What is the smallest possible depth of a leaf in a decision tree for a comparison sort? Name a sorting technique to which this smallest depth would correspond.

The smallest possible depth of a leaf in a decision tree for a comparison sort is θ(log n), where n is the number of elements being sorted. This depth corresponds to the best-case scenario in terms of the number of comparisons needed to sort the elements.

A sorting technique that can achieve this best-case depth is Merge Sort. Merge Sort is a comparison-based sorting algorithm that divides the array into halves, recursively sorts each half, and then merges the sorted halves. The depth of the decision tree in Merge Sort is proportional to log⁡𝑛logn because the algorithm repeatedly divides the array in half, leading to a balanced binary recursion tree where the height (or depth) of the tree is log⁡𝑛logn.