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.
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