Challenge: 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 $n$ segments $[l_{1} , r_{1} ],...,[l_{n}, r_{n}]$ on a line.
Output: A set of points of minimum size such that each segment $[l_{i}, r_{i}]$ contains a point, i.e., there exists a point $x$ from this set such that $l_{i} ≤ x ≤ r_{i}$.

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