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: 909 Output: 5 There are 5 substrings which recursively add to nine, 9, 90, 909, 09, 9
This article is about an optimized solution of problem stated below article :
Given a number as a string, find the number of contiguous subsequences which recursively add up to 9 | Set 1.
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.
Initialize an array d of size 10 with 0 d<-1 Initialize mod_sum = 0, continuous_zero = 0 for every character if character == '0'; continuous_zero++ else continuous_zero=0 compute mod_sum update result += d[mod_sum] update d[mod_sum]++ subtract those cases from result which have only 0s
If sum of digits from index i to j add up to 9, then sum(0 to i-1) = sum(0 to j) (mod 9).
We just have to remove cases which contain only zeroes.We can do this by remembring the no. of continuous zeroes upto this character(no. of these cases ending on this index) and subtracting them from the result.
Following is a simple implementation based on this approach.
The implementation assumes that there are can be leading 0’s in the input number.
8 5 3
Time Complexity of the above program is O(n). Program also supports leading zeroes.
This article is contributed by Gulab Arora. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. 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.
- Given a number as a string, find the number of contiguous subsequences which recursively add up to 9
- Number of subsequences in a string divisible by n
- Number of subsequences as "ab" in a string repeated K times
- Number of ways to partition a string into two balanced subsequences
- Minimum number of palindromic subsequences to be removed to empty a binary string
- String Range Queries to find the number of subsets equal to a given String
- Find number of times a string occurs as a subsequence in given string
- Number of subsequences with zero sum
- Number of Subsequences with Even and Odd Sum | Set 2
- Sum of all subsequences of a number
- Number of Subsequences with Even and Odd Sum
- Check if the product of every contiguous subsequence is different or not in a number
- Number of subsequences of the form a^i b^j c^k
- Number of palindromic subsequences of length k where k <= 3
- Number of K length subsequences with minimum sum