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

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  • Difficulty Level : Hard
  • Last Updated : 21 Sep, 2022
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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 <bits/stdc++.h>
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




<script>
// Javascript 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
function findNumber(s, d)
{
 
    // To store the final number
    var num = [] ;
 
    // To store the value that is evenly
    // distributed among all the digits
    var val = parseInt(s / d);
 
    // To store the remaining sum that still
    // remains to be distributed among d digits
    var 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 (var i = 1; i <= d - rem; i++)
    {
     
       // num = num.concat(toString(val));
       num.push(val.toString());
    }
 
    // In the last rem digits one is added to
    // the value obtained by equal distribution
    if (rem != 0)
    {
        val++;
        for (var i = d - rem + 1; i <= d; i++)
        {
            // num = num + toString(val);
             num.push(val.toString());
        }
    }
 
    return num;
}
 
var s = 25, d = 4;
var n=findNumber(s, d);
for(var i = 0; i < n.length; i++)
{
    document.write(n[i]);
}
 
// This code is contributed by SoumikMondal
</script>

Output: 

6667

 

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


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