Find Next number having distinct digits from the given number N

Last Updated : 26 May, 2022

Given a natural number N, the task is to find the next number having distinct digits from the given number.
Examples:

Input: N = 19
Output: 20
Explanation:
Next number to 19 whose digits are different from 19 is 20.
Input: N = 2019
Output: 3333
Explanation:
Next number to 2019 whose digits are different from 2019 is 3333.

Approach: The idea is to use hashing to compute the next number with distinct digit from the given number -

Create a hash array to store the digits present in the number, store the most significant digit and also store the number of digits present in the number in a count variable
Find the next digit for the most significant bit which is not present in the number and greater than the current most significant digit.
If the next most significant digit is not found then increase the number of digits by incrementing the count and find the most significant digit between 1 to 9 which is not present in the number.
If the next most significant digit is found then find the minimum digit next which is not present in the number between 0 to 9.
Iterate over the number of digits from 1 to count
- Multiply the most significant digit by 10 and add the next digit which is not present in the given number.

Below is the implementation of the above approach:

C++

// C++ implementation to find
// the next distinct digits number

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

// Function to find the
// next distinct digits number
void findNextNumber(int n)
{
    int h[10] = { 0 };
    int i = 0, msb = n, rem = 0;
    int next_num = -1, count = 0;

    // Loop to find the distinct 
    // digits using hash array
    // and the number of digits
    while (msb > 9) {
        rem = msb % 10;
        h[rem] = 1;
        msb /= 10;
        count++;
    }
    h[msb] = 1;
    count++;

    // Loop to find the most significant
    // distinct digit of the next number
    for (i = msb + 1; i < 10; i++) {
        if (h[i] == 0) {
            next_num = i;
            break;
        }
    }
    
    // Condition to check if the number
    // is possible with the same number
    // of digits count
    if (next_num == -1){
        for (i = 1; i < msb; i++){
            if (h[i] == 0){
                next_num = i;
                count++;
                break;
            }
        }
    }
    
    // Condition to check if the desired
    // most significant distinct 
    // digit is found
    if (next_num > 0){
        
        // Loop to find the minimum next digit
        // which is not present in the number
        for (i = 0; i < 10; i++) {
            if (h[i] == 0) {
                msb = i;
                break;
            }
        }
        
        // Computation of the number 
        for (i = 1; i < count; i++) {
            next_num = ((next_num * 10) + msb);
        }
        
        // Condition to check if the number is 
        // greater than the given number
        if (next_num > n)
            cout << next_num << "\n";
        else
            cout << "Not Possible \n";
    }
    else{
        cout << "Not Possible \n";
    }
}

// Driver Code
int main()
{
    int n = 2019;
    findNextNumber(n);
    return 0;
}

// C implementation to find
//next distinct digits number
#include <stdio.h>

// Function to find the
// next distinct digits number
void findNextNumber(int n)
{
    int h[10] = { 0 };
    int i = 0, msb = n, rem = 0;
    int next_num = -1, count = 0;

    // Loop to find the distinct
    // digits using hash array
    // and the number of digits
    while (msb > 9) {
        rem = msb % 10;
        h[rem] = 1;
        msb /= 10;
        count++;
    }
    h[msb] = 1;
    count++;

    // Loop to find the most significant
    // distinct digit of the next number
    for (i = msb + 1; i < 10; i++) {
        if (h[i] == 0) {
            next_num = i;
            break;
        }
    }
    
    // Condition to check if the number
    // is possible with the same number
    // of digits count
    if (next_num == -1){
        for (i = 1; i < msb; i++){
            if (h[i] == 0){
                next_num = i;
                count++;
                break;
            }
        }
    }
    
    // Condition to check if the desired
    // most significant distinct
    // digit is found
    if (next_num > 0){
        
        // Loop to find the minimum next digit
        // which is not present in the number
        for (i = 0; i < 10; i++) {
            if (h[i] == 0) {
                msb = i;
                break;
            }
        }
        
        // Computation of the number
        for (i = 1; i < count; i++) {
            next_num = ((next_num * 10) + msb);
        }
        
        // Condition to check if the number is
        // greater than the given number
        if (next_num > n)
            printf("%d\n", next_num);
        else
            printf("\nNot Possible");
    }
    else{
        printf("Not Possible \n");
    }
}

// Driver Code
int main()
{
    int n = 2019;
    findNextNumber(n);
    return 0;
}

// This code is contributed by allwink45

Java

// Java implementation to find
// the next distinct digits number
class GFG{
 
// Function to find the
// next distinct digits number
static void findNextNumber(int n)
{
    int h[] = new int[10];
    int i = 0, msb = n, rem = 0;
    int next_num = -1, count = 0;
 
    // Loop to find the distinct 
    // digits using hash array
    // and the number of digits
    while (msb > 9) {
        rem = msb % 10;
        h[rem] = 1;
        msb /= 10;
        count++;
    }
    h[msb] = 1;
    count++;
 
    // Loop to find the most significant
    // distinct digit of the next number
    for (i = msb + 1; i < 10; i++) {
        if (h[i] == 0) {
            next_num = i;
            break;
        }
    }
     
    // Condition to check if the number
    // is possible with the same number
    // of digits count
    if (next_num == -1){
        for (i = 1; i < msb; i++){
            if (h[i] == 0){
                next_num = i;
                count++;
                break;
            }
        }
    }
     
    // Condition to check if the desired
    // most significant distinct 
    // digit is found
    if (next_num > 0){
         
        // Loop to find the minimum next digit
        // which is not present in the number
        for (i = 0; i < 10; i++) {
            if (h[i] == 0) {
                msb = i;
                break;
            }
        }
         
        // Computation of the number 
        for (i = 1; i < count; i++) {
            next_num = ((next_num * 10) + msb);
        }
         
