Nesting Boxes ( Due 28 Feb 2014 )

Imagine a room full of boxes. Each box has a length, width, and height. Since the boxes can be rotated those terms are inter- changeable. The dimensions are integral values in a consistent system of units. The boxes have rectangular surfaces and can be nested inside each other. A box can nest inside another box if all its dimensions are strictly less than the corresponding dimensions of the other. You may only nest a box such that the corresponding surfaces are parallel to each other. A box may not be nested along the diagonal. You cannot also put two or more boxes side by side inside another box.

The list of boxes is given in a file called boxes.txt. The first line gives the number of boxes n. The next n lines gives a set of three integers separated by one or more spaces. These integers represent the 3 dimensions of a box. Since you can rotate the boxes, the order of the dimensions does not matter. It may be to your advantage to sort the dimensions in ascending order.

The output of your code will be the largest subset of boxes that nest inside each other starting with the inner most box to the outer most box. There should be one line for each box.

Largest Subset of Nesting Boxes
(2, 2, 3)
(3, 4, 4)
(5, 5, 6)
(6, 7, 9)

If there is two or more subsets of equal lengths that qualify as being the largest subset, then print all the largest qualifying subsets with a one line space between each subset. The minimum number of boxes that qualify as nesting is 2. If there are no boxes that nest in another, then write "No Nesting Boxes" instead of "Largest Subset of Nesting Boxes".

For the data set that has been given to you, here is the solution set.

The file that you will be turning in will be called Boxes.py. The file will have a header of the following form:

/*
  File: Boxes.py

  Description:

  Student's Name:

  Student's UT EID:

  Course Name: CS 313E 
  
  Unique Number: 53580 

  Date Created:

  Date Last Modified:

*/

Use the turnin program to submit your Boxes.py file. The proctor should receive your work by 11 PM on Friday, 28 February 2014. There will be substantial penalties if you do not adhere to the guidelines. The student assistant in charge of this assignment is Bon Koo (bonkoo@utexas.edu).