16. String's Count

The problem can be found at the following link: Question Link

My Approach

To count the number of strings that can be formed using 'a', 'b', and 'c' under given conditions, I have used a mathematical formula that represents the total count of strings. The formula is derived based on the possible combinations of these characters.

1. The first term (1) represents the case where there is no 'b' or 'c' in the string.

2. The second term (2 * n) represents the case where 'b' appears once in the string.

3. The third term (n * (n - 1)) represents the case where 'b' appears twice in the string.

4. The fourth term ((n * (n - 1)) / 2) represents the case where 'c' appears once in the string.

5. The fifth term (n * (n - 1) * (n - 2)) / 2) represents the case where 'b' appears once and 'c' appears once in the string.

Time and Auxiliary Space Complexity

• Time Complexity : O(1)

• Auxiliary Space Complexity : O(1)

Code (C++)

long long int countStr(long long int n){
    return 1 + 2 * n + (n * (n - 1)) + ((n * (n - 1)) / 2) + (n * (n - 1) * (n - 2)) / 2;
}

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