Background背景
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.栈和队列常常被视为数据结构中的面包和黄油，广泛应用在体系结构、分析、操作系统和离散事件等领域。栈同时也在形式语言理论中发挥着重要的作用。
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.这个问题是让一个挑剔的厨师按照独特而完备的一组规则翻动煎饼，以保持煎饼（而不是面包）中的黄油和营养素不被烧坏。（这句话实在不知道怎么翻译才好，还望各位老师指正！Ps. 这道题翻译的难度要比解题大多了！！）
The Problem问题
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.给定一叠煎饼，你要写一个程序计算出如何才能使这叠煎饼自底向上由大至小的排列。给定煎饼的半径作为其尺寸，一叠煎饼的大小各不相同。
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) 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 position n.
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):比如下面三个煎饼叠（煎饼8是左边一叠的最上面的一个）
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输入
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.输入包括一系列煎饼叠。每叠都由1到30个煎饼组成，并且每个煎饼的直径都在 1到100之间。输入由EOF结束。每叠煎饼独占一行，最上面的在行首，最下面的在行尾，各煎饼中间由空格隔开。
The Output输出
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 be made.
Sample Input输入示例
1 2 3 4 55 4 3 2 15 1 2 3 4
Sample Output输出示例
1 2 3 4 505 4 3 2 11 05 1 2 3 41 2 0
Analysis分析
算法很简单，给你一组煎饼，用笔在纸上一画就知道该怎么办了。还是动态规划的思想，从底至上，保持已经遍例过的煎饼都是最大且有序的。比如输入的数据为：
2 4 1 3 5
按题目要求，4在顶5在底。5已经是最大的了，则移动到上一个煎饼3。3之上（含）最大的是4，先将4翻转到最顶，形成：
4 2 1 3 5
然后将4到3的子叠翻转，，形成：
3 1 2 4 5
移动到上一个煎饼2，2之上（含）最大的是3，而3就在顶部，因此直接将2到3翻转，形成：
2 1 3 4 5
最后将2和1翻转，就完成了。注意：一定不要忘了在输入的一行数据下再将原数据复制输出一行，漏掉必然WA。按照上面的算法来做就不会出现多余的翻转操作，因此不用担心。
也有伤心的，既有令人兴奋的，也有令人灰心的，
