Powerset from array
Copyright (c) 2011 Max Lovenheim Irwin, http://binarymax.com
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/*******************************************
* Powerset calculation from array 'o'.
*
* The cardinality of a set's Powerset is 2^n,
* where n is the cardinality of the set.
*
* This conveniently translates into an algorithm
* whereby all the binary representation of (0...2^n)
* are representitive of all possible combinations of
* the set, with 0.toString(2) as the empty set, and
* ((2^n)-1).toString() as the full set.
*
* For example, with set ['A','B','C']:
* 0 == 000 == [null]
* 1 == 001 == ['C']
* 2 == 010 == ['B']
* 3 == 011 == ['B','C']
* 4 == 100 == ['A']
* 5 == 101 == ['A','C']
* 6 == 110 == ['A','B']
* 7 == 111 == ['A','B','C']
*
*******************************************/
function P(
o, //array passed in as only parameter.
w, //binary representation of iterator 0...(2^n)-1 (see 's' below)
e, //represents an iterator that loops through each bit in w
r, //the powerset array that will be returned, an array of subset arrays
s, //iterator that steps -1 as ((2^n)-1)...0
E, //the length of the original set
t //accounts for lack of preceding 0's in w. For example (1).toString(2) == "1", not "001"
) {
for(r=[s=1<<(E=o.length)];s;) //initialize r=[(2^n)].
for(w=s.toString(2), //Store binary representaion
e=t=w.length, //Length of the binary (see parameter t)
r[--s]=[]; //new subset
e;) //e iterates over (t-1)...0
~-w[--e]|| //if bit in position e is 1
r[s].push(o[e+E-t]); // ... add respective set item to subset
// ... NOTE: the subset order is reversed
return r //return the powerset
}
<!doctype html>
<html>
<head>
<title>Powerset</title>
<meta charset="utf-8" />
<script src="index.js" type="text/javascript"></script>
<script language="javascript" type="text/javascript">
function page_load() {
/*Powerset:*/
var Set = [1,2,3,4,5,6];
var Powerset = P(Set);
document.body.innerHTML+=JSON.stringify(Powerset);
document.body.innerHTML+='<br />';
document.body.innerHTML+=Powerset.length;
}
</script>
</head>
<body onload="page_load();">
</body>
</html>
function P(o,w,e,r,s,E,t){for(r=[s=1<<(E=o.length)];s;)for(w=s.toString(2),e=t=w.length,r[--s]=[];e;)~-w[--e]||r[s].push(o[e+E-t]);return r}
{
"name": "Powerset",
"description": "P(a) returns the powerset for array a.",
"keywords": [
"Powerset",
"set",
"P"
]
}