1641. Count Sorted Vowel Strings

Description

Given an integer n, return the number of strings of length n that consist only of vowels (a, e, i, o, u) and are lexicographically sorted.

A string s is lexicographically sorted if for all valid i, s[i] is the same as or comes before s[i+1] in the alphabet.

 

Example 1:

Input: n = 1
Output: 5
Explanation: The 5 sorted strings that consist of vowels only are ["a","e","i","o","u"].

Example 2:

Input: n = 2
Output: 15
Explanation: The 15 sorted strings that consist of vowels only are
["aa","ae","ai","ao","au","ee","ei","eo","eu","ii","io","iu","oo","ou","uu"].
Note that "ea" is not a valid string since 'e' comes after 'a' in the alphabet.

Example 3:

Input: n = 33
Output: 66045

 

Constraints:

• 1 <= n <= 50 

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(n*5)
• Space complexity: O(5)

 

JavaScript

/**
 * @param {number} n
 * @return {number}
 */
const countVowelStrings = function (n) {
  const dp = Array.from({length: 5}).fill(1);

  for (let count = 2; count <= n; count++) {
    let sum = 0;
    for (let index = 0; index < 5; index++) {
      sum += dp[index];
      dp[index] = sum;
    }
  }
  return dp.reduce((result, count) => result + count);
};