Given a binary string of length N and an integer K, we need to find out how many substrings of this string are exist which contains exactly K ones.
Input : s = “10010” K = 1 Output : 9 The 9 substrings containing one 1 are, “1”, “10”, “100”, “001”, “01”, “1”, “10”, “0010” and “010”
In this problem we need to find count of substrings which contains exactly K ones or in other words sum of digits in those substring is K. We first create a prefix sum array and loop over that and stop when sum value is greater than or equal to K. Now if sum at current index is (K + a) then we know that substring sum, from all those indices where sum is (a), till current index will be K, so count of indices having sum (a), will be added to result. This procedure is explained with an example below,
string s = “100101” K = 2 prefix sum array = [1, 1, 1, 2, 2, 3] So, at index 3, we have prefix sum 2, Now total indices from where sum is 2, is 1 so result = 1 Substring considered = [“1001”] At index 4, we have prefix sum 2, Now total indices from where sum is 2, is 1 so result = 2 Substring considered = [“1001”, “10010”] At index 5, we have prefix sum 3, Now total indices from where sum is 2, is 3 so result = 5 Substring considered = [“1001”, “10010”, “00101”, “0101”, “101”]
So we need to track two things, prefix sum and frequency of particular sum. In below code, instead of storing complete prefix sum, only prefix sum at current index is stored using one variable and frequency of sums in stored in an array. Total time complexity of solution is 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 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.
- Given a binary string, count number of substrings that start and end with 1.
- Number of substrings with odd decimal value in a binary string
- Counting even decimal value substrings in a binary string
- Split the binary string into substrings with equal number of 0s and 1s
- Count number of substrings of a string consisting of same characters
- Count the number of vowels occurring in all the substrings of given string
- Queries to find the count of vowels in the substrings of the given string
- Count of distinct substrings of a string using Suffix Trie
- Count of distinct substrings of a string using Suffix Array
- Count of 1-bit and 2-bit characters in the given binary string
- Count of cyclic permutations having XOR with other binary string as 0
- Count of non-overlapping sub-strings "101" and "010" in the given binary string
- Count of operations to make a binary string"ab" free
- Count all substrings having character K
- Count substrings with same first and last characters