Formatted question description: https://leetcode.ca/all/2063.html

# 2063. Vowels of All Substrings (Medium)

Given a string `word`

, return *the sum of the number of vowels (*

`'a'`

, `'e'`

*,*

`'i'`

*,*

`'o'`

*, and*

`'u'`

*)*

*in every substring of*

`word`

.A **substring** is a contiguous (non-empty) sequence of characters within a string.

**Note:** Due to the large constraints, the answer may not fit in a signed 32-bit integer. Please be careful during the calculations.

**Example 1:**

Input:word = "aba"Output:6Explanation:All possible substrings are: "a", "ab", "aba", "b", "ba", and "a". - "b" has 0 vowels in it - "a", "ab", "ba", and "a" have 1 vowel each - "aba" has 2 vowels in it Hence, the total sum of vowels = 0 + 1 + 1 + 1 + 1 + 2 = 6.

**Example 2:**

Input:word = "abc"Output:3Explanation:All possible substrings are: "a", "ab", "abc", "b", "bc", and "c". - "a", "ab", and "abc" have 1 vowel each - "b", "bc", and "c" have 0 vowels each Hence, the total sum of vowels = 1 + 1 + 1 + 0 + 0 + 0 = 3.

**Example 3:**

Input:word = "ltcd"Output:0Explanation:There are no vowels in any substring of "ltcd".

**Example 4:**

Input:word = "noosabasboosa"Output:237Explanation:There are a total of 237 vowels in all the substrings.

**Constraints:**

`1 <= word.length <= 10`

^{5}`word`

consists of lowercase English letters.

**Similar Questions**:

## Solution 1.

If `s[i]`

is vowel, there are `(i + 1) * (N - i)`

substrings that contain `s[i]`

where `i + 1`

and `N - i`

are the number of possible left and right end points of the substrings, respectively.

```
// OJ: https://leetcode.com/problems/vowels-of-all-substrings/
// Time: O(N)
// Space: O(1)
class Solution {
bool isVowel(char c) {
return c == 'a' || c == 'e' || c == 'i' || c == 'o' || c == 'u';
};
public:
long long countVowels(string s) {
long long N = s.size(), ans = 0;
for (long long i = 0; i < N; ++i) {
if (!isVowel(s[i])) continue;
ans += (i + 1) * (N - i);
}
return ans;
}
};
```

## Discuss

https://leetcode.com/problems/vowels-of-all-substrings/discuss/1563756/C%2B%2B-O(N)-Time