LCS最长公共子序列

此算法是动态规划中的经典：

LCS即求数组 a b 中最长的公共子序列，其中序列不一定要相邻 。

用动态规划解有两种，一种是正着解，一种是倒着解，即备忘录法

贴下我写的代码：

int  LCS(char a[],int la,char b[],int lb)
{
    int** c = new int*[la+1];
    int** path = new int*[la+1];
    for(int i = 0;i<la+1;i++)
    {
        path[i] = new int[lb+1];
        c[i] = new int[lb+1];
        memset(path[i],0,sizeof(int)*lb);
        memset(c[i],0,sizeof(int)*lb);
    }
    for(i = 1;i<=la;i++)
    {
        for(int j = 1;j<=lb;j++)
        {
            if(a[i-1] == b[j-1])
            {
                c[i][j] =  1+ c[i-1][j-1];
                path[i][j] = 2;
            }
            else
            {
                if(c[i-1][j] >c[i][j-1])
                {
                    c[i][j] = c[i-1][j];
                    path[i][j] = 1;
                }
                else
                {
                    c[i][j] = c[i][j-1];
                    path[i][j] = 3;
                }
            }
        }
    }
    int ttt=  c[la][lb];

    //print path
    char* p = new char[ttt];
    p = p+ttt;
    int lla = la,llb = lb;
    while(path[lla][llb] != 0)
    {
        if(path[lla][llb] == 2)
        {
            *(--p) = a[lla-1];
            lla--;llb--;
        }
        else if(path[lla][llb] == 1)
        {
            lla--;
        }
        else //if (path[lla][llb] == 3)
        {
            llb--;
        }
    }
    for(i = 0 ;i<ttt;i++)
        cout<<p[i]<<" ";
    cout<<endl;
    delete [] p;

    for(  i = 0;i<la+1;i++)
    {
        delete [] path[i] ;
        delete [] c[i];
        path[i] = c[i] = NULL;
    }
    delete [] c;
    delete [] path; 
    c = path = NULL;
    return ttt;
}


void main()
{
    char a[] = "a12b3c23d231`ah";
    char b[]= "abcdefgh";
    cout<<LCS(a,sizeof(a)-1,b,sizeof(b)-1);
}