将所有可能的二进制矩阵生成为字符串或生成所有可能的矩阵

Question

I have 12*3 matrix as below

matrix = 0- [0,0,0]
         1- [0,0,0]
         2- [0,0,0]
            .......
        11- [0,0,0]

Each row must have only one selection as value 1

matrix = 0- [1,0,0]
         1- [1,0,0]
         2- [1,0,0]
            .......
        11- [1,0,0]

My answer array in this case is

Ans = {1,0,0,1,0,0,1,0,0,....,1,0,0}

I want to generate all answers, like this:

Ans = {1,0,0,1,0,0,1,0,0,....,1,0,0}
Ans = {0,1,0,1,0,0,1,0,0,....,1,0,0}
Ans = {0,0,1,1,0,0,1,0,0,....,1,0,0}
Ans = {1,0,0,0,1,0,1,0,0,....,1,0,0}

Could you please help me to select best algorithm.

Edit: preferable language is C#

Answer 1

You can think of each such an array as coding a number in base 3 in the range 0 to 3^12 - 1. The following Python script (with comments suggesting how to convert to C# -- a language I don't use) shows how you can go from such a number to the array:

def decode(n):
     A = [0]*36 #initialize array of 36 zeros
     for i in range(0,12): #for(int i = 0; i < 12; i++) in C#
          r = n % 3
          n = n // 3 #integer division, just use / in C# if n is an int
          A[3*i+r] = 1
     return A

#test:
n = 1*3**0 + 2*3**1 + 1*3**2 + 2*3**3 + 1*3**5
A = decode(n)
print(A)

Output:

[0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]

Note that the 1 is in the second position in the first group of 3, the third position in the second group of 3, the second position in the next, the fist position in the fourth, the third position in the fifth, and then in the first position in the remaining blocks.

Answer 2

To make a full solution I used c++:

#include <stdio.h>
void printarr(int arr[]);
FILE *fileptr;
FILE **file;
int main()
{
    int finarr[12] = {0,0,0,0,0,0,0,0,0,0,0,0};
    int aux=0;
    file=&fileptr;
    fopen_s(file,"fichero.txt","w");

    while(finarr[11]!=3)
    {
        finarr[0]=aux;
        printarr(finarr);
        aux++;
        if(aux==3)
        {
            aux=0;
            finarr[0]++;
            for(int idx=0;idx<11;idx++)
            {
                if(finarr[idx]==3)
                {
                    finarr[idx]=0;
                    finarr[idx+1]++;
                }
            }
        }

    }

    printarr(finarr);

    return 0;
}

void printarr(int arr[])
{
    if(arr[11]==3)
        return;
    fprintf(fileptr,"Ans = {");
    for(int idx=0;idx<12;idx++)
    {
        if(idx!=0)
            fprintf(fileptr,",");

        switch(arr[idx])
        {
        case 0:
            fprintf(fileptr,"1,0,0");
            break;
        case 1:
            fprintf(fileptr,"0,1,0");
            break;
        case 2:
            fprintf(fileptr,"0,0,1");
            break;
        }

    }
    fprintf(fileptr,"}\n");
}

Answer 3

Solution in c# that write all the answers in a file with the format that you asked.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.IO;

namespace DozeFilastres
{
    class Program
    {
        static void Main(string[] args)
        {
            List<string> lines = new List<string>();
            int[] finarr = new int[]{0,0,0,0,0,0,0,0,0,0,0,0};
            int aux=0;


            while(finarr[11]!=3)
            {
                finarr[0]=aux;
                lines.Add(printarr(finarr));
                aux++;
                if(aux==3)
                {
                    aux=0;
                    finarr[0]++;
                    for(int idx=0;idx<11;idx++)
                    {
                        if(finarr[idx]==3)
                        {
                            finarr[idx]=0;
                            finarr[idx+1]++;
                        }
                    }
                }

            }

            File.WriteAllLines("fichero.txt",lines.ToArray());
        }

        static string printarr(int[] arr)
        {
            string all="Ans = {";
            for(int idx=0;idx<12;idx++)
            {
                if(idx!=0)
                    all+=",";

                switch(arr[idx])
                {
                case 0:
                    all+="1,0,0";
                    break;
                case 1:
                    all+="0,1,0";
                    break;
                case 2:
                    all+="0,0,1";
                    break;
                }

            }
            all+="}";

            return all;
        }
    }
}