Editing Greedy algorithm (section)

===Cases of failure===
{{multiple image
   | align = 
| direction = vertical
   | width     = 300
   | header    = Examples on how a greedy algorithm may fail to achieve the optimal solution.
   | image1    = Greedy Glouton.svg
   | alt1      = 
   | caption1  = Starting from A, a greedy algorithm that tries to find the maximum by following the greatest slope will find the local maximum at "m", oblivious to the global maximum at "M".
   | image2    = Greedy-search-path-example.gif
   | alt2      = 
   | caption2  =

To reach the largest sum, at each step, the greedy algorithm will choose what appears to be the optimal immediate choice, so it will choose 12 instead of 3 at the second step, and will not reach the best solution, which contains 99.
}}

Greedy algorithms fail to produce the optimal solution for many other problems and may even produce the ''unique worst possible'' solution. One example is the [[travelling salesman problem]] mentioned above: for each number of cities, there is an assignment of distances between the cities for which the nearest-neighbour heuristic produces the unique worst possible tour.<ref>{{cite journal|doi=10.1016/S0166-218X(01)00195-0|title=Traveling salesman should not be greedy: Domination analysis of greedy-type heuristics for the TSP|journal=Discrete Applied Mathematics|volume=117|issue=1–3|pages=81–86|year=2002|last1=Gutin|first1=Gregory|last2=Yeo|first2=Anders|last3=Zverovich|first3=Alexey|doi-access=free}}</ref>
For other possible examples, see [[horizon effect]].