940. Distinct Subsequences II

Problem Link

Description

---

Given a string s, return the number of distinct non-empty subsequences of s. Since the answer may be very large, return it modulo 109 + 7.

A subsequence of a string is a new string that is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (i.e., "ace" is a subsequence of "abcde" while "aec" is not.

 

Example 1:

Input: s = "abc"
Output: 7
Explanation: The 7 distinct subsequences are "a", "b", "c", "ab", "ac", "bc", and "abc".

Example 2:

Input: s = "aba"
Output: 6
Explanation: The 6 distinct subsequences are "a", "b", "ab", "aa", "ba", and "aba".

Example 3:

Input: s = "aaa"
Output: 3
Explanation: The 3 distinct subsequences are "a", "aa" and "aaa".

 

Constraints:

• 1 <= s.length <= 2000
• s consists of lowercase English letters.

Solution

---

Python3

class Solution:
    def distinctSubseqII(self, s: str) -> int:
        n = len(s)
        M = 10 ** 9 + 7
        res = 0
        dp = [1] * n
        
        for i in range(n):
            for j in range(i):
                if s[i] != s[j]:
                    dp[i] += dp[j]
                    dp[i] %= M
            
            res += dp[i]
            res %= M
        
        return res