# Find Next number having distinct digits from the given number N

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 ` `using` `namespace` `std;`   `// Function to find the` `// next distinct digits number` `void` `findNextNumber(``int` `n)` `{` `    ``int` `h = { 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

 `// C implementation to find` `//next distinct digits number` `#include `   `// Function to find the` `// next distinct digits number` `void` `findNextNumber(``int` `n)` `{` `    ``int` `h = { 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#

 `// 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``;` `        ``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

 ``

Output:

`3333`

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

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