D3: What is a Bisector?

Question

The underlying idea behind bisect is this:

Consider the array that you mention - var data = [3, 6, 2, 7, 5, 4, 8]

You want to insert a new value let's say 3.5 into data array and want to know how would that 'partition' it. In other words, you want to know what would be the index of 3.5 if it were inserted when data array is sorted.

   var data = [3, 6, 2, 7, 5, 4, 8]

   //Sorted data

  [2, 3, 4, 5, 6, 7, 8]

  //You want to insert 3.5


  The sorted array after insertion of 3.5 should look something like:

  [2, 3, 3.5, 4, 5, 6, 7, 8]


  So the index of 3.5 in sorted data array is "2".

There are situations where you would want to know how the insertion of that element 'bisects' or 'divides' an array. In that case, you would want to first sort that array and do what we call a Binary Search to find out the correct position for insertion of that element.

bisectLeft and bisectRight take care to clarify the anomaly in a situation where you want to enter an element that already exists in the array. Let's say you want to enter another 3 into the array. There are two situations:

   3* -> The new element to be entered


   [2, 3*, 3, 4, 5, 6, 7, 8] -> entered at "1" (array is still sorted)


   [2, 3, 3*, 4, 5, 6, 7, 8] -> entered at "2" (array is still sorted)

So depending upon how we take care of this ambiguity, we can enter that element to the 'left' or 'right' of the already existing element. From the docs (Mark the emphasis):

The returned insertion point i partitions the array into two halves so that all v < x for v in array.slice(lo, i) for the left side and all v >= x for v in array.slice(i, hi) for the right side.

In bisectLeft we get 1 as the suitable index, all the duplicate entries will be on the right of that index and the situation is exactly the opposite in bisecRight.

Now that you know how bisectLeft and bisectRight work, the bisector just allows us to define a custom comparator or accessor function to parition the values or make sense of < and > on objects as well.

So this piece of code:

  var bisect = d3.bisector(function(d) { return d.date; }).right;

  var bisect = d3.bisector(function(a, b) { return a.date - b.date; }).right;

Just specifies to use the bisectRight option and return a suitable index for the insertion of an element assuming the array is sorted(in ascending order).

So if I were to build up on your example and assuming a bisector named bisect. And you did:

 bisect(data, 3); //it would return 2.

I hope it clarifies things and gets you started in the right direction.

From the documentation (that you've linked to):

Locate the insertion point for x in array to maintain sorted order.

That's what it does. It tells you where a new element should be inserted to still have a sorted array after that. The array can be any kind of structure, which is why there's an accessor function that allows you to "decompose" this structure for the purposes of searching.

The difference between left and right bisects is where the insertion point is (to the left or right of the closest element) -- whether the array is sorted ascending or descending.

One use case for the bisectors is where you want to highlight the closest data point when moving the mouse over a graph, see e.g. this example.