Proving Greedy Algorithms Optimal

Need to prove 1) optimal substructure and 2) greedy choice property.

The proof of 2 typically involves:

a.

Consider globally-optimal solution.

b.

Show greedy choice at first step reduces problem to the same but smaller problem.
Greedy choice must be

• Part of an optimal solution, and
• Can be made first

c.

Use induction to show greedy choice is best at each step (i.e., optimal substructure)