Programming Assignment Checklist: Traveling Salesperson Problem

Frequently Asked Questions (general)

What are the main goals of this assignment? The goals of this assignment are to:

What preparation do I need before beginning this assignment? Read Section 4.3. Pay particular attention to the parts that deal with linked lists.

Can I program with a partner on this assignment? Yes. You are encouraged (not required) to work with a partner provided you practice pair programming.

Do I need to follow the prescribed API? Yes, we will be testing the methods in the API directly. If your method has a different signature or does not behave as specified, you will lose a substantial number of points. You may not add public methods to the API; however, you may add private methods (which are only accessible in the class in which they are declared).

Frequently Asked Questions (Tour)

What should the various methods do if the tour has no points? The size() method should return 0; the length() method should return 0.0; the show() method should print nothing to standard output; the draw() method should draw nothing to standard drawing.

How do I represent infinity in Java? Use Double.POSITIVE_INFINITY.

How can I produce an animation of the heuristic in action? It's easy and instructive—just redraw the tour after each insertion. See the instructions in It could take a while on a big input file, so you might want to modify it so that it redraws only after every 20 insertions or so. Note: when timing your program, don't show the animation or else this may become the bottleneck.

What is the file Tour$Node.class? When you declare a nested class like Node, the Java compiler uses the $ symbol to mark its name.

How can the suggested definition of private class Node work when it has no constructor declared? For any class, Java will by default already define a no-argument constructor that sets all of the instance variables to their default values (here null since Point and Node are reference types).

What is a NullPointerException? You can get one by initializing a variable of type Node, say x, to null and then accessing or x.p. This can happen in your insertion routine if you inadvertently break up the circular linked list.

When should I create a new linked-list node with the keyword new? To create a tour with N points, you should use new exactly N times with Node, once per invocation of insert(). It is unnecessary (and bad style) to use new with your list traversal variables since this allocates memory that you never use.

Running with N = 10,000 already takes more than a minute. What should I do? You have a performance error. It should take only a few seconds when N is 10,000. If your code takes much much longer, try to discover why (think analysis of algorithms), and explain it in your readme.txt file.

When I run for 10,000 points, my nearest insertion heuristic runs quickly, but my smallest insertion heuristic takes more than 10 seconds to run. How can I fix this? You probably have a loop that looks at inserting the new point at each possible insertion point. That is fine. However, if you are calling the length() method to compute the new tour length at each potential insertion point, you are effectively adding a second loop inside your first loop (even though it is a single method call), which is too slow. You do not need to recompute the entire tour length for each possible insertion point. You only need to compute the change in the tour length and keep track of which insertion point results in the smallest such change.

Can I use Java's built in LinkedList class? Absolutely not! One of the main goals of this assignment is to gain experience writing and using linked structures. The Java libraries can only take you so far, and you will quickly discover applications which cannot be solved without devising your own linked structures.

Do I have to use a linked list for the leaderboard? No, you are not required to use the Tour data type or linked lists for the leaderboard. Of course, you should exercise good modular design.

What is the length of the best known tour for tsp1000.txt? Eric Mitchell '18 holds the COS 126 record with a tour of length 15566.37. Using the Concorde TSP solver, we found a tour of length 15476.519.

Input, Output, and Testing

Input.   The files for this assignment include many sample inputs. Most are taken from TSPLIB.

Debugging.   A good debugging strategy for most programs is to test your code on inputs that you can easily solve by hand. Start with 1 and 2 city problems. Then, do a 4 city problem. Choose the data so that it is easy to work through the code by hand. Draw pictures. If your code does not do exactly what your hand calculations indicate, determine where they differ. Use the StdOut.println() method to trace.

Checking your work.  For usa13509.txt we get tour lengths of 77449.9794 and 45074.7769 for nearest insertion and smallest insertion, respectively. For circuit1290.txt we get 25029.7905 and 14596.0971.

Timing.   You may use the client program to help you estimate the running time as a function of the input size N. It takes a command-line argument N, runs the two heuristics on a random input of size N, and prints out how long each took.

Interactive visualizer. in an interactive visualizer. It reads the points from standard input: it displays both the nearest neighbor heuristic tour (in red) and the smallest insertion heuristic (in blue). When you click a point in the window, it will add it to your tour. You can toggle the visibility o the two tours by typing n (for nearest neighbor) or s (for smallest insertion).

