How can I create every combination possible for the contents of two arrays?

Question

Or if you'd like to create combinations with an arbitrary number of arrays of arbitrary sizes...(I'm sure you can do this recursively, but since this isn't a job interview, I'm instead using an iterative "odometer" for this...it increments a "number" with each digit a "base-n" digit based on the length of each array)...for example...

combineArrays([ ["A","B","C"],
                ["+", "-", "*", "/"],
                ["1","2"] ] )

...returns...

[
   "A+1","A+2","A-1", "A-2",
   "A*1", "A*2", "A/1", "A/2", 
   "B+1","B+2","B-1", "B-2",
   "B*1", "B*2", "B/1", "B/2", 
   "C+1","C+2","C-1", "C-2",
   "C*1", "C*2", "C/1", "C/2"
]

...each of these corresponding to an "odometer" value that picks an index from each array...

[0,0,0], [0,0,1], [0,1,0], [0,1,1]
[0,2,0], [0,2,1], [0,3,0], [0,3,1]
[1,0,0], [1,0,1], [1,1,0], [1,1,1]
[1,2,0], [1,2,1], [1,3,0], [1,3,1]
[2,0,0], [2,0,1], [2,1,0], [2,1,1]
[2,2,0], [2,2,1], [2,3,0], [2,3,1]

The "odometer" method allows you to easily generate the type of output you want, not just the concatenated strings like we have here. Besides that, by avoiding recursion we avoid the possibility of -- dare I say it? -- a stack overflow...

function combineArrays( array_of_arrays ){

    // First, handle some degenerate cases...

    if( ! array_of_arrays ){
        // Or maybe we should toss an exception...?
        return [];
    }

    if( ! Array.isArray( array_of_arrays ) ){
        // Or maybe we should toss an exception...?
        return [];
    }

    if( array_of_arrays.length == 0 ){
        return [];
    }

    for( let i = 0 ; i < array_of_arrays.length; i++ ){
        if( ! Array.isArray(array_of_arrays[i]) || array_of_arrays[i].length == 0 ){
            // If any of the arrays in array_of_arrays are not arrays or zero-length, return an empty array...
            return [];
        }
    }

    // Done with degenerate cases...

    // Start "odometer" with a 0 for each array in array_of_arrays.
    let odometer = new Array( array_of_arrays.length );
    odometer.fill( 0 ); 

    let output = [];

    let newCombination = formCombination( odometer, array_of_arrays );

    output.push( newCombination );

    while ( odometer_increment( odometer, array_of_arrays ) ){
        newCombination = formCombination( odometer, array_of_arrays );
        output.push( newCombination );
    }

    return output;
}/* combineArrays() */


// Translate "odometer" to combinations from array_of_arrays
function formCombination( odometer, array_of_arrays ){
    // In Imperative Programmingese (i.e., English):
    // let s_output = "";
    // for( let i=0; i < odometer.length; i++ ){
    //    s_output += "" + array_of_arrays[i][odometer[i]]; 
    // }
    // return s_output;

    // In Functional Programmingese (Henny Youngman one-liner):
    return odometer.reduce(
      function(accumulator, odometer_value, odometer_index){
        return "" + accumulator + array_of_arrays[odometer_index][odometer_value];
      },
      ""
    );
}/* formCombination() */

function odometer_increment( odometer, array_of_arrays ){

    // Basically, work you way from the rightmost digit of the "odometer"...
    // if you're able to increment without cycling that digit back to zero,
    // you're all done, otherwise, cycle that digit to zero and go one digit to the
    // left, and begin again until you're able to increment a digit
    // without cycling it...simple, huh...?

    for( let i_odometer_digit = odometer.length-1; i_odometer_digit >=0; i_odometer_digit-- ){ 

        let maxee = array_of_arrays[i_odometer_digit].length - 1;         

        if( odometer[i_odometer_digit] + 1 <= maxee ){
            // increment, and you're done...
            odometer[i_odometer_digit]++;
            return true;
        }
        else{
            if( i_odometer_digit - 1 < 0 ){
                // No more digits left to increment, end of the line...
                return false;
            }
            else{
                // Can't increment this digit, cycle it to zero and continue
                // the loop to go over to the next digit...
                odometer[i_odometer_digit]=0;
                continue;
            }
        }
    }/* for( let odometer_digit = odometer.length-1; odometer_digit >=0; odometer_digit-- ) */

}/* odometer_increment() */

Just in case anyone is looking for Array.map solution

var array1=["A","B","C"];

var array2=["1","2","3","4"];

console.log(array1.flatMap(d => array2.map(v => d + v)))

A loop of this form

combos = [] //or combos = new Array(2);

for(var i = 0; i < array1.length; i++)
{
     for(var j = 0; j < array2.length; j++)
     {
        //you would access the element of the array as array1[i] and array2[j]
        //create and array with as many elements as the number of arrays you are to combine
        //add them in
        //you could have as many dimensions as you need
        combos.push(array1[i] + array2[j])
     }
}

Seeing a lot of for loops in all of the answers...

Here's a recursive solution I came up with that will find all combinations of N number of arrays by taking 1 element from each array:

const array1=["A","B","C"]
const array2=["1","2","3"]
const array3=["red","blue","green"]

const combine = ([head, ...[headTail, ...tailTail]]) => {
  if (!headTail) return head

  const combined = headTail.reduce((acc, x) => {
    return acc.concat(head.map(h => `${h}${x}`))
  }, [])

  return combine([combined, ...tailTail])
}

console.log('With your example arrays:', combine([array1, array2]))
console.log('With N arrays:', combine([array1, array2, array3]))

Assuming you're using a recent web browser with support for Array.forEach:

var combos = [];
array1.forEach(function(a1){
  array2.forEach(function(a2){
    combos.push(a1 + a2);
  });
});

If you don't have forEach, it is an easy enough exercise to rewrite this without it. As others have proven before, there's also some performance advantages to doing without... (Though I contend that not long from now, the common JavaScript runtimes will optimize away any current advantages to doing this otherwise.)

Part II: After my complicated iterative "odometer" solution of July 2018, here's a simpler recursive version of combineArraysRecursively()...

function combineArraysRecursively( array_of_arrays ){

        // First, handle some degenerate cases...

        if( ! array_of_arrays ){
            // Or maybe we should toss an exception...?
            return [];
        }

        if( ! Array.isArray( array_of_arrays ) ){
            // Or maybe we should toss an exception...?
            return [];
        }

        if( array_of_arrays.length == 0 ){
            return [];
        }

        for( let i = 0 ; i < array_of_arrays.length; i++ ){
            if( ! Array.isArray(array_of_arrays[i]) || array_of_arrays[i].length == 0 ){
                // If any of the arrays in array_of_arrays are not arrays or are zero-length array, return an empty array...
                return [];
            }
        }

        // Done with degenerate cases...
        let outputs = [];

        function permute(arrayOfArrays, whichArray=0, output=""){

            arrayOfArrays[whichArray].forEach((array_element)=>{
                if( whichArray == array_of_arrays.length - 1 ){            
                    // Base case...
                    outputs.push( output + array_element );
                }
                else{
                    // Recursive case...
                    permute(arrayOfArrays, whichArray+1, output + array_element );
                }
            });/*  forEach() */
        }

        permute(array_of_arrays);

        return outputs;
        

}/* function combineArraysRecursively() */

const array1 = ["A","B","C"];
const array2 = ["+", "-", "*", "/"];
const array3 = ["1","2"];

console.log("combineArraysRecursively(array1, array2, array3) = ", combineArraysRecursively([array1, array2, array3]) );