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 CSE 417, Wi '06: FAQ
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  1. Q.  When a homework or test question says "Give an algorithm...", how detailed should I be?

    E.g., if I want the vertex that has the lowest number, may I write?:

            Vertex := Min (VertexA, VertexB);
    
    Or should I be more detailed?:
            temp := vertexA; 
            if(vertexB < vertexA) temp:=vertexA;
    
    --- N. T. Know.

    A:   Dear Need,
    I don't want code, I want a clear, understandable description of the method. A program is a communication between you and a machine; an algorithm is a communication between you and another human about a program.

    E.g., "Min (VertexA, VertexB)" is fine, but I'd be just as happy with English: "between vertices A and B, choose the one with the smaller vertex number", or "keep an array with an entry for each vertex holding the count of the number of times that vertex is reached during process X and find the vertex with the min count." If you need a balanced binary search tree, say "using an WhizBlat tree from chapter 4 or my data structures class, we can ..."; definitely don't give me WhizBlat code.

    The basic issue is that you should break the problem down into steps that are clear enough that everyone else in the class should be able to:

    And it should be clearly organized so that the "big picture" is evident and so that you can argue that your algorithm is correct. In general, I want at least a sketch of correctness with all your algorithms, unless I say otherwise.

  2. Q.  How do I time my program?

    You've asked us to measure the time taken by our algorithms. How do I to this? Should I buy that $3.99 Rolex I keep getting emails about? --- T. Treasure

    A:   Dear Timeless,
    No, save the Rolex to impress that Certain Someone. Computers generally have built-in clocks. Accesssing them depends on the language. For example, in C/C++, you do:

          #include <time.h>
          int main(void) {
            clock_t start_tick, end_tick;
            double elapsed;
    
            start_tick = clock();
            my_really_fast_algorithm(42);
            end_tick = clock();
            elapsed = (end_tick - start_tick) / (double)CLOCKS_PER_SEC;
            printf("My Really Fast Algorithm took %f seconds!\n", elapsed);
            return 0;
          }
    
    CLOCKS_PER_SEC, defined in time.h, tells how to scale the system-dependent clock() results to seconds. (It is often 1000, but that does not tell you the resolution of the timer, which is often 10 or 16.7 or .001 milliseconds.)

    Similarly, in Java public static long currentTimeMillis() returns the current time in millisecond units (but not necessarily millisecond accuracy).

  3. Q.  How do I time my really, really fast program?

    I did what you outlined above, but I always get 0 seconds?!? ---S. LaCode

    A:   Dear Swifty,
    Congratulations! Your algorithm is a blazing marvel of speed. But just to be on the safe side, I always do this, too: Since the system clock may tick only once every 10 milliseconds or so, and my computer executes about a billion operations per second, a fair bit of work gets done between clock ticks. To time an algorithm more accurately for small n, repeat it r times, for some number r ≥ 1 judiciously chosen so that the elapsed time for all repetitions is, say, 500 milliseconds or greater, then report the elapsed time divided by r. It's OK to use a different r for different input sizes, just so each chunk you time is bigger than 500 ms or so. A big-O estimate of running time might suggest how r should be scaled with n.

    Specific systems may have additional features. These will be less portable, but may be more convenient. E.g., I learned about the following Windows functions from a 417 student: "Here are some links to high performance timer functions for windows. The first is QueryPerformanceFrequency, which returns a Boolean indicating whether the system supports HPCs (and everything NT4+ does, maybe much earlier), and takes a pointer to a 64 bit integer in which to store the clock frequency, in ticks per second. The second is QueryPerformanceCounter; it also returns a Boolean indicating support, and takes a pointer to a 64 bit integer in which to store the current clock."


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