Why is pivot quality central to the running time of partition-based selection?

Which statements correctly compare shortest-path trees and minimum spanning trees? Select all that apply.

In the deterministic linear-time selection algorithm, after choosing the pivot recursively from the medians of groups of 5, the algorithm makes at most one recursive call on one side of the partition in addition to the pivot-selection recursion.

In the closest-pair algorithm in 2 dimensions, why is it not sufficient to recurse on the left half and right half and simply take the smaller of the two distances?

In deterministic selection with groups of 5, which parts are essential to obtaining the worst-case recurrence `T(n) = T(n/5) + T(7n/10) + O(n)`? Select all that apply.

After partitioning around pivot `w`, if `k > |S_(w)` with adjusted rank `k – |S_

Which data structure is the standard way to implement the efficient interval-partitioning algorithm so that each lecture can be assigned in `O(log n)` time after sorting?

Suppose a pivot `w` partitions the input into `S_(w)`, with `|S_

Consider the ternary plot in Q22. If we change the significance level from 0.05 to 0.0001 and keep everything else unchanged, how will the two blue curves move?

Consider the ternary plot in Q22. Should we reject the null hypothesis?