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: 6
Explanation: 
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: 3
Explanation: 
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: 0
Explanation: There are no vowels in any substring of "ltcd".

Example 4:

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

Constraints:

• 1 <= word.length <= 105
• word consists of lowercase English letters.

Solution: Math

For a vowel at index i,
we can choose 0, 1, … i as starting point
choose i, i+1, …, n -1 as end point.
There will be (i – 0 + 1) * (n – 1 – i + 1) possible substrings that contains word[i].

Time complexity: O(n)
Space complexity: O(1)

class Solution {
public:
  long long countVowels(string word) {
    const long long n = word.size();
    long long ans = 0;
    for (long long i = 0; i < n; ++i) {
      switch (word[i]) {
        case 'a':
        case 'e':
        case 'i':
        case 'o':
        case 'u':
          ans += (i + 1) * (n - 1 - i + 1);
          break;
      }
    }
    return ans;
  }
};

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