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General principles of pruning:
The general principles are such that:
1. Given a node N that can be chosen by player one, thus if there is another node, X, along any path, like that (a) X can be chosen by player two (b) X is on a higher level than N and (c) X has been shown to guarantee a worse score for player one than N, after then all the nodes with the same parent as N can be pruned.
2. Given a node N that can be chosen by player two, after then if there is a node X along any path just like that (a) player one can choose X (b) X is on a higher level so than N and (c) X has been shown to guarantee a better score for player one than N, after then all the nodes with the equal parent as N can be pruned.
As an exercise: in which one of these principles did we need in the M1 - M4 pruning example above? (For this type of puzzle to make it easy, I've written on the N's and X's).
(1-x^2 ) (d^2 y)/?dx?^(2 ) -x dy/dx-4y=0
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