# Find smallest number with given number of digits and sum of digits under given constraints

Given two integers S and D, the task is to find the number having D number of digits and the sum of its digits as S such that the difference between the maximum and the minimum digit in the number is as minimum as possible. If multiple such numbers are possible, print the smallest number.
Examples:

Input: S = 25, D = 4
Output: 6667
The difference between maximum digit 7 and minimum digit 6 is 1.

Input: S = 27, D = 3
Output: 999

Approach:

• Finding smallest number for given number of digits and sum is already discussed in this article.
• In this article, the idea is to minimize the difference between the maximum and minimum digit in the required number. Therefore, the sum s should be evenly distributed among d digits.
• If the sum is evenly distributed then the difference can be at most 1. The difference is zero when sum s is divisible by d. In that case, each of the digits has the same value equal to s/d.
• The difference is one when sum s is not divisible by d. In that case, after each digit is assigned value s/d, s%d sum value is still left to be distributed.
• As the smallest number is required, this remaining value is evenly distributed among last s%d digits of the number, i.e., last s%d digits in the number are incremented by one.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `// Function to find the number having` `// sum of digits as s and d number of` `// digits such that the difference between` `// the maximum and the minimum digit` `// the minimum possible` `string findNumber(``int` `s, ``int` `d)` `{` `    ``// To store the final number` `    ``string num = ``""``;`   `    ``// To store the value that is evenly` `    ``// distributed among all the digits` `    ``int` `val = s / d;`   `    ``// To store the remaining sum that still` `    ``// remains to be distributed among d digits` `    ``int` `rem = s % d;`   `    ``int` `i;`   `    ``// rem stores the value that still remains` `    ``// to be distributed` `    ``// To keep the difference of digits minimum` `    ``// last rem digits are incremented by 1` `    ``for` `(i = 1; i <= d - rem; i++) {` `        ``num = num + to_string(val);` `    ``}`   `    ``// In the last rem digits one is added to` `    ``// the value obtained by equal distribution` `    ``if` `(rem) {` `        ``val++;` `        ``for` `(i = d - rem + 1; i <= d; i++) {` `            ``num = num + to_string(val);` `        ``}` `    ``}`   `    ``return` `num;` `}`   `// Driver function` `int` `main()` `{` `    ``int` `s = 25, d = 4;`   `    ``cout << findNumber(s, d);`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the approach` `import` `java.util.*;`   `class` `GFG` `{`   `// Function to find the number having` `// sum of digits as s and d number of` `// digits such that the difference between` `// the maximum and the minimum digit` `// the minimum possible` `static` `String findNumber(``int` `s, ``int` `d)` `{` `    ``// To store the final number` `    ``String num = ``""``;`   `    ``// To store the value that is evenly` `    ``// distributed among all the digits` `    ``int` `val = s / d;`   `    ``// To store the remaining sum that still` `    ``// remains to be distributed among d digits` `    ``int` `rem = s % d;`   `    ``int` `i;`   `    ``// rem stores the value that still remains` `    ``// to be distributed` `    ``// To keep the difference of digits minimum` `    ``// last rem digits are incremented by 1` `    ``for` `(i = ``1``; i <= d - rem; i++)` `    ``{` `        ``num = num + String.valueOf(val);` `    ``}`   `    ``// In the last rem digits one is added to` `    ``// the value obtained by equal distribution` `    ``if` `(rem > ``0``) ` `    ``{` `        ``val++;` `        ``for` `(i = d - rem + ``1``; i <= d; i++)` `        ``{` `            ``num = num + String.valueOf(val);` `        ``}` `    ``}` `    ``return` `num;` `}`   `// Driver function` `public` `static` `void` `main(String[] args)` `{` `    ``int` `s = ``25``, d = ``4``;`   `    ``System.out.print(findNumber(s, d));` `}` `}`   `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 implementation of the approach `   `# Function to find the number having ` `# sum of digits as s and d number of ` `# digits such that the difference between ` `# the maximum and the minimum digit ` `# the minimum possible ` `def` `findNumber(s, d) :`   `    ``# To store the final number ` `    ``num ``=` `""`   `    ``# To store the value that is evenly ` `    ``# distributed among all the digits ` `    ``val ``=` `s ``/``/` `d`   `    ``# To store the remaining sum that still ` `    ``# remains to be distributed among d digits ` `    ``rem ``=` `s ``%` `d`   `    ``# rem stores the value that still remains ` `    ``# to be distributed ` `    ``# To keep the difference of digits minimum ` `    ``# last rem digits are incremented by 1 ` `    ``for` `i ``in` `range``(``1``, d ``-` `rem ``+` `1``) :` `        ``num ``=` `num ``+` `str``(val)`   `    ``# In the last rem digits one is added to ` `    ``# the value obtained by equal distribution ` `    ``if` `(rem) :` `        ``val ``+``=` `1` `        ``for` `i ``in` `range``(d ``-` `rem ``+` `1``, d ``+` `1``) :` `            ``num ``=` `num ``+` `str``(val)`   `    ``return` `num`   `# Driver function ` `if` `__name__ ``=``=` `"__main__"` `: `   `    ``s ``=` `25` `    ``d ``=` `4`   `    ``print``(findNumber(s, d))`   `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach` `using` `System;`   `class` `GFG ` `{`   `    ``// Function to find the number having` `    ``// sum of digits as s and d number of` `    ``// digits such that the difference between` `    ``// the maximum and the minimum digit` `    ``// the minimum possible` `    ``static` `String findNumber(``int` `s, ``int` `d)` `    ``{` `        ``// To store the readonly number` `        ``String num = ``""``;`   `        ``// To store the value that is evenly` `        ``// distributed among all the digits` `        ``int` `val = s / d;`   `        ``// To store the remaining sum that still` `        ``// remains to be distributed among d digits` `        ``int` `rem = s % d;`   `        ``int` `i;`   `        ``// rem stores the value that still remains` `        ``// to be distributed` `        ``// To keep the difference of digits minimum` `        ``// last rem digits are incremented by 1` `        ``for` `(i = 1; i <= d - rem; i++) ` `        ``{` `            ``num = num + String.Join(``""``, val);` `        ``}`   `        ``// In the last rem digits one is added to` `        ``// the value obtained by equal distribution` `        ``if` `(rem > 0)` `        ``{` `            ``val++;` `            ``for` `(i = d - rem + 1; i <= d; i++)` `            ``{` `                ``num = num + String.Join(``""``, val);` `            ``}` `        ``}` `        ``return` `num;` `    ``}`   `    ``// Driver function` `    ``public` `static` `void` `Main(String[] args)` `    ``{` `        ``int` `s = 25, d = 4;`   `        ``Console.Write(findNumber(s, d));` `    ``}` `}`   `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output:

`6667`

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

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