A binary search tree $T$ contains $n$ distinct elements. What is the time complexity of picking an element in $T$ that is smaller than the maximum element in $T$?

Let $T$ be a binary search tree with $n \ge 2$ distinct elements with root $R$.

We need to find any element that is strictly smaller than the maximum element in $T$:

1. If $R$ has a left child (or left subtree): Any node in the left subtree is smaller than $R$. Therefore, the left child of $R$ is strictly smaller than $R$, which means it must be strictly smaller than the maximum element of $T$.

2. If $R$ does not have a left child: Since $n \ge 2$, $R$ must have a right child. All nodes in the right subtree are strictly greater than $R$. Thus, $R$ is strictly smaller than all elements in its right subtree, including the maximum element.

In either case, we only need to inspect the root and potentially its left child, which takes a constant number of operations: $\Theta(1)$.

Therefore, the time complexity is $\Theta(1)$ (Option D).