# 23. Count Sorted Vowel Strings

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
```

### Solution: (Using Backtracking to generate all possible strings and counting length)

## Solution: (DP)

**Approach:**\
**Count the no of ways from 'u' in each case and check the pattern.**

```cpp
class Solution
{
public:
    int countVowelStrings(int n)
    {
        
        //No of ways when n = 1 
        vector<int> dp{5, 4, 3, 2, 1, 0};
        
        // for higher n
        // the number of ways(i) = number of ways(i) + number of ways(i+1)
        
        for (int i = 1; i < n; i++)
        {
            for (int j = 4; j >= 0; j--)
            {
                dp[j] += dp[j + 1];
            }
        }

        return dp[0];
    }
};
```

