Generalisation of pancake sorting with arbitrary flipped slices?

In pancake sort, the primary operation is: flip all pancakes above a given position. What about flipping all pancakes between two given positions? Anybody knows if this has been studied?

To illustrate the problem, here is a quick brute-force, greedy implementation in Python 2.7 (not quite sure it always converges though):

def sort(a):
entropy = 0
for i in range(len(a) - 1):
entropy += abs(a[i] - a[i+1])
while True:
max_improvement = 0
for i in range(len(a) - 1):
for j in range(i + 1, len(a)):
improvement = 0
if i > 0:
improvement += abs(a[i] - a[i-1]) - abs(a[j] - a[i-1])
if j < len(a) - 1:
improvement += abs(a[j] - a[j+1]) - abs(a[i] - a[j+1])
if improvement > max_improvement:
max_improvement = improvement
(next_i, next_j) = (i, j)
if max_improvement == 0:
if a and a[0] > a[-1]:
a[:] = a[::-1]
print a
return
entropy -= max_improvement
a[next_i:next_j+1] = a[next_i:next_j+1][::-1]
print a

a = [7, 1, 3, 8, 6, 0, 4, 9, 2, 5]
print a
sort(a)


Output:

[7, 1, 3, 8, 6, 0, 4, 9, 2, 5]
[7, 6, 8, 3, 1, 0, 4, 9, 2, 5]
[7, 6, 8, 9, 4, 0, 1, 3, 2, 5]
[7, 6, 8, 9, 4, 5, 2, 3, 1, 0]
[9, 8, 6, 7, 4, 5, 2, 3, 1, 0]
[9, 8, 7, 6, 4, 5, 2, 3, 1, 0]
[9, 8, 7, 6, 5, 4, 2, 3, 1, 0]
[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

• But what's your question? – David Richerby Feb 12 '15 at 23:11