Stack Block C ++ implementation

Stacking blocks is an interesting question. The original question is described:

We use a 2-dimensional array n [I] [j] to represent the height of the raised plane. Or stacked cubes on a two-dimensional plane to satisfy (each array element is a non-negative integer)

N [I] [j] <= n [I] [j + 1] n [I] [j] <= n [I + 1] [j]

Is a valid method. The corresponding two-dimensional array is: 5 4 2 1 13 2 0 0 02 2 0 0 0 (note that the positive direction is from bottom up, from right to left) given a, B, c, where a and B are the dimensions of a 2-dimensional array. c indicates that the element does not exceed c (that is, n [I, j] <= c), and calculates the number of 2-dimensional arrays that meet the condition. (0 <a, B, c <= 6)

I have analyzed this question before. This question has a lot to do with the ferrers diagram. Let's look at the Ferrers diagram:

The ferrers graph is a top-down n-layer grid, where mi is the number of grids in the I-layer. When mi> = mi + 1 (I =, n-1 ), that is, the number of grids on the upper layer is not less than that on the lower layer.

The following are some ferrers diagrams:

Therefore, we can see that each reasonable layer is a ferrers graph, and the number of cells in the lower layer GRAPH Cannot be smaller than that in the upper layer, that is, each column cannot be smaller, then stack c layers at most. In this way, the idea is ready.

Because I do not write java, I first use the c ++ implementation to create a table. below is my C ++ code implementation;

