Frequently Asked Questions (General)

Is a point on the boundary of a rectangle considered inside it? Do two rectangle intersect if they have just one point in common? Yes and yes, consistent with the implementation of

Can I use the distanceTo() method in Point2D and RectHV? No, you may use only the subset of the methods listed. You should be able to accomplish the same result (more efficiently) with distanceSquaredTo().

Can I use the X_ORDER() and Y_ORDER() comparators in Point2D? No, you may use only the subset of the methods listed. You should be able to accomplish the same result by calling the methods x() and y().

What should I do if a point is inserted twice in the data structure? The data structure represents a symbol table, so you should replace the old value with the new value.

What should points() return if there are no points in the data structure? What should range() return if there are no points in the range? The API says to return an Iterable<Point2D>, so you should return an iterable with zero points.

What should nearest() return if there are two (or more) nearest points? The API does not specify, so you may return any nearest point (up to floating-point precision).

I run out of memory when running some of the large sample files. What should I do? Be sure to ask Java for additional memory, e.g., java-algs4 -Xmx1600m RangeSearchVisualizer input1M.txt.

Frequently Asked Questions (PointST)

In which order should the points() method in PointST return the points? The API does not specify the order, so any order is fine.

Frequently Asked Questions (KdTreeST)

What makes KdTreeST difficult? How do I make the best use of my time? Debugging performance errors is one of the biggest challenges. It is very important that you understand and implement the key optimizations described in the assignment specification:

Do not begin range() or nearest() until you understand these rules.

I'm nervous about writing recursive search tree code. How do I even start on Use as a guide. The trickiest part is understanding how the put() method works. You do not need to include code that involves storing the subtree sizes (since this is used only for ordered symbol table operations).

Will I lose points for a non-recursive implementation of range search? No. While we recommend using a recursive implementation (both for elegance and as a warmup for nearest-neighbor search), you are free to implement it without using recursion.

What should I do if a point has the same x-coordinate as the point in a node when inserting or searching in a 2d-tree? Go to the right subtree as specified in the assignment under Search and insert.

Frequently Asked Questions (Timing)

How do I generate a uniformly random point in the unit square? Make two calls to StdRandom.uniform(0.0, 1.0)—one for the x-coordinate and one for the y-coordinate.


Sample input files.   Download It contains sample input files in the specified format.

Testing put() and points() in KdTreeST. The client reads a sequence of points from a file (given as a command-line argument) and draws the corresponding kd-tree. It does so by reconstruting the kd-tree from the level-order traversal returned by points(). Note that it doesn’t seem to work when there are two (or more) points with the same x- or y-coordinate.





Testing range() and nearest() in KdTreeST. A good way to test these methods is to perform the same sequence of operations on both the PointST and KdTreeST data types and identify any discrepancies. The key is to implement a reference solution in which you have confidence. The brute-force implementation PointST can serve this purpose in your testing.

Warning: both of these clients will be slow for large inputs because (1) the methods in the brute-force implementation are slow and (2) drawing the points is slow.

Possible Progress Steps

These are purely suggestions for how you might make progress on You do not have to follow these steps.

  1. Complete the KdTree worksheet. Here is a set of practice problems for the core kd-tree methods. Here are the answers.

  2. Node data type. There are several reasonable ways to represent a node in a 2d-tree. One approach is to include the point, a link to the left/bottom subtree, a link to the right/top subtree, and an axis-aligned rectangle corresponding to the node.
    private class Node {
       private Point2D p;     // the point
       private Value val;     // the symbol table maps the point to this value
       private RectHV rect;   // the axis-aligned rectangle corresponding to this node
       private Node lb;       // the left/bottom subtree
       private Node rt;       // the right/top subtree

  3. Writing KdTreeST.

A video, worksheet, and coding tips are provided for those wishing additional assistance. Warning: the videos were produced in 2014 and are somewhat out of date. For example the API has changed.


These are many ways to improve performance of your 2d-tree. Here are some ideas.