Given a number as a string, write a function to find the number of substrings (or contiguous subsequences) of the given string which recursively add up to 9.
For example digits of 729 recursively add to 9,
7 + 2 + 9 = 18
Recur for 18
1 + 8 = 9
Input: 4189 Output: 3 There are three substrings which recursively add to 9. The substrings are 18, 9 and 189. Input: 999 Output: 6 There are 6 substrings which recursively add to 9. 9, 99, 999, 9, 99, 9
All digits of a number recursively add up to 9, if only if the number is multiple of 9. We basically need to check for s%9 for all substrings s. One trick used in below program is to do modular arithmetic to avoid overflow for big strings.
Following is a simple implementation based on this approach. The implementation assumes that there are no leading 0’s in input number.
Time complexity of the above program is O(n2). Please let me know if there is a better solution.