Python Algorithms: Mastering Basic Algorithms in the Python Language, Second Edition by Magnus Lie Hetland

Author:Magnus Lie Hetland [Magnus Lie Hetland]
Language: eng
Format: epub
Tags: Python
Publisher: Apress
Published: 2015-09-07T21:00:00+00:00

Figure 7-4. A set of random intervals where at most four mutually compatible intervals (for example, a, c, e and g) can be found

There are two obvious candidates for greedy selection here: If we go from left to right on the timeline, we might want to start with either the interval that starts first or the one that ends first, eliminating any other overlapping intervals. I hope it is clear that the first alternative can’t work (Exercise 7-18), which leaves us to show that the other one does work.

The algorithm is (roughly) as follows:

Include the interval with the lowest finish time in the solution.

Remove all of the remaining intervals that overlap with the one from step 1.

Any remaining intervals? Go to step 1.

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