Introduction to Greedy Algorithms

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For this I am using Tim Roughgarden's Algorithms Illuminated, Part3: Greedy Algorithms and Dynamic Programming.
He describes the greedy paradigm as: Construct a solution iteratively, via a sequence of myoptic decisions, and hope that everything works out in the end.
That might be a bit flippant
CLRS says: Always make a choice that seems best at the moment.
This is a strategy that can work really well if you make the right greedy choice,
But it is problematic if you do not.
Roughgarden says that greedy algorithms are
- Usually easy to come up with
- Generally easy to analyze
- Hard to establish correctness
In his first chapter, he repeats over and over again
- Warning: Most greedy algorithms are not always correct.
Frequently greed solutions miss edge cases or other special cases.
Proving that your greed solution is optimal is frequently very difficult
or impossible because it is not.
CLRS lists the following as the elements of a greedy strategy
- Determine the optimal substructure of the problem
- Develop a solution (most likely recursive)
- Show that if you make the greedy choice, then only one subproblem remains
- Prove that it is always safe to make the greedy choice
- Develop an algorithm that implements the greedy strategy