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Give an example of a type of binary tree for which the height is bound by a constant times log(n), n being the number of nodes. Define the type of tree you chose.

Which of the following sorting algorithms has a complexity of Q(n log(n)) in the best case?

Consider the image to the right: Below are summaries of three recent research papers that have studied neurons in the labeled structures. Based on your knowledge of brain structures, match the research with the most likely relevant brain structure in the image above. Sniffing is a motivated behavior displayed by nearly all terrestrial vertebrates. While sniffing is associated with acquiring and processing odors, sniffing is also intertwined with emotional (affective) and motivated behavior. A 2025 study reported sniffing involves neurons in this structure. [BC]   In 2022, researchers reported that a subset of neurons in this structure express FoxP2. Activating these neurons made male mice more likely to attack another male mouse when it was introduced into their cages. [D]   The intricate organization of circuits that store memory traces remains poorly understood. To address this knowledge gap, researchers used three-dimensional electron microscopy of neurons in this structure to uncover the structural correlates associative memory. They published their results in March of 2025. [A]

What is Theta(log n) for a binary tree with n nodes? 

A red-black tree is a binary search tree.

Which of the following notations can ignore the constant coefficient of the largest term in a function?

Which of the following algorithms is not Q(n) in all cases?

How many comparisons of individual characters between the pattern and the text are done when searching for the pattern “twin” in the text “tea for twins” using the brute force or naïve algorithm? Explain your answer.

Which of the following algorithms is Theta(log(n)) in the worst case?  

Give an example of a loop for which the number of iterations is Theta(sqrt(n)).