## The Binary Search algorithm

Long time since I last wrote here so I’ll take the opportunity to introduce (just joking) the Binary Search algorithm.

I was looking for a safe way to find the line of text where a user clicks the mouse. I needed this for the TextArea+ editor. Fortunately Mozilla supports the DOM3’s compareDocumentPosition() function, so I took advantatge of it. Since I’m using a UL with an LI child element for each line of text, I can say that UL.childNodes is an ordered array, which fits perfectly for the Binary Search algorithm.

The algorithm is really simple (I’m sure most of you have used it before), we just need to find the middle point between two points and compare its value with the one we’re looking for. We do this recursively until we either find the value or the right point becomes smaller than the left one, which means that the value is just not there.

Here comes a really simple example of this algorithm (without using recursive calls)

```
var left = 0;
var right = 100;
while (left <= right) {
middle = floor( (right-left)/2 ) + left;
if (haystack[mid] == needle) {
alert('Found!');
break;
}
if ( needle < haystack[middle] )
right = middle-1;
else
left = middle+1;
}
```

The Binary Search algorithm performs at O(log n) time, but for TextArea+ I use a number of further optimizations. Since it’s likely that the user will click closely to where the cursor currently is, I just check the N precedding and following lines before. If this fails I check the current viewport and if still not found, then just do a full search. And this is just for the Mozilla code path! hell, how I hate cross-browser coding!

This post is meant to remind us how important is to learn already known and proved algorithms and that even when having a good algorithm, there is always room to optimize by taking advantge of our specific problem.