Consider an algorithm that aims to evaluate the validity of a string containing just the characters $\text{'}(\text{'},\text{'})\text{'},\text{'}\{\text{'},\text{'}\}\text{'},\text{'}[\text{'}$ and $\text{'}]\text{'}.$ The string is considered valid if:

Open brackets are closed by the same type of brackets.

Open brackets are closed in the correct order.

Each close bracket has a corresponding open bracket of the same type.

To solve this problem, you decide to use a stack with the following steps:

Initialize an empty stack.

Iterate through each character $c$ in the string.

If $c$ is an open bracket, push it onto the stack.

If $c$ is a close bracket, check if the stark is empty or the bracket on the top of the stack does not match the corresponding open bracket for $c.$ If either condition is true, return false. Otherwise, pop the top element from the stack.

After the iteration, if the stack is empty, return true, indicating the string is valid. Otherwise, return false.

Which of the following statements correctly evaluates the proposed algorithm?

The algorithm has a time complexity of $0(n^{{?}^{{?}^{?}}}2)$ due to the need to match each closing bracket with its corresponding opening bracket.

To solve this problem, you decide to use a stack with the following steps:

Initialize an empty stack.

Iterate through each character $c$ in the string.

If $c$ is an open bracket, push it onto the stack.

If $c$ is a close bracket, check if the stack is empty or the bracket on the top of the stack does not match the corresponding open bracket for $c.$ If either condition is true, return false. Otherwise, pop the top element from the stack.

After the iteration, if the stack is empty, return true, indicating the string is valid. Otherwise, return false.

Which of the following statements correctly evaluates the proposed algorithm?

The algorithm has a time complexity of $0(n^{{?}^{{?}^{?}}}2)$ due to the need to match each closing bracket with its corresponding opening bracket.

The algorithm efficiently evaluates the validity of the bracket sequence with a time complexity of $0(n),$ where $n$ is the length of the string.

The algorithm will return true for strings that contain standalone closing brackets, as it does not check for matching pairs.

The algorithm cannot correctly handle nested bracket sequences, resulting in false negatives for valid strings.