Challenge: Collecting Signatures

Solve the Collecting Signatures Problem.

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This problem is similar to the Covering Segments by Points Problem.

Covering Segments by Points

Find the minimum number of points needed to cover all given segments on a line.

Input: A sequence of nn segments [l1,r1],...,[ln,rn][l_{1} , r_{1} ],...,[l_{n}, r_{n}] on a line.
Output: A set of points of minimum size such that each segment [li,ri][l_{i}, r_{i}] contains a point, i.e., there exists a point xx from this set such that lixril_{i} ≤ x ≤ r_{i}.

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