Minimum number with digits as 4 and 7 only and given sum

Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. 
What minimum lucky number has the sum of digits equal to n. 

Examples: 

Input : sum = 11
Output : 47
Sum of digits in 47 is 11 and 47
is the smallest number with given sum.

Input :  sum = 10
Output : -1    

The approach is based on below facts :  

1. Since digits are 4 and 7 only, given digit sum can be written as a*4 + b*7 = sum where a and b are some positive integers (greater than or equal to 0) representing number of 4s and 7s respectively.
2. Since we need to find minimum number, the result would always be in the form which has all 4s first, then all 7s, i.e., 44…477…7.

We basically need to find values of ‘a’ and ‘b’. We find these values using below facts:  

1. If sum is multiple of 4, then result has all 4s.
2. If sum is multiple of 7, then result has all 7s.
3. If sum is not multiple of 4 or 7, then we can subtract one of them till sum becomes multiple of other.

C++

// C++ program to find smallest number
// with given sum of digits.
#include <bits/stdc++.h>
using namespace std;

// Prints minimum number with given digit
// sum and only allowed digits as 4 and 7.
void findMin(int sum)
{
    int a = 0, b = 0;
    while (sum > 0)
    {
        // Cases where all remaining digits
        // are 4 or 7 (Remaining sum of digits
        // should be multiple of 4 or 7)
        if (sum % 7 == 0)
        {
            b++;
            sum -= 7;
        }
        else if (sum % 4 == 0)
        {
            a++;
            sum -= 4;
        }

        // If both 4s and 7s are there
        // in digit sum, we subtract a 4.
        else
        {
            a++;
            sum -= 4;
        }
    }

    if (sum < 0)
    {
        printf("-1n");
        return;
    }

    for (int i=0; i<a; i++)
        printf("4");

    for (int i=0; i<b; i++)
        printf("7");

    printf("n");
}

// Driver code
int main()
{
    findMin(15);
    return 0;
}

Java

// Java program to find smallest number
// with given sum of digits.
import java.io.*;

class GFG {

    // Prints minimum number with given digit
    // sum and only allowed digits as 4 and 7.
    static void findMin(int sum)
    {
        int a = 0, b = 0;
        while (sum > 0)
        {
            // Cases where all remaining digits
            // are 4 or 7 (Remaining sum of digits
            // should be multiple of 4 or 7)
            if (sum % 7 == 0)
            {
                b++;
                sum -= 7;
            }
            else if (sum % 4 == 0)
            {
                a++;
                sum -= 4;
            }

            // If both 4s and 7s are there
            // in digit sum, we subtract a 4.
            else
            {
                a++;
                sum -= 4;
            }
        }

        if (sum < 0)
        {
            System.out.print("-1n");
            return;
        }

        for (int i = 0; i < a; i++)
            System.out.print("4");

        for (int i = 0; i < b; i++)
            System.out.print("7");

        System.out.println();
    }

    // Driver code
    public static void main(String args[])
                            throws IOException
    {
        findMin(15);
    }
}

/* This code is contributed by Nikita tiwari.*/

Python3

# Python program to find smallest number
# with given sum of digits.

# Prints minimum number with given digit
# sum and only allowed digits as 4 and 7.
def findMin(s):
    a, b = 0, 0
    while (s > 0):

        # Cases where all remaining digits
        # are 4 or 7 (Remaining sum of digits
        # should be multiple of 4 or 7)
        if (s % 7 == 0):
            b += 1
            s -= 7
        else if (s % 4 == 0):
            a += 1
            s -= 4

        # If both 4s and 7s are there
        # in digit sum, we subtract a 4.
        else:
            a += 1
            s -= 4

    string = ""
    if (s < 0):
        string = "-1"
        return string


    string += "4" * a
    string += "7" * b

    return string

# Driver code
print(findMin(15))

# This code is contributed by Sachin Bisht

C#

// C# program to find smallest number
// with given sum of digits.
using System;

class GFG {

    // Prints minimum number with given digit
    // sum and only allowed digits as 4 and 7.
    static void findMin(int sum)
    {
        int a = 0, b = 0;
        while (sum > 0)
        {

            // Cases where all remaining digits
            // are 4 or 7 (Remaining sum of digits
            // should be multiple of 4 or 7)
            if (sum % 7 == 0)
            {
                b++;
                sum -= 7;
            }
            else if (sum % 4 == 0)
            {
                a++;
                sum -= 4;
            }

            // If both 4s and 7s are there
            // in digit sum, we subtract a 4.
            else
            {
                a++;
                sum -= 4;
            }
        }

        if (sum < 0)
        {
            Console.Write("-1n");
            return;
        }

        for (int i = 0; i < a; i++)
            Console.Write("4");

        for (int i = 0; i < b; i++)
            Console.Write("7");

        Console.WriteLine();
    }

    // Driver code
    public static void Main()
    {
        findMin(15);
    }
}

// This code is contributed by Nitin Mittal.

PHP

<?php
// PHP program to find smallest number
// with given sum of digits.

// Prints minimum number with given digit
// sum and only allowed digits as 4 and 7.
function findMin($sum)
{
    $a = 0;
    $b = 0;
    while ($sum > 0)
    {

        // Cases where all remaining digits
        // are 4 or 7 (Remaining sum of digits
        // should be multiple of 4 or 7)
        if ($sum % 7 == 0)
        {
            $b++;
            $sum -= 7;
        }
        else if ($sum % 4 == 0)
        {
            $a++;
            $sum -= 4;
        }

        // If both 4s and 7s are there
        // in digit sum, we subtract a 4.
        else
        {
            $a++;
            $sum -= 4;
        }
    }

    if ($sum < 0)
    {
        echo("-1n");
        return;
    }

    for ($i = 0; $i < $a; $i++)
        echo("4");

    for ($i = 0; $i < $b; $i++)
        echo("7");

    echo("\n");
}

    // Driver code
    findMin(15);

// This code is contributed by nitin mittal
?>

Javascript

<script>

// Javascript program to find smallest number
// with given sum of digits.

// Prints minimum number with given digit
// sum and only allowed digits as 4 and 7.
function findMin(sum)
{
    var a = 0, b = 0;

    while (sum > 0)
    {

        // Cases where all remaining digits
        // are 4 or 7 (Remaining sum of digits
        // should be multiple of 4 or 7)
        if (sum % 7 == 0)
        {
            b++;
            sum -= 7;
        }
        else if (sum % 4 == 0)
        {
            a++;
            sum -= 4;
        }

        // If both 4s and 7s are there
        // in digit sum, we subtract a 4.
        else
        {
            a++;
            sum -= 4;
        }
    }

    if (sum < 0)
    {
        document.write("-1n");
        return;
    }

    for(i = 0; i < a; i++)
        document.write("4");

    for(i = 0; i < b; i++)
        document.write("7");

    document.write();
}

// Driver code
findMin(15);

// This code is contributed by todaysgaurav

</script>

Output: 

447

Time Complexity: O(sum).