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Distinct Subsequences II⚓︎

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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 10^9 + 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:

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

Example 2:

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

Example 3:

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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⚓︎

See reference (Chinese).

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class Solution {
public:
    int distinctSubseqII(string s) {
        const int MOD = 1e9 + 7;
        array<int, 26> count{};
        int all = 1, newAdd;

        for (const char& ch : s) {
            newAdd = (all - count[ch - 'a'] + MOD) % MOD;
            count[ch - 'a'] = (count[ch - 'a'] + newAdd) % MOD;
            all = (all + newAdd) % MOD;
        }
        return (all - 1 + MOD) % MOD;
    }
};
  • Time complexity: \(O(N)\);
  • Space complexity: \(O(26)\).