/*******************************************************************************//* OS           : Linux fc20.x86_64 #1 SMP Tue Dec  UTC 2013 x86_64  GNU/Linux * Compiler     : 4.8.2 20131212 (Red Hat 4.8.2-7) (GCC) * Encoding     : UTF8 * Date         : 2014-03-21 * All Rights Reserved by alop.*****************************************************************************//* Description: ********************************************************************************************************************************************//* Analysis: ***********************************************************************************************************************************************//*****************************************************************************/#include<iostream>#include<cstdio>#include<cstring>#include<cstdlib>using namespace std;long long D[7][7][7][7][7][7][7];int main(){freopen("in.txt","w",stdout);   int a[7],b[7];   for(a[1]=1;a[1]<7;a[1]++)     for(a[2]=0;a[2]<=a[1];a[2]++)      for(a[3]=0;a[3]<=a[2];a[3]++)        for(a[4]=0;a[4]<=a[3];a[4]++)          for(a[5]=0;a[5]<=a[4];a[5]++)            for(a[6]=0;a[6]<=a[5];a[6]++)             D[a[1]][a[2]][a[3]][a[4]][a[5]][a[6]][1]=1;for(int i=2;i<=6;i++)   for(a[1]=1;a[1]<7;a[1]++)     for(a[2]=0;a[2]<=a[1];a[2]++)      for(a[3]=0;a[3]<=a[2];a[3]++)        for(a[4]=0;a[4]<=a[3];a[4]++)          for(a[5]=0;a[5]<=a[4];a[5]++)            for(a[6]=0;a[6]<=a[5];a[6]++)            {               D[a[1]][a[2]][a[3]][a[4]][a[5]][a[6]][i]=0;               for(b[1]=1;b[1]<=a[1];b[1]++)                 for(b[2]=0;b[2]<=min(b[1],a[2]);b[2]++)                  for(b[3]=0;b[3]<=min(b[2],a[3]);b[3]++)                    for(b[4]=0;b[4]<=min(b[3],a[4]);b[4]++)                        for(b[5]=0;b[5]<=min(b[4],a[5]);b[5]++)                            for(b[6]=0;b[6]<=min(b[5],a[6]);b[6]++)                                D[a[1]][a[2]][a[3]][a[4]][a[5]][a[6]][i]+= D[b[1]][b[2]][b[3]][b[4]][b[5]][b[6]][i-1];                            }for(int c=1;c<=6;c++)  {    long long fer=1;    for(int d=1;d<=6;d++)    {    for(a[1]=1;a[1]<=d;a[1]++)      for(int i=1;i<=c;i++)       fer+= D[a[1]][0][0][0][0][0][i];      cout<<"fs["<<d<<"][1]["<<c<<"]="<<fer<<"L ;";      fer=1;      }    cout<<endl;for(int d=1;d<=6;d++){for(a[1]=1;a[1]<=d;a[1]++)for(a[2]=0;a[2]<=a[1];a[2]++)      for(int i=1;i<=c;i++)       fer+= D[a[1]][a[2]][0][0][0][0][i];      cout<<"fs["<<d<<"][2]["<<c<<"]="<<fer<<"L;  ";      fer=1;      }    cout<<endl;for(int d=1;d<=6;d++){for(a[1]=1;a[1]<=d;a[1]++)  for(a[2]=0;a[2]<=a[1];a[2]++)     for(a[3]=0;a[3]<=a[1];a[3]++)      for(int i=1;i<=c;i++)       fer+= D[a[1]][a[2]][a[3]][0][0][0][i];      cout<<"fs["<<d<<"][3]["<<c<<"]="<<fer<<"L  ; ";      fer=1;      }    cout<<endl;for(int d=1;d<=6;d++){for(a[1]=1;a[1]<=d;a[1]++)  for(a[2]=0;a[2]<=a[1];a[2]++)     for(a[3]=0;a[3]<=a[1];a[3]++)       for(a[4]=0;a[4]<=a[3];a[4]++)      for(int i=1;i<=c;i++)       fer+= D[a[1]][a[2]][a[3]][a[4]][0][0][i];      cout<<"fs["<<d<<"][4]["<<c<<"]="<<fer<<"L   ;";      fer=1;      }    cout<<endl;    for(int d=1;d<=6;d++){for(a[1]=1;a[1]<=d;a[1]++)  for(a[2]=0;a[2]<=a[1];a[2]++)     for(a[3]=0;a[3]<=a[1];a[3]++)       for(a[4]=0;a[4]<=a[3];a[4]++)         for(a[5]=0;a[5]<=a[4];a[5]++)      for(int i=1;i<=c;i++)       fer+= D[a[1]][a[2]][a[3]][a[4]][a[5]][0][i];      cout<<"fs["<<d<<"][5]["<<c<<"]="<<fer<<"L   ;";      fer=1;      }    cout<<endl;for(int d=1;d<=6;d++){for(a[1]=1;a[1]<=d;a[1]++)  for(a[2]=0;a[2]<=a[1];a[2]++)     for(a[3]=0;a[3]<=a[1];a[3]++)       for(a[4]=0;a[4]<=a[3];a[4]++)         for(a[5]=0;a[5]<=a[4];a[5]++)           for(a[6]=0;a[6]<=a[5];a[6]++)            for(int i=1;i<=c;i++)       fer+= D[a[1]][a[2]][a[3]][a[4]][a[5]][a[6]][i];      cout<<"fs["<<d<<"][6]["<<c<<"]="<<fer<<"L  ;";      fer=1;      }    cout<<endl;  }    return 0;fclose(stdout);}

As you can see, I have written a lot of for loops, but the idea is very clear, that is, the layer-by-layer addition of the ferrers diagram; below is the output data:

