How to find the smallest number with given digit sum s and number of digits d?
Input : s = 9, d = 2 Output : 18 There are many other possible numbers like 45, 54, 90, etc with sum of digits as 9 and number of digits as 2. The smallest of them is 18. Input : s = 20, d = 3 Output : 299
A Simple Solution is to consider all m digit numbers and keep track of minimum number with digit sum as s. A close upper bound on time complexity of this solution is O(10m).
There is a Greedy approach to solve the problem. The idea is to one by one fill all digits from rightmost to leftmost (or from least significant digit to most significant).
We initially deduct 1 from sum s so that we have smallest digit at the end. After deducting 1, we apply greedy approach. We compare remaining sum with 9, if remaining sum is more than 9, we put 9 at the current position, else we put the remaining sum. Since we fill digits from right to left, we put the highest digits on the right side. Below is implementation of the idea.
Smallest number is 18
Time Complexity of this solution is O(m).
We will soon be discussing approach to find the largest possible number with given sum of digits and number of digits.
This article is contributed by Vaibhav Agarwal. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Find smallest number with given number of digits and sum of digits under given constraints
- Smallest number with given sum of digits and sum of square of digits
- Find the Largest number with given number of digits and sum of digits
- Smallest odd number with even sum of digits from the given number N
- Find the smallest number whose digits multiply to a given number n
- Find smallest possible Number from a given large Number with same count of digits
- Find smallest number formed by inverting digits of given number N
- Find the smallest number whose sum of digits is N
- Find the smallest positive number which can not be represented by given digits
- Smallest number with sum of digits as N and divisible by 10^N
- Smallest multiple of a given number made of digits 0 and 9 only
- Smallest number by rearranging digits of a given number
- Get the kth smallest number using the digits of the given number
- Immediate smallest number after re-arranging the digits of a given number
- Smallest number greater than or equal to X whose sum of digits is divisible by Y
- Smallest number whose sum of digits is square of N
- Smallest number greater than Y with sum of digits equal to X
- Sum of the digits of square of the given number which has only 1's as its digits
- Number formed by deleting digits such that sum of the digits becomes even and the number odd
- Numbers with sum of digits equal to the sum of digits of its all prime factor