Geometry Basics Checkpoint

Reason through segment degeneracy, event ties, crossing closest pairs, and integer bounds.

Get every question correct to pass this checkpoint. You can review feedback, revise your answers, and submit again.

1. For A=(1,2), B=(5,2), C=(3,-1), what is orient(A,B,C)? Enter the signed integer.

2. All four orientation values for two closed segments are zero. What additional check decides whether they intersect?

Select one answer.

Their lengths must match At least one collinear endpoint must lie within the other segment’s inclusive coordinate bounds The result is always true The result is always false

3. What is the maximum overlap of inclusive intervals [2,4], [4,4], [4,6], [7,8]? Enter one integer.

4. An integer sweep uses +1 at start and -1 at end+1. For [1,2] and [3,4], both events occur at 3. Which handling avoids a false peak?

Select one answer.

Process the addition first and immediately record 2 Treat 3 as belonging to neither interval Apply the combined delta, or process removal before addition Always use start-before-end even with successor removals

5. A closest-pair split is [(-3,0),(-1,4)] and [(1,4),(6,0)]. What is the minimum squared distance over all four entries? Enter one integer.

6. A recursive closest-pair call returns its points sorted by y. What should the parent do with the two returned orders to keep the combine step linear?

Select one answer.

Merge them, then filter the strip without changing y order Sort the entire strip from scratch at every recursive node Compare the next seven points in original input order Discard the y order and keep only each child’s closest pair

7. The current squared distance bound is d2=25. A later strip point has squared vertical separation 25. Can it strictly improve the current answer?

Select one answer.

Yes, because horizontal separation is unknown Only if the two points have equal x No; vertical separation alone already reaches the bound Yes, whenever it crosses the split

8. Two allowed entries are (-10^9,-10^9) and (10^9,10^9). Which initialization safely permits the minimum squared distance to be found?

Select one answer.

best=0 best=the actual squared distance of that pair, computed in signed 64-bit arithmetic best=1<<62 best=the ordinary distance before squaring

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