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Lets say I have several sets of options in Javascript

var color  =  ["red", "blue", "green","yellow"];
var size   =  ["small", "medium", "large"];
var weight =  ["heavy", "light"];

what is an efficient algorithm to get all the binations of these options in an array that looks like this

["red and small and heavy", "red and small and light", "red and medium and heavy" ...]

Here's the caveat though

This function must be able to take any number of sets of options

I have a feeling that the proper way to do this is through some sort of tree traversal, but its too early to have fully thought this through and I haven't had my coffee yet

Lets say I have several sets of options in Javascript

var color  =  ["red", "blue", "green","yellow"];
var size   =  ["small", "medium", "large"];
var weight =  ["heavy", "light"];

what is an efficient algorithm to get all the binations of these options in an array that looks like this

["red and small and heavy", "red and small and light", "red and medium and heavy" ...]

Here's the caveat though

This function must be able to take any number of sets of options

I have a feeling that the proper way to do this is through some sort of tree traversal, but its too early to have fully thought this through and I haven't had my coffee yet

• javascript
• algorithm
• binations
• cartesian-product

Share Improve this question Follow edited Jan 11, 2012 at 16:56 Marcin 49.9k1818 gold badges136136 silver badges207207 bronze badges asked Jan 11, 2012 at 16:33 Greg GuidaGreg Guida 7,51244 gold badges3131 silver badges4040 bronze badges

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4 Answers 4

Sorted by: Reset to default 8

function permutations(choices, callback, prefix) {
    if(!choices.length) {
        return callback(prefix);
    }
    for(var c = 0; c < choices[0].length; c++) {
        permutations(choices.slice(1), callback, (prefix || []).concat(choices[0][c]));
    }
}

var color  =  ["red", "blue", "green","yellow"];
var size   =  ["small", "medium", "large"];
var weight =  ["heavy", "light"];

permutations([color, size, weight], console.log.bind(console));

Seems to work...

[ 'red', 'small', 'heavy' ]
[ 'red', 'small', 'light' ]
[ 'red', 'medium', 'heavy' ]
[ 'red', 'medium', 'light' ]
[ 'red', 'large', 'heavy' ]
[ 'red', 'large', 'light' ]
[ 'blue', 'small', 'heavy' ]
[ 'blue', 'small', 'light' ]
[ 'blue', 'medium', 'heavy' ]
[ 'blue', 'medium', 'light' ]
[ 'blue', 'large', 'heavy' ]
[ 'blue', 'large', 'light' ]
[ 'green', 'small', 'heavy' ]
[ 'green', 'small', 'light' ]
[ 'green', 'medium', 'heavy' ]
[ 'green', 'medium', 'light' ]
[ 'green', 'large', 'heavy' ]
[ 'green', 'large', 'light' ]
[ 'yellow', 'small', 'heavy' ]
[ 'yellow', 'small', 'light' ]
[ 'yellow', 'medium', 'heavy' ]
[ 'yellow', 'medium', 'light' ]
[ 'yellow', 'large', 'heavy' ]
[ 'yellow', 'large', 'light' ]

That would be the cartesian product of those sets: http://en.wikipedia/wiki/Cartesian_product

Also see: https://stackoverflow./questions/4796678/javascript-golf-cartesian-product

Tree traversal is the way to go, well recursion to be exact.

The working principle is, at each depth you would iterate through all the options for that depth, in your case the options for a list. When you choose element form last depth, you have one full set.

The console.log function mentioned in #1 above should be as:

function log(message){
    if(typeof console == "object"){
        console.log(message);
    }
}

Then, change the call to the function to:

binations([color, size, weight], log);

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