Stacks of Flapjacks
Time Limit: 1000 ms Memory Limit: 10000 KiB
Stacks and Queues are often considered the bread and butter of data
structures and find use in architecture, parsing, operating systems,
and discrete event simulation. Stacks are also important in the
theory of formal languages.
This problem involves both butter and sustenance in the form of
pancakes rather than bread in addition to a finicky server who flips
pancakes according to a unique, but complete set of rules.
Given a stack of pancakes, you are to write a program that indicates
how the stack can be sorted so that the largest pancake is on the
bottom and the smallest pancake is on the top. The size of a
pancake is given by the pancake's diameter. All pancakes in a stack
have different diameters.
Sorting a stack is done by a sequence of pancake ``flips''. A
flip consists of inserting a spatula between two pancakes in a stack
and flipping (reversing) all the pancakes on the spatula (reversing
the sub-stack). A flip is specified by giving the position of the
pancake on the bottom of the sub-stack to be flipped (relative to
the whole stack). The pancake on the bottom of the whole stack has
position 1 and the pancake on the top of a stack of n pancakes has
A stack is specified by giving the diameter of each pancake in
the stack in the order in which the pancakes appear.
For example, consider the three stacks of pancakes below (in
which pancake 8 is the top-most pancake of the left stack):
8 7 2
4 6 5
6 4 8
7 8 4
5 5 6
2 2 7
The stack on the left can be transformed to the stack in the middle
via flip(3). The middle stack can be transformed into the right
stack via the command flip(1).
The input consists of a sequence of stacks of pancakes. Each stack
will consist of between 1 and 30 pancakes and each pancake will have
an integer diameter between 1 and 100. The input is terminated by
end-of-file. Each stack is given as a single line of input with the
top pancake on a stack appearing first on a line, the bottom pancake
appearing last, and all pancakes separated by a space.
For each stack of pancakes, the output should echo the original
stack on one line, followed by some sequence of flips that results
in the stack of pancakes being sorted so that the largest diameter
pancake is on the bottom and the smallest on top. For each stack
the sequence of flips should be terminated by a 0 (indicating no
more flips necessary). Once a stack is sorted, no more flips should
1 2 3 4 5 5 4 3 2 1 5 1 2 3 4
1 2 3 4 5 0 5 4 3 2 1 1 0 5 1 2 3 4 1 2 0