Intervals — Reasoning Check

1. After merging closed intervals [[1,4],[2,3],[6,7],[7,9]], how many intervals remain? Enter one integer.

2. During merging, current=[1,8] and next=[3,4]. Which update preserves the active union?

Select one answer.

Emit [1,8] immediately because the ends are different. Keep current.end=8 by taking max(current.end,next.end). Set current.end=4 because next is later in start order.

3. For scheduling intervals [[1,2],[2,4],[1,4],[4,5]], where touching endpoints are compatible, what is the minimum removal count? Enter one integer.

4. You need the fewest arrows to hit closed balloon intervals [[1,5],[2,3],[4,6]]. Why is choosing the earliest-ending balloon's end 3 safe?

Select one answer.

Sorting by end means all balloons contain the first chosen endpoint. The longest balloon must be selected first because its midpoint hits every overlap. Any arrow hitting [2,3] can move right to 3 without losing any remaining balloon it already hit.

5. How many output intervals result from intersecting A=[[0,2],[5,7]] with B=[[1,5],[6,8]]? Enter one integer.

6. The current intersection candidates are A[i]=[1,4] and B[j]=[2,6], with both input lists sorted and internally disjoint. Which advance is justified after recording [2,4]?

Select one answer.

Advance j, because B[j] has already contributed one intersection. Advance i, because A[i] ends before any later B interval can begin. Advance both, because every interval contributes at most one intersection.