammahato348

Python3

# Python3 program to implement
# the above approach

# Function to obtain the largest number not exceeding
# num which does not contain any digits present in S
def greatestReducedNumber(num, s) :

    # Stores digits of S
    vis_s = [False] * 10

    # Traverse the string S
    for i in range(len(s)) :

      # Set occurrence as true
      vis_s[(ord)(s[i]) - 48] = True
    n = len(num)
    In = -1

    # Traverse the string n
    for i in range(n) :
      if (vis_s[ord(num[i]) - ord('0')]) :
        In = i
        break

    # All digits of num are not
    # present in string s
    if (In == -1) :
      return num
    for dig in range(ord(num[In]), ord('0') - 1, -1) :
      if (vis_s[dig - ord('0')] == False) :
        num = num[0 : In] + chr(dig) + num[In + 1 : n - In - 1]
        break
    LargestDig = '0'
    for dig in range(ord('9'), ord('0') - 1, -1) :
      if (vis_s[dig - ord('0')] == False) :

        # Largest Digit not present
        # in the string s
        LargestDig = dig
        break

    # Set all digits from positions
    # in + 1 to n - 1 as LargestDig
    for i in range(In + 1, n) :
      num = num[0 : i] + chr(LargestDig)

    # Counting leading zeroes
    Count = 0
    for i in range(n) :
      if (num[i] == '0') :
        Count += 1
      else :
        break

    # Removing leading zeroes
    num = num[Count : n]

    # If the string becomes null
    if (int(len(num)) == 0) :
      return "0"

    # Return the largest number
    return num

    # Driver code
N = "12345"
S = "23"

print(greatestReducedNumber(N, S))

# This code is contributed by divyeshrabadiya07.

C#

// C# program to implement
// the above approach
using System;
using System.Collections.Generic;
class GFG
{

  // Function to obtain the largest number not exceeding
  // num which does not contain any digits present in S
  static string greatestReducedNumber(string num, string s)
  {

    // Stores digits of S
    bool[] vis_s = new bool[10];

    // Traverse the string S
    for (int i = 0; i < (int)s.Length; i++) {

      // Set occurrence as true
      vis_s[(int)(s[i]) - 48] = true;
    }

    int n = num.Length;
    int In = -1;

    // Traverse the string n
    for (int i = 0; i < n; i++) {
      if (vis_s[(int)num[i] - '0']) {
        In = i;
        break;
      }
    }

    // All digits of num are not
    // present in string s
    if (In == -1) {
      return num;
    }

    for (char dig = num[In]; dig >= '0'; dig--) {
      if (vis_s[(int)dig - '0'] == false) {
        num = num.Substring(0, In) + dig + num.Substring(In + 1, n - In - 1);
        break;
      }
    }

    char LargestDig = '0';

    for (char dig = '9'; dig >= '0'; dig--) {
      if (vis_s[dig - '0'] == false) {

        // Largest Digit not present
        // in the string s
        LargestDig = dig;
        break;
      }
    }

    // Set all digits from positions
    // in + 1 to n - 1 as LargestDig
    for (int i = In + 1; i < n; i++) {
      num = num.Substring(0, i) + LargestDig;
    }

    // Counting leading zeroes
    int Count = 0;
    for (int i = 0; i < n; i++) {
      if (num[i] == '0')
        Count++;
      else
        break;
    }

    // Removing leading zeroes
    num = num.Substring(Count, n);

    // If the string becomes null
    if ((int)num.Length == 0)
      return "0";

    // Return the largest number
    return num;
  }

  // Driver code
  static void Main() {
    string N = "12345";
    string S = "23";

    Console.Write(greatestReducedNumber(N, S));
  }
}

// This code is contributed by divyesh072019

Javascript

<script>
// JavaScript program to implement
// the above approach

// Function to obtain the largest number not exceeding
// num which does not contain any digits present in S
function greatestReducedNumber( num, s){
    // Stores digits of S
    let vis_s = [false,false,false,false,false,false,false,false,false,false];

    // Traverse the string S
    for (let i = 0; i < s.length; i++) {
        // Set occurrence as true
        vis_s[Number(s[i]) - 48] = true;
    }

    let n = num.length;
    let inn = -1;

    // Traverse the string n
    for (let i = 0; i < n; i++) {
        if (vis_s[Number(num[i]) - '0']) {
            inn = i;
            break;
        }
    }

    // All digits of num are not
    // present in string s
    if (inn == -1) {
        return num;
    }

    for (let dig = String(num[inn]); dig >= '0'; dig--) {
        if (vis_s[Number(dig) - '0'] == 0) {
            num[inn] = dig;
            break;
        }
    }

    let LargestDig = '0';

    for (let dig = '9'; dig >= '0'; dig--) {
        if (vis_s[dig - '0'] == false) {

            // Largest Digit not present
            // in the string s
            LargestDig = dig;
            break;
        }
    }

    // Set all digits from positions
    // in + 1 to n - 1 as LargestDig
    for (let i = inn + 1; i < n; i++) {
        num[i] = LargestDig;
    }

    // Counting leading zeroes
    let Count = 0;
    for (let i = 0; i < n; i++) {
        if (num[i] == '0')
            Count++;
        else
            break;
    }

    // Removing leading zeroes
    num = Number(num).toString();

    // If the string becomes null
    if (num.length == 0)
        return "0";

    // Return the largest number
    return num;
}

// Driver Code
let N = "12345";
let S = "23";
document.write( greatestReducedNumber(N, S));

// This code is contributed by rohitsingh07052
</script>

Output:

11999

Time complexity: O(|N| + |s|) 
Auxiliary space: O(1)