% java-introcs TspVisualizer tsp1000.txt
1000 points both smallest and nearest 1000 points smallest

If you want to test afterimplementing only one of the insertion methods, you must declare the other method (even if it does nothing).

Possible Progress Steps

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

  1. Make sure you fully understand the CircularQuote exercise from precept. This exercise also demonstrates how to use the do {...} while (...) loop.

  2. Download the .zip file mentioned on the assignment page. Extract it; later you should save in the same directory.

  3. Study the Point API. Its main() method reads in data from standard input in the TSP input format and draws the points to standard draw. In this assignment, you will use distanceTo() to compute the distance between two points and the drawTo() method to draw a line segment connecting two points.

  4. Create a file Include the standard linked list data type Node. Include one instance variable, say first, of type Node that is a reference to the "first" node of the circular linked list.

  5. For debugging purposes only, make a constructor that takes four points as arguments, and constructs a circular linked list using those four Point objects. First, create four nodes and assign one point to each. Then, link the nodes one to another in a circle.

  6. Implement the method show(). It should traverse each Node in the circular linked list, starting at first, and printing each Point using StdOut.println(). This method requires only a few lines of code, but it is important to think about it carefully, because debugging linked-list code is notoriously difficult and frustrating. Start by just printing out the first Point. With circular linked-lists the last node on the list points back to the first node, so watch out for infinite loops.

    Test your method by writing a main() function that defines four points, creates a new Tour object using those four points, and calls its show() method. Below is a suggested four point Tour for main(). Use it for testing.

      // main method for testing
      public static void main(String[] args) {
        // define 4 points forming a square
        Point a = new Point(100.0, 100.0);
        Point b = new Point(500.0, 100.0);
        Point c = new Point(500.0, 500.0);
        Point d = new Point(100.0, 500.0);
        // Set up a Tour with those four points
        // The constructor should link a->b->c->d->a
        Tour squareTour = new Tour(a, b, c, d);
        // Output the Tour;
    If your method is working properly, you will get the following output for the 4 city problem above.
    (100.0, 100.0)
    (500.0, 100.0)
    (500.0, 500.0)
    (100.0, 500.0)
    Test your method show() on tours with 0, 1 and 2 points to check that it still works. You can create such instances by modifying the 4-node debugging constructor to only link 0, 1 or 2 of the four points to the Tour. (If you don't define first, you will have an empty Tour. If you define first and link it back to itself, you will have a 1 point Tour.)

    Put the debugging constructor back to the original four point Tour before continuing.

  7. Implement the method size(). It is very similar to show().

    Test the size() method on some sample Tour objects in the main method.

  8. Implement the method length(). It is very similar to show(), except that you will need to invoke the method distanceTo() in the Point data type.

    Test! Add a call to the length() method in the main() and print the length and size. The 4-point example has a length of 1600.0.

  9. Implement the method draw(). It is also very similar to show(), except that you will need to invoke the method drawTo() in the Point data type.

    Test! You will also need to include the statements

    StdDraw.setXscale(0, 600);
    StdDraw.setYscale(0, 600);
    in your main() before you call the Tour draw() method. The four point example above should produce a square.
After arriving at this point, you should feel a sense of accomplishment: working with a linked list is quite difficult at first!

  1. Implement insertNearest(). To determine which node to insert the point p after, compute the Euclidean distance between each point in the tour and p by traversing the circular linked list. As you proceed, store the node containing the closest point and its distance to p. After you have found the closest node, create a node containing p, and insert it after the closest node. This involves changing the next field of both the newly created node and the closest node. As a check, here is the resulting tour for the 10 city problem which has length 1566.1363. Note that the optimal tour has length 1552.9612 so this rule does not, in general, yield the best tour.

  2. After doing the nearest insertion heuristic, you should be able write the method insertSmallest() by yourself, without any hints. The only difference is that you want to insert the point p where it will result in the least possible increase in the total tour length. As a check, here is the resulting tour which has length 1655.7462. In this case, the smallest insertion heuristic actually does worse than the nearest insertion heuristic (although this is not typical).