Possible Letter Combinations

[johnnyg24]

I am looking to write a script that generates every possible combination of 4 different letters. I need to be able to represent a null value using 'x'.Each combination needs to have 4 characters separated by a '.'.Here's an example: A.B.C.DX.X.X.XX.X.X.DX.X.C.DX.B.C.DX.X.C.XX.B.X.XX.B.C.XA.X.X.XA.B.X.XA.B.C.XA.X.X.DA.X.C.XA.B.X.DX.B.C.DA.X.C.D The order of the letters will never change, so it doesn't need to generate a value of: d.c.b.a or anything like that. There should be 16 different combinations I think. Is there a way to use JavaScript to do this? Thanks.

[Ingolme]

The letters don't really matter. They're just true or false. With four bits you can represent values from 0 to 16. We can use bitwise logic operators for that. The bitwise operator takes the binary value of a number and compares it with the binary value of another.

var str = "";for(i = 0; i < 16; i++) {  str += (i & 8 ? "A." : "X.");  str += (i & 4 ? "B." : "X.");  str += (i & 2 ? "C." : "X.");  str += (i & 1 ? "D\n" : "X\n");}alert(str);

[johnnyg24]

Wow, thank you so much. I've literally gone through an entire note pad trying to figure out the logic. What if there were 5 different letter such as A..B.C.D.E?, How would I set it up then? Thanks

[ShadowMage]

The number of possible combinations is n^x where n is how many possibilities for each slot (in this case, 2: a letter or null) and x is the number of slots (5 in the case of ABCDE) so the number of combinations is 2^5 or 32. In the code Ingolme showed you, just change the 16 to 32. If you want this to be dynamic or easily manipulated, you can create a function to do it:

function combinations(n, x) {   return Math.pow(n, x);} var str = "";for (i = 0; i < combinations(2, 5); i++) {   str += (i & 16 ? "A." : "X.");   str += (i & 8 ? "B." : "X.");   str += (i & 4 ? "C." : "X.");   str += (i & 2 ? "D" : "X");   str += (i & 1 ? "E\n" : "X\n");}alert(str);

Now all you have to do is change the 5 to whatever length you want. EDIT: Oops, forgot you'll also have to add another line in there for printing the E. I'm not sure if I've got the bitwise operations correct, but I'm sure Ingolme can verify.

[johnnyg24]

Thank you everyone for the help. Thought I would add my spin on this with a completely dynamic way of doing this based on an array of possible letters

function combinations(n, x) {   return Math.pow(n, x);}var att = ['A','B','C','D','E','F','G']var pw = []var n = 1for(p=0;p<att.length;p++){n = n * 2pw.push(combinations(2, att.length)/n)} var str = ""; for (i = 0; i < combinations(2, att.length); i++) {   var cnt = 0   for(l=0;l<att.length;l++){    if(l<att.length-1){   str += (i & pw[cnt] ? att[cnt] + "." : "X.");   cnt++}else{str += (i & pw[cnt] ? att[cnt] + "<br>" : "X<br>");   cnt++}   }}  document.getElementById('here').innerHTML = str

[ShadowMage]

Nice work! Glad to see you got it worked out.