烙饼排序

问题：            

 星期五的晚上，一帮同事在希格玛大厦附近的“硬盘酒吧”多喝了几杯。程序员多喝了几杯之后谈什么呢？自然是算法问题。有个同事说：“我以前在餐馆打工，顾客经常点非常多的烙饼。店里的饼大小不一，我习惯在到达顾客饭桌前，把一摞饼按照大小次序摆好——小的在上面，大的在下面。由于我一只手托着盘子，只好用另一只手，一次抓住最上面的几块饼，把它们上下颠倒个个儿，反复几次之后，这摞烙饼就排好序了。我后来想，这实际上是个有趣的排序问题：假设有n块大小不一的烙饼，那最少要翻几次，才能达到最后大小有序的结果呢？”

       你能否写出一个程序，对于n块大小不一的烙饼，输出最优化的翻饼过程呢？

#include<iostream>#include<cassert>using namespace std;class CPrefixSorting{private:int* m_CakeArray;//烙饼信息数组int m_nCakeCnt;//烙饼个数  int m_nMaxSwap;//最多翻转次数，即上界  int* m_SwapArray;//交换结果数组，即保存最优解的每一步交换  int* m_ReverseCakeArray; //当前翻转烙饼信息数组  int* m_ReverseCakeArraySwap;//当前翻转烙饼交换结果数组  int m_nSearch;//当前遍历次数信息  public:CPrefixSorting(){m_nCakeCnt=0;m_nMaxSwap=0;} void Run(int *pCakeArray,int nCakeCnt){Init(pCakeArray,nCakeCnt);m_nSearch=0;Search(0);}void Init(int* pCakeArray,int nCakeCnt){assert(pCakeArray!=NULL);assert(nCakeCnt>0);m_nCakeCnt=nCakeCnt;m_CakeArray=new int[m_nCakeCnt];assert(m_CakeArray!=NULL);for(int i=0;i<m_nCakeCnt;i++){m_CakeArray[i]=pCakeArray[i];}m_nMaxSwap=UpBound(m_nCakeCnt);m_SwapArray=new int[m_nMaxSwap];assert(m_SwapArray!=NULL);m_ReverseCakeArray=new int[m_nCakeCnt];for(int i=0;i<m_nCakeCnt;i++){m_ReverseCakeArray[i]=m_CakeArray[i];}m_ReverseCakeArraySwap=new int[m_nMaxSwap];}int UpBound(int nCakeCnt){return (nCakeCnt-1)*2;}int LowerBound(int* pCakeArray,int nCakeCnt){int t,ret=0;for(int i=1;i<nCakeCnt;i++){t=pCakeArray[i]-pCakeArray[i-1];if(t==1 || t==-1){}else{ret++;}}if (ret==0 && pCakeArray[nCakeCnt-1] != nCakeCnt-1)ret++;return ret;}void Search(int step){int i,nEstimate;m_nSearch++;nEstimate=LowerBound(m_ReverseCakeArray,m_nCakeCnt);if(step+nEstimate>=m_nMaxSwap)return;if(IsSorted(m_ReverseCakeArray,m_nCakeCnt)){if(step<m_nMaxSwap){m_nMaxSwap=step;for(i=0;i<m_nMaxSwap;i++)m_SwapArray[i]=m_ReverseCakeArraySwap[i];}return;}for(i=1;i<m_nCakeCnt;i++){Revert(0,i);m_ReverseCakeArraySwap[step]=i;Search(step+1);Revert(0,i);}}bool IsSorted(int* pCakeArray,int nCakeCnt){for(int i=1;i<nCakeCnt;i++){if(pCakeArray[i-1]>pCakeArray[i]){return false;}}return true;}void Revert(int nBegin,int nEnd){assert(nEnd>nBegin);int i,j,t;for(i=nBegin,j=nEnd;i<j;i++,j--){t=m_ReverseCakeArray[i];m_ReverseCakeArray[i]=m_ReverseCakeArray[j];m_ReverseCakeArray[j]=t;}}void Output(){for (int i = 0; i < m_nMaxSwap; i++)          printf("%d\n", m_SwapArray[i]);  printf("Search Times : %d\n", m_nSearch);          printf("Total Swap times = %d\n", m_nMaxSwap); }};int main(){int a[] = {3, 2, 1, 6, 5, 4, 9, 8, 7, 0};      CPrefixSorting test;      test.Run(a, 10);      test.Output();        system("pause");   return 0;}