I'm trying to count the number of subsequences of a long string. Suppose we have a string S, we have to count the number of distinct subsequences of S. The result can be large, so we will return the answer modulo 10^9 + 7. Given a string consisting of lower case English alphabets, the task is to find the number of distinct subsequences of the string. It will be useful to be able to compute the number of new distinct subsequences in a string; to do so we modify a result from Elzinga et al. (2008). Given a string S and a string T, count the number of distinct subsequences of T in S. A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. Pr[Sn =Tn]. 2. The problem of counting distinct subsequences is easy if all characters of input string are distinct. Case 1: When A[i-1] != B[j-1] Here, when current character of A is not equal to current character of B, we will not be able to increase the number of distinct subsequences. As an example, take the sequence $1,2,3$ and try to find all the subsequences … BANANA -> B, A, N, BA, BN, AA, NN, NA, BAN, BAA, BNA, BNN, ANA, AAA, NAN, NNA, etc There's the horribly inefficient way, which is to iterate all of the substrings and keep hash of some sort to keep track of the ones already seen. 1. Given a string S and a string T, count the number of distinct subsequences of T in S. A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. It is the same as finding the number of subsets of a set, the order carries over from the original sequence to the subsequence. Lemma 2.5(Elzinga,Rahmann,andWang). Input Format A String Output Format A number Constraints 1 = length of string = 60 Sample Input abc Sample Output 7 You have to print the count of distinct and non-empty subsequences of the given string. The count is equal to n C 0 + n C 1 + n C 2 + … n C n = 2 n. How to count distinct subsequences when there can be repetition in input string? Suppose we have strings S and T. We have to count number of distinct sequences of S which is equal to T. We know that a subsequence of a string is a new string which is formed from the original string by removing some (can be none) of the characters without disturbing the relative positions of the remaining characters. Note -> String contains only lowercase letters. Note: Answer can be very large, so, ouput will be answer modulo 10 9 … Given a string S and a string T, count the number of distinct subsequences of T in S. A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. e.g. [Leetcode] Distinct Subsequences Given a string S and a string T , count the number of distinct subsequences of T in S . A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. You are given a string. Given a string S and a string T, count the number of distinct subsequences of T in S. A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. Distinct Subsequences.