Pancake Flipping Is Hard — NP Hard

mikejuk writes "French computer scientists have finally proved that sorting pancakes is hard — NP hard. No really — this isn't a joke. Well, it is slightly amusing but that's just because it is being presented as pancake flipping. The algorithm in question is sorting a permutation using prefix reversal — which is much easier to understand in terms of pancakes. Basically you have to sort a pancake stack by simply inserting your spatula and flipping the top part of the stack. We now know that if you can do the this in polynomial time then you have proved that P=NP."

Solution?

[Erich]

I had something like this was an interview question once. My solution:

Assume we are stacking pancakes with largest at the bottom.

1. Find the largest unsorted pancake
2. Flip that to the top
3. Flip from the bottom-most unsorted pancake. (One additional pancake is now sorted)
4. Repeat until sorted

To me, assuming that you consider "Find the largest unsorted pancake" to be O(N), the algorithm is O(N^2). Number of flips is 2N. Where's my turing award?

So I must be missing something... Is one not able to find the largest unsorted pancake easily? Perhaps you are only able to look at the size of the topmost pancake. The article was unclear.