​​Lab 4.5: Evaluating Algorithms
​​Bard College – Computer Science – Data Structures
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​​We’ll practice the experimental approach for evaluating algorithms outlined in section 1.4 (pg 174–179).
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​​ThreeSum

​​First, develop run-time models ​​T(N)T(N)​ of ThreeSum​ and ThreeSumFast​ on your own machine. 
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  1. ​​Gather run-time statistics for both programs using varying input sizes (e.g.  1K, 2K, 4K, 8K) using StopWatch​ . (Best to record the means of many experiments per input size, why?)
  1. ​​Enter those findings into a spreadsheet.
  1. ​​Plot the running time of both algorithms (a scatter chart with standard axes and a trend line).
  1. ​​Log-transform the data.
  1. ​​Plot the log-transformed data and compute the best-fit line (i.e., linear trend-line). 
  • ​​You can use the =SLOPE(D2:D16, C2:C16)​ and =INTERCEPT(D2:D16, C2:C16)​ formulas for finding the equation of the best-fit line.
  1. ​​Report your estimate of ​​T(N)=aNmT(N)=aN^m​ and use it to predict the run-times of the various input sizes (pg. 176).
  1. ​​Reflect on how well your model summarizes and predicts (16K) run-times.

​​Traveling Salesperson

​​Second, develop run-time models for the heuristics for finding Traveling Salesperson tours we developed last week;  follow the same process as you did with ThreeSum​ . Compare a simple insert (LIFO or FIFO) with one or both of your heuristics. If you were not able to get either heuristic working, use the reversing task instead (see below).

​​Reversing a Stream

​​Explore the performance of array-based data structures to reverse a stream of data. Compare the book’s resizing strategy (doubling the size of the array) with the naive approach where you grow and shrink the array by one.
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​​ ResizingArrayStack<Integer> stack = new ResizingArrayStack<Integer>();
​​ while (!q.isEmpty()) stack.push(q.dequeue());
​​ while (!stack.isEmpty()) q.enqueue(stack.pop());
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​​Develop models for both types of array-based data structures. You will have to modify the book’s  ResizingArrayQueue​ & ResizingArrayStack​ to grow and shrink by one.
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​​EXTRA: You might also compare with the linked-list variety:  Queue​ and Stack​ .  
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​​Submission

​​Bring a hard copy of your PDF describing your findings: include the graphs, tables of the data, and the resulting mathematical models. Include graphics showing your TSP solution working. Also bring a hardcopy of your final Tour.java​ file.
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