Given a integer represented as a string, we need to get the sum of all possible substrings of this string.
Input : num = “1234” Output : 1670 Sum = 1 + 2 + 3 + 4 + 12 + 23 + 34 + 123 + 234 + 1234 = 1670 Input : num = “421” Output : 491 Sum = 4 + 2 + 1 + 42 + 21 + 421 = 491
We can solve this problem using dynamic programming. We can write summation of all substrings on basis of digit at which they are ending in that case,
Sum of all substrings = sumofdigit + sumofdigit + sumofdigit … + sumofdigit[n-1] where n is length of string.
Where sumofdigit[i] stores sum of all substring ending at ith index digit, in above example,
Example : num = "1234" sumofdigit = 1 = 1 sumofdigit = 2 + 12 = 14 sumofdigit = 3 + 23 + 123 = 149 sumofdigit = 4 + 34 + 234 + 1234 = 1506 Result = 1670
Now we can get the relation between sumofdigit values and can solve the question iteratively. Each sumofdigit can be represented in terms of previous value as shown below,
For above example, sumofdigit = 4 + 34 + 234 + 1234 = 4 + 30 + 4 + 230 + 4 + 1230 + 4 = 4*4 + 10*(3 + 23 +123) = 4*4 + 10*(sumofdigit) In general, sumofdigit[i] = (i+1)*num[i] + 10*sumofdigit[i-1]
Using above relation we can solve the problem in linear time. In below code a complete array is taken to store sumofdigit, as each sumofdigit value requires just previous value, we can solve this problem without allocating complete array also.
Time Complexity : O(n) where n is length of input string.
Auxiliary Space : O(n)
This article is contributed by Utkarsh Trivedi. 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.
- Sum of all substrings of a string representing a number | Set 2 (Constant Extra Space)
- Number of substrings of a string
- Number of even substrings in a string of digits
- Number of substrings of one string present in other
- Number of substrings with odd decimal value in a binary string
- Number of substrings divisible by 6 in a string of integers
- Given a binary string, count number of substrings that start and end with 1.
- Count the number of vowels occurring in all the substrings of given string
- Rearrange the string to maximize the number of palindromic substrings
- Replace two substrings (of a string) with each other
- Different substrings in a string that start and end with given strings
- Program to print all substrings of a given string
- Lexicographical concatenation of all substrings of a string
- Count of substrings of a binary string containing K ones
- Split the string into substrings using delimiter