Learn from Prelim 1

If you have done well, congratulations! If you have not done well, be sure to catch up and then you can show us at the next exams what you have learned! Remember, Prelim 1 is worth only 20% so you have plenty of opportunities to improve.

Question 1 (Trace, function scope)

Question 2 (Linear interpolation, iterating through a vector, adjacent vector elements and keeping vector indices within range)

Part (b): For a vector to be perfect or imperfect, every element in the vector had to differ by no more than 5 from its neighbors. You can't tell that a vector is perfect until after you have checked all the adjacent elements. A common mistake was to print 'perfect' or 'imperfect' after every comparison between two elements, before going working through the vector or finding the first difference greater than 5. You should keep track of whether the whole vector is perfect, e.g., by finding the first difference greater than 5, and print once at the end of the program.
Students did a good job realizing that a loop should be used to move through the positions in the vector. The most efficient way to solve this problem recognizes that once two elements are found that differ by more than 5, the whole vector is imperfect and there is no need to continue checking subsequent elements of the vector. To allow the loop to end early before reaching the end of the vector, when a pair difference greater than 5 is found, you need a while loop with two continuation criteria: the current index has not exceeded the length of the vector and the current pair being checked has a difference no greater than 5.

Question 3 (Iterating over a vector, accumulation and “best-so-far” patterns, if-construct)

• Students generally did a great job with part (a) and recognized that it was important to initialize a variable to hold the maximum height so far, and then update that value as appropriate (conditional) as each element of the vector h is examined using a for-loop.
• Many students did well on part (b) as well, correctly using an if-statement to identify the different cases (ranges of height). Some students dealt with the sampling rate, which was the the number of samples per minute, incorrectly--the rate already was per-minute so there was no need divide by k (the number of minutes).
• A few students used a while-loop to iterate over the height vector, continuing while h(k) was in some particular height range. The problem with this approach is that all the values in the height vector might not be examined, since the loop stops once a height value outside that range is found--but the remaining values in the vector could still contain height values that are within the range of interest.
• The simplest method is to use a for-loop that iterates over the whole height vector and checks the height at each time k, and then accumulates the appropriate number of samples depending on that value of h(k) and whether or not the velocity was greater than 110--see the example solution for this approach.
• Some students chose to use a while-loop but forgot to increment the loop variable, which would lead to