It seems to me that the best strategy is to always take the element that is best in relation to its neighbor. So if you have a list a b ... c d, you shift if a-b > d-c, and pop if the reverse is true. If the differences are equal, then you should probably resort to lookahead, but it's not clear to me what lookahead strategy should be.

Update: Tilly shot a hole in that strategy, so I'll try again here rather than proliferating response nodes. If the number of nodes is fewer than 6, the above strategy should hold. For > 6, a b c ... d e f, calculate the differences a-b, b-c, e-d, and f-e. Call the "current score" of the field a-b + f-e. Depending on whether you shift or pop, the "new score" would be a-b + e-d or b-c + f-e. Choose whichever makes the bigger negative difference (changing the game the most to your opponent's disadvantage).

Update 2: But it still doesn't get the best result for the example data. :-(

Caution: Contents may have been coded under pressure.

In reply to Re: Puzzle: Given an array of integers, find the best sequence of pop / shift... by Roy Johnson
in thread Puzzle: Given an array of integers, find the best sequence of pop / shift... by TedPride

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