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.
Input: S = 25, D = 4
The difference between maximum digit 7 and minimum digit 6 is 1.
Input: S = 27, D = 3
- 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:
Time Complexity: O(d)
Auxiliary Space: O(1)
- Find smallest number with given number of digits and sum of digits
- Find the smallest number whose digits multiply to a given number n
- Find the kth smallest number with sum of digits as m
- Smallest number with given sum of digits and sum of square of digits
- Find the smallest positive number which can not be represented by given digits
- Find the average of k digits from the beginning and l digits from the end of the given number
- Find the Largest number with given number of digits and sum of digits
- Smallest number by rearranging digits of a given number
- Immediate smallest number after re-arranging the digits of a given number
- Smallest odd digits number not less than N
- Smallest even digits number not less than N
- Smallest odd number with N digits
- Smallest Even number with N digits
- Smallest number with at least n digits in factorial
- Smallest number with sum of digits as N and divisible by 10^N
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