940. Distinct Subsequences II

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.

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(n * 26)
• Space complexity: O(26)

 

JavaScript

/**
 * @param {string} s
 * @return {number}
 */
const distinctSubseqII = function (s) {
  const MODULO = 10 ** 9 + 7;
  const BASE_CODE = 'a'.charCodeAt(0);
  const dp = Array.from({length: 26}).fill(0);
  const accumulate = nums => nums.reduce((sum, num) => sum + num);

  for (const letter of s) {
    const code = letter.charCodeAt(0) - BASE_CODE;

    dp[code] = (accumulate(dp) + 1) % MODULO;
  }
  return accumulate(dp) % MODULO;
};