        // Condition to check if the number is 
        // greater than the given number
        if (next_num > n)
            System.out.print(next_num+ "\n");
        else
            System.out.print("Not Possible \n");
    }
    else{
        System.out.print("Not Possible \n");
    }
}
 
// Driver Code
public static void main(String[] args)
{
    int n = 2019;
    findNextNumber(n);
}
}

// This code is contributed by 29AjayKumar

// C# implementation to find
// the next distinct digits number
using System;

class GFG{
 
    // Function to find the
    // next distinct digits number
    static void findNextNumber(int n)
    {
        int []h = new int[10];
        int i = 0, msb = n, rem = 0;
        int next_num = -1, count = 0;
     
        // Loop to find the distinct 
        // digits using hash array
        // and the number of digits
        while (msb > 9) {
            rem = msb % 10;
            h[rem] = 1;
            msb /= 10;
            count++;
        }
        h[msb] = 1;
        count++;
     
        // Loop to find the most significant
        // distinct digit of the next number
        for (i = msb + 1; i < 10; i++) {
            if (h[i] == 0) {
                next_num = i;
                break;
            }
        }
         
        // Condition to check if the number
        // is possible with the same number
        // of digits count
        if (next_num == -1){
            for (i = 1; i < msb; i++){
                if (h[i] == 0){
                    next_num = i;
                    count++;
                    break;
                }
            }
        }
         
        // Condition to check if the desired
        // most significant distinct 
        // digit is found
        if (next_num > 0){
             
            // Loop to find the minimum next digit
            // which is not present in the number
            for (i = 0; i < 10; i++) {
                if (h[i] == 0) {
                    msb = i;
                    break;
                }
            }
             
            // Computation of the number 
            for (i = 1; i < count; i++) {
                next_num = ((next_num * 10) + msb);
            }
             
            // Condition to check if the number is 
            // greater than the given number
            if (next_num > n)
                Console.WriteLine(next_num);
            else
                Console.WriteLine("Not Possible");
        }
        else{
            Console.WriteLine("Not Possible");
        }
    }
     
    // Driver Code
    public static void Main(string[] args)
    {
        int n = 2019;
        findNextNumber(n);
    }
}

// This code is contributed by Yash_R

Python 3

# Python 3 implementation to find
# the next distinct digits number

# Function to find the
# next distinct digits number
def findNextNumber(n):
    h = [0 for i in range(10)]
    i = 0
    msb = n
    rem = 0
    next_num = -1
    count = 0

    # Loop to find the distinct 
    # digits using hash array
    # and the number of digits
    while (msb > 9):
        rem = msb % 10
        h[rem] = 1
        msb //= 10
        count += 1

    h[msb] = 1
    count += 1

    # Loop to find the most significant
    # distinct digit of the next number
    for i in range(msb + 1,10,1):
        if (h[i] == 0):
            next_num = i
            break
    
    # Condition to check if the number
    # is possible with the same number
    # of digits count
    if (next_num == -1):
        for i in range(1,msb,1):
            if (h[i] == 0):
                next_num = i
                count += 1
                break
    
    # Condition to check if the desired
    # most significant distinct 
    # digit is found
    if (next_num > 0):
        
                # Loop to find the minimum next digit
        # which is not present in the number
        for i in range(0,10,1):
            if (h[i] == 0):
                msb = i
                break
        
        # Computation of the number 
        for i in range(1,count,1):
            next_num = ((next_num * 10) + msb)
        
        # Condition to check if the number is 
        # greater than the given number
        if (next_num > n):
            print(next_num)
        else:
            print("Not Possible")
    else:
        print("Not Possible")

# Driver Code
if __name__ == '__main__':
    n = 2019
    findNextNumber(n)

# This code is contributed by Surendra_Gangwar

JavaScript

<script>

// Javascript implementation to find
// the next distinct digits number

// Function to find the
// next distinct digits number
function findNextNumber(n)
{
    let h =  Array.from({length: 10}, (_, i) => 0);
    let i = 0, msb = n, rem = 0;
    let next_num = -1, count = 0;
   
    // Loop to find the distinct 
    // digits using hash array
    // and the number of digits
    while (msb > 9) {
        rem = msb % 10;
        h[rem] = 1;
        msb = Math.floor(msb / 10);
        count++;
    }
    h[msb] = 1;
    count++;
   
    // Loop to find the most significant
    // distinct digit of the next number
    for (i = msb + 1; i < 10; i++) {
        if (h[i] == 0) {
            next_num = i;
            break;
        }
    }
       
    // Condition to check if the number
    // is possible with the same number
    // of digits count
    if (next_num == -1){
        for (i = 1; i < msb; i++){
            if (h[i] == 0){
                next_num = i;
                count++;
                break;
            }
        }
    }
       
    // Condition to check if the desired
    // most significant distinct 
    // digit is found
    if (next_num > 0){
           
        // Loop to find the minimum next digit
        // which is not present in the number
        for (i = 0; i < 10; i++) {
            if (h[i] == 0) {
                msb = i;
                break;
            }
        }
           
        // Computation of the number 
        for (i = 1; i < count; i++) {
            next_num = ((next_num * 10) + msb);
        }
           
        // Condition to check if the number is 
        // greater than the given number
        if (next_num > n)
            document.write(next_num+ "\n");
        else
            document.write("Not Possible \n");
    }
    else{
        document.write("Not Possible \n");
    }
}
  
      
// Driver code
    
          let n = 2019;
    findNextNumber(n);
                                                                                
</script>

Output:

Time Complexity: O(logN)
Auxiliary Space: O(logN)

Find smallest number formed by inverting digits of given number N

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Find Next number having distinct digits from the given number N

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