What does the "^=" operator do in this find non-paired number algorithm?

Question

Saw an interesting piece of code to find a lonely number in a list of duplicate numbers (where every number in the list occurs twice except for one).

function findNonPaired(listOfNumbers) {
  let nonPairedNumber = 0

  listOfNumbers.forEach((n) => {
      nonPairedNumber ^= n
  })

  return nonPairedNumber
}

const x = [1,5,4,3,9,2,3,1,4,5,9]
console.log(findNonPaired(x))

This solution looks very elegant, but I'm curious at to what the ^= operator is actually doing here?

@CumuloNimbus Those are carrots (different word). Just to note, `^=` also has a meaning in CSS, to [match the beginning of an attribute](https://developer.mozilla.org/en-US/docs/Web/CSS/Attribute_selectors). The meaning is similar to the ["start of string" anchor](http://www.regular-expressions.info/anchors.html) from regular expressions. You can apply CSS's `^=` to JavaScript by using `document.querySelectorAll('[name^=form1-]')` which finds all elements with a "name" attribute that begins with "form1-" — Pluto, May 24 '17 at 17:20
As a side note, this function can be a one-liner: `findUnique = list => list.reduce((out, n) => out ^ n, 0)` — Joe Frambach, May 24 '17 at 19:01
@CumuloNimbus _Carets_. Carrots are the things in the ground that Bugs Bunny likes. — David Given, May 24 '17 at 21:03
Have you considered consulting a reference manual? https://www.w3schools.com/js/js_assignment.asp — Hot Licks, May 24 '17 at 22:09

score 19 · Accepted Answer · edited May 24 '17 at 20:36

19

a ^= b is the same as a = a ^ b where ^ is the bitwise XOR operator.

0 ^ 0 === 0
1 ^ 0 === 1
0 ^ 1 === 1
1 ^ 1 === 0

This is a neat algorithm. Let's trace one execution with the list [8, 12, 8] for example:

0 ^ 8 = 0000 ^ 1000 = 1000
        1000 ^ 1100 = 0100
        0100 ^ 1000 = 1100 = 12

The word "duplicate" isn't correct. This algorithm tests for parity. A simple but somewhat wrong definition is "when everything has a pair". pair...parity.

[2,2,2,3,3,5,5,5,5] will return 2 because everything else has a pair.

[3,4,5] will actually return 2 (011^100^101 -> 010) because that is the xor of all the unpaired items.

edited May 24 '17 at 20:36

mbomb007

3,077
2
30
51

answered May 24 '17 at 17:10

Joe Frambach

25,568
9
65
95

Cool stuff, thanks for the explanation and examples – Cumulo Nimbus May 24 '17 at 18:37
2

Therefore, the algorithm isn't "neat" at all, because it pretends to find "unique number", while in your example [2,2,2,3,3,5,5,5,5] it falsely finds 2 despite 2 being part of a triplet, and therefore not unique, and in your [3,4,5] finding 2, which isn't even in the list, and failing to find the three unique numbers that are actually there. This is one of those things a programmer can "get away with" until those conditions no longer apply, at which point it fails spectacularly, as your last example demonstrates. – Monty Harder May 24 '17 at 21:35
@MontyHarder Usually people make an argument before saying "Therefore"... Also thanks for your opinion on this algorithm's neatness. However, it correctly finds 2 in this example b/c it is the only unpaired number. Admittedly "unique" was a bad word choice by me, and "non-paired" would be a better choice of words, as pointed out by JoeFrambach – Cumulo Nimbus May 24 '17 at 22:09
1

@MontyHarder You could say the same thing about any algorithm if you fail to satisfy its preconditions. The question was quite clear that it operates on a list of numbers where each number appears twice except for one. While you have certainly shown that it doesn't work outside of that, that's a strawman argument; no one was claiming that it would. – Chris Hayes May 24 '17 at 22:41
@MontyHarder Did I say something wrong in my answer? – Joe Frambach May 24 '17 at 22:58

score 4 · Answer 2 · answered May 24 '17 at 17:15

Like other answers say - it is a bitwise XOR.

About the algorythm - it is cool if you are sure that the duplicates are even count. When a number is XOR-ed with x and later again XOR-ed with x it will return to it's previuos value. If one number is seen 3 times in this chain, the 3-rd occurence will fool this algorythm. Also if there is one more value that is single in the chain, like:

a, b, c, X, a, c, b, Y

the result will be (X ^ Y) and you can't be sure if you have one unique value or more.

No sane person wants to inherit responsibility for code like this, which doesn't document the assumptions (and we know what happens when we ASS|U|ME) it makes. — Monty Harder, May 24 '17 at 21:39

What does the "^=" operator do in this find non-paired number algorithm?

2 Answers2