Greedy algorithms for optimization problems

For the Knapsack problem

while knapsack is not full
  put the best valued item in the knapsack

What does “best” mean? $v a l u e$ ? Or ratio $v a l u e / w e i g h t$ ?

Efficiency: $O (n lo g n)$ (from sorting $O (n lo g n)$ and iterating over items to add them $O (n)$ ).

Greedy algorithms make a sequence of local optimizations, and it might not make it to the global solution.

Pros and cons of greedy algorithms

Pro: really easy to implement
Pro: really fast ( $O (n lo g n)$ )
Con: does not always get to the best solution (not really optimized?)
Con: we don’t know how close to optimal it is