Consider a graph where a vertex `u` currently has the smallest tentative distance and is about to be settled. A different path to another unsettled vertex `v` goes through one negative-weight edge later in the path. Which statement best explains the danger?

In the priority-queue implementation of Dijkstra’s algorithm, which of the following operation counts are valid upper bounds? Select all that apply.

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?

If a set of open intervals has depth `d`, then every valid interval-partitioning schedule needs at least `d` rooms.

Suppose a student proposes the following interval-scheduling rule: “At each step, choose the interval that conflicts with the fewest remaining intervals; if tied, break ties by shortest length.” Which of the following are valid critiques? Select all that apply.

A flawed closest-pair implementation recursively solves the left and right halves, sets `delta` to the better of those two answers, forms the strip, and then compares every strip point to the next 20 points above it. Which statement is the best diagnosis?

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

If your only goal is to find the shortest path from source `s` to one target vertex `v`, when is it safe to stop Dijkstra’s algorithm?

In interval scheduling with one shared resource, which greedy rule is guaranteed to produce a maximum-size compatible set of intervals?

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