fastest way to determine if an element is in a sorted array

Question

I have an array of sorted ints with a 1,000 or more values (could be up to 5000+). I need to write a function that receives an int and returns a bool based on the element being in the array. I know I can write a for loop with a break, I know I can use jquery .InArray.

What would be the best way to implement this, KNOWING that the array is sorted.

Thanks.

Answer 1

Knowing that the array is sorted a binary search would be the best approach.

Answer 2

I think you'd want to use a binary search routine. A binary search routine is

whereas a linear search is, on average,

.

There are many variations to choose form. Here's one I found in this article:

function binarySearch(items, value){

    var startIndex  = 0,
        stopIndex   = items.length - 1,
        middle      = Math.floor((stopIndex + startIndex)/2);

    while(items[middle] != value && startIndex < stopIndex){

        //adjust search area
        if (value < items[middle]){
            stopIndex = middle - 1;
        } else if (value > items[middle]){
            startIndex = middle + 1;
        }

        //recalculate middle
        middle = Math.floor((stopIndex + startIndex)/2);
    }

    //make sure it's the right value
    return (items[middle] != value) ? -1 : middle;
}

Or this simpler looking version from this article that has a binary search function in a zillion different languages.

function binary_search_iterative(a, value) {
    var lo = 0, hi = a.length - 1, mid;
    while (lo <= hi) {
        mid = Math.floor((lo+hi)/2);
        if (a[mid] > value)
            hi = mid - 1;
        else if (a[mid] < value)
            lo = mid + 1;
        else
            return mid;
    }
    return null;
}

There's also a binary search in Google closure with the code here.

And, a good description of how the binary search algorithm works on Wikipedia.

Answer 3

If the array's sorted, then the answer's sorted - use a binary chop.

Answer 4

If doing lookups more than once, migrate to a map-like object.

var fastLookup = {};
mySortedArray.forEach(function(i){fastLookup[i]=true)});

//Each time:
  if (fastLookup[key]===true){ //do thing
  }

Answer 5

Many languages already have this implemented for example in java you can just use CollectionsCollections.binarySearch(List> list, T key) method and I'm pretty sure C# also has some sort of BinarySearch method.