Fs [1] [1] [1] = 2L; fs [2] [1] [1] = 3L; fs [3] [1] [1] = 4L; fs [4] [1] [1] = 5L; fs [5] [1] [1] = 6L; fs [6] [1] [1] = 7L;
Fs [1] [2] [1] = 3L; fs [2] [2] [1] = 6L; fs [3] [2] [1] = 10L; fs [4] [2] [1] = 15L; fs [5] [2] [1] = 21L; fs [6] [2] [1] = 28L;
Fs [1] [3] [1] = 4L; fs [2] [3] [1] = 10L; fs [3] [3] [1] = 20L; fs [4] [3] [1] = 35L; fs [5] [3] [1] = 56L; fs [6] [3] [1] = 84L;
Fs [1] [4] [1] = 5L; fs [2] [4] [1] = 15L; fs [3] [4] [1] = 35L; fs [4] [4] [1] = 70L; fs [5] [4] [1] = 126L; fs [6] [4] [1] = 210L;
Fs [1] [5] [1] = 6L; fs [2] [5] [1] = 21L; fs [3] [5] [1] = 56L; fs [4] [5] [1] = 126L; fs [5] [5] [1] = 252L; fs [6] [5] [1] = 462L;
Fs [1] [6] [1] = 7L; fs [2] [6] [1] = 28L; fs [3] [6] [1] = 84L; fs [4] [6] [1] = 210L; fs [5] [6] [1] = 462L; fs [6] [6] [1] = 924L;
Fs [1] [1] [2] = 3L; fs [2] [1] [2] = 6L; fs [3] [1] [2] = 10L; fs [4] [1] [2] = 15L; fs [5] [1] [2] = 21L; fs [6] [1] [2] = 28L;
Fs [1] [2] [2] = 6L; fs [2] [2] [2] = 20L; fs [3] [2] [2] = 50L; fs [4] [2] [2] = 105L; fs [5] [2] [2] = 196L; fs [6] [2] [2] = 336L;
Fs [1] [3] [2] = 10L; fs [2] [3] [2] = 50L; fs [3] [3] [2] = 175L; fs [4] [3] [2] = 490L; fs [5] [3] [2] = 1176L; fs [6] [3] [2] = 2520L;
Fs [1] [4] [2] = 15L; fs [2] [4] [2] = 105L; fs [3] [4] [2] = 490L; fs [4] [4] [2] = 1764L; fs [5] [4] [2] = 5292L; fs [6] [4] [2] = 13860L;
Fs [1] [5] [2] = 21L; fs [2] [5] [2] = 196L; fs [3] [5] [2] = 1176L; fs [4] [5] [2] = 5292L; fs [5] [5] [2] = 19404L; fs [6] [5] [2] = 60984L;
Fs [1] [6] [2] = 28L; fs [2] [6] [2] = 336L; fs [3] [6] [2] = 2520L; fs [4] [6] [2] = 13860L; fs [5] [6] [2] = 60984L; fs [6] [6] [2] = 226512L;
Fs [1] [1] [3] = 4L; fs [2] [1] [3] = 10L; fs [3] [1] [3] = 20L; fs [4] [1] [3] = 35L; fs [5] [1] [3] = 56L; fs [6] [1] [3] = 84L;
Fs [1] [2] [3] = 10L; fs [2] [2] [3] = 50L; fs [3] [2] [3] = 175L; fs [4] [2] [3] = 490L; fs [5] [2] [3] = 1176L; fs [6] [2] [3] = 2520L;
Fs [1] [3] [3] = 20L; fs [2] [3] [3] = 175L; fs [3] [3] [3] = 980L; fs [4] [3] [3] = 410000l; fs [5] [3] [3] = 1410000l; fs [6] [3] [3] = 11680l;
Fs [1] [4] [3] = 35L; fs [2] [4] [3] = 490L; fs [3] [4] [3] = 4l L; fs [4] [4] [3] = 24696L; fs [5] [4] [3] = 116424L; fs [6] [4] [3] = 457380L;
Fs [1] [5] [3] = 56L; fs [2] [5] [3] = 1176L; fs [3] [5] [3] = 14w.l; fs [4] [5] [3] = 116424L; fs [5] [5] [3] = 731808L; fs [6] [5] [3] = 3737448L;
Fs [1] [6] [3] = 84L; fs [2] [6] [3] = 2520L; fs [3] [6] [3] = 11680l; fs [4] [6] [3] = 457380L; fs [5] [6] [3] = 3737448L; fs [6] [6] [3] = 24293412L;
Fs [1] [1] [4] = 5L; fs [2] [1] [4] = 15L; fs [3] [1] [4] = 35L; fs [4] [1] [4] = 70L; fs [5] [1] [4] = 126L; fs [6] [1] [4] = 210L;
Fs [1] [2] [4] = 15L; fs [2] [2] [4] = 105L; fs [3] [2] [4] = 490L; fs [4] [2] [4] = 1764L; fs [5] [2] [4] = 5292L; fs [6] [2] [4] = 13860L;
Fs [1] [3] [4] = 35L; fs [2] [3] [4] = 490L; fs [3] [3] [4] = 4l L; fs [4] [3] [4] = 24696L; fs [5] [3] [4] = 116424L; fs [6] [3] [4] = 457380L;
Fs [1] [4] [4] = 70L; fs [2] [4] [4] = 1764L; fs [3] [4] [4] = 24696L; fs [4] [4] [4] = 232848L; fs [5] [4] [4] = 1646568L; fs [6] [4] [4] = 9343620L;
Fs [1] [5] [4] = 126L; fs [2] [5] [4] = 5292L; fs [3] [5] [4] = 116424L; fs [4] [5] [4] = 1646568L; fs [5] [5] [4] = 16818516L; fs [6] [5] [4] = 133613766L;
Fs [1] [6] [4] = 210L; fs [2] [6] [4] = 13860L; fs [3] [6] [4] = 457380L; fs [4] [6] [4] = 9343620L; fs [5] [6] [4] = 133613766L; fs [6] [6] [4] = 1447482465L;
Fs [1] [1] [5] = 6L; fs [2] [1] [5] = 21L; fs [3] [1] [5] = 56L; fs [4] [1] [5] = 126L; fs [5] [1] [5] = 252L; fs [6] [1] [5] = 462L;
Fs [1] [2] [5] = 21L; fs [2] [2] [5] = 196L; fs [3] [2] [5] = 1176L; fs [4] [2] [5] = 5292L; fs [5] [2] [5] = 19404L; fs [6] [2] [5] = 60984L;
Fs [1] [3] [5] = 56L; fs [2] [3] [5] = 1176L; fs [3] [3] [5] = 14w.l; fs [4] [3] [5] = 116424L; fs [5] [3] [5] = 731808L; fs [6] [3] [5] = 3737448L;
Fs [1] [4] [5] = 126L; fs [2] [4] [5] = 5292L; fs [3] [4] [5] = 116424L; fs [4] [4] [5] = 1646568L; fs [5] [4] [5] = 16818516L; fs [6] [4] [5] = 133613766L;
Fs [1] [5] [5] = 252L; fs [2] [5] [5] = 19404L; fs [3] [5] [5] = 731808L; fs [4] [5] [5] = 16818516L; fs [5] [5] [5] = 267227532L; fs [6] [5] [5] = 3184461423L;
Fs [1] [6] [5] = 462L; fs [2] [6] [5] = 60984L; fs [3] [6] [5] = 3737448L; fs [4] [6] [5] = 133613766L; fs [5] [6] [5] = 3184461423L; fs [6] [6] [5] = 55197331332L;
Fs [1] [1] [6] = 7L; fs [2] [1] [6] = 28L; fs [3] [1] [6] = 84L; fs [4] [1] [6] = 210L; fs [5] [1] [6] = 462L; fs [6] [1] [6] = 924L;
Fs [1] [2] [6] = 28L; fs [2] [2] [6] = 336L; fs [3] [2] [6] = 2520L; fs [4] [2] [6] = 13860L; fs [5] [2] [6] = 60984L; fs [6] [2] [6] = 226512L;
Fs [1] [3] [6] = 84L; fs [2] [3] [6] = 2520L; fs [3] [3] [6] = 11680l; fs [4] [3] [6] = 457380L; fs [5] [3] [6] = 3737448L; fs [6] [3] [6] = 24293412L;
Fs [1] [4] [6] = 210L; fs [2] [4] [6] = 13860L; fs [3] [4] [6] = 457380L; fs [4] [4] [6] = 9343620L; fs [5] [4] [6] = 133613766L; fs [6] [4] [6] = 1447482465L;
Fs [1] [5] [6] = 462L; fs [2] [5] [6] = 60984L; fs [3] [5] [6] = 3737448L; fs [4] [5] [6] = 133613766L; fs [5] [5] [6] = 3184461423L; fs [6] [5] [6] = 55197331332L;
Fs [1] [6] [6] = 924L; fs [2] [6] [6] = 226512L; fs [3] [6] [6] = 24293412L; fs [4] [6] [6] = 1447482465L; fs [5] [6] [6] = 55197331332L; fs [6] [6] [6] = 1478619421136L;

In this way, this question is perfectly solved!