generate unique combinations of different sizes using javascript[efficient method]

Question

I am having a hard time to generate a list of unique collection combinations of different sizes for a set, say ,where n=6 [variable]

set = {2,3,4,5,6,7}

I need to generate all unique combinations for the above set using javascript (Ordered collection) like this

6C1  +  6C2  +  6C3  +   6C4   +   6C5   +   6C6

2       2,3    2,3,4   2,3,4,5  2,3,4,5,6  2,3,4,5,6,7
3       2,4    2,3,5   2,3,4,6  2,3,4,5,7 
4       2,5    2,3,6   2,3,4,7  
5       2,6    2,3,7            2,4,5,6,7
        2,7            2,4,5,6  
.              2,4,5   2,4,5,7  3,4,5,6,7
.       3,4    2,4,6            .
8       3,5    2,4,7   2,5,6,7  .
        3,6                     
        3,7    2,5,6   3,4,5,6 
               2,5,7   3,4,5,7
        4,5              
        4,6    2,6,7   3,5,6,7
        4,7    
               3,4,5   .
        5,6    3,4,6   .
        5,7    3,4,7   .
        .      
        .      3,5,6    
        6,7    3,5,7   4,5,6,7 

               3,6,7
               .       
               .       

               5,6,7

Now the complication comes when I need to assign each of these values to alphabetical order.The order is small letters first a,b,c.. and then capital letters A,B,C,.. and after that aA,aB,aC and so on

a=2     h=2,3    o=2,3,4   I=2,3,4,5  2,3,4,5,6  2,3,4,5,6,7
b=3     i=2,4    p=2,3,5   J=2,3,4,6  2,3,4,5,7 
c=4     j=2,5    q=2,3,6   K=2,3,4,7  
d=5     k=2,6    r=2,3,7              2,4,5,6,7
        l=2,7              L=2,4,5,6  
.                s=2,4,5   M=2,4,5,7  3,4,5,6,7
.       m=3,4    t=2,4,6            .
g=8     n=3,5    u=2,4,7   N=2,5,6,7  .
        o=3,6                     
        p=3,7    v=2,5,6   O=3,4,5,6 
                 w=2,5,7   P=3,4,5,7
        q=4,5              
        r=4,6    x=2,6,7   Q=3,5,6,7
        s=4,7    
                 y=3,4,5   .
        t=5,6    z=3,4,6   .
        u=5,7    A=3,4,7   .
          .      
          .      B=3,5,6    
          6,7    C=3,5,7   W=4,5,6,7 

                 D=3,6,7
                 .       
                 .       

                 H=5,6,7

I know that a normal Brute Force way of approach would be the simplest solution to the problem but for large values this would be quite inefficient.

I am looking for a more efficient method of solving this problem. Any good solutions would be of great help.

Thanks in Advance, Neal

I am generating unique combinations nCr which are ordered and assigning each combination to a variable — Neal
– Neal, Commented Sep 17, 2012 at 8:02
Don't you think that using an array instead of variables is a better approach of saving these combinations? — Nippey
– Nippey, Commented Sep 17, 2012 at 8:23
I need to assign each combination to a variable . How can this be done using arrays? — Neal
– Neal, Commented Sep 17, 2012 at 8:35

Gloomcore · Accepted Answer · 2012-09-17 10:29:50Z

Function generate combinations:

function generate(index, array, used, result)
{
    if (index == array.length && used.length > 0)
    {
         var a = new Array();
         for (var i = 0; i < used.length; i++)
            a.push(used[i]);

         result.push(a);
    }
    else {
       generate(index+1, array, used, result);

       used.push(a[index]);
       generate(index+1, array, used, result);
       used.pop();
    }
}

function generateAllCombinations(array)
{ 
    var result = new Array();
    generate(0, array, [], result);
    return result;
}

Functions generateAllCmobinations will return you array of all possible non-empty combinations. If you wish I will write function wich will return all combinations of length K ;-)

And you cannot find better algorithms. Because solution is always has complexity O(C), where C is number of total combinations. So complexity according to the size of array is exponential O(2^N)

Nippey · Accepted Answer · 2012-09-17 08:54:25Z

If you want to create variables for each combination, I suggest using an object. In Javascript, elements of an object can be accessed in two ways:

var obj = {};
obj["element"] = "foo";
alert(obj.element);    // Will alert: "foo".

Instead of writing a string each time, you can save you variable names in an array and use this array to assign the names:

var names = ["a", "b", "c", "d"];
var obj = {};
for (var idx = 0; idx < names.length; idx++)
    obj[names[idx]] = idx;

alert(obj.a);          //Will alert: "0".
alert(obj.c);          //Will alert: "2".

If you need to create global variables, you could use the window object instead of obj. Although I do not recommend messing around with the window object.

And the names array, you can see in code above can be created programmatically. So, no need to "brute force hardcoding".

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