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g0001_0100.s0022_generate_parentheses.complexity.md Maven / Gradle / Ivy

**Time Complexity (Big O Time):**

The time complexity of this program can be described as O(2^n), where n is the input value. This is because, in the worst case, the program generates all possible combinations of parentheses for a given value of `n`. For each position, it can either add an open parenthesis '(' or a close parenthesis ')'. Since there are 2 choices (open or close) for each position, and there are a total of 2n positions, the total number of combinations is 2^(2n), which simplifies to O(2^n) in big O notation.

**Space Complexity (Big O Space):**

The space complexity of this program is O(n), where n is the input value. This space is used for storing the current combination of parentheses in the `StringBuilder` `sb` and also for storing the final list of valid combinations in the `List str`. In each recursive call to the `generate` method, a new character is appended to the `StringBuilder`, and the `StringBuilder` is modified. However, the space used for the `StringBuilder` is not accumulated across recursive calls because characters are added and removed. Therefore, the space complexity is mainly determined by the depth of the recursion, which is proportional to the value of `n`.

In summary, the time complexity of the provided program is O(2^n), and the space complexity is O(n), where n is the input value representing the number of pairs of parentheses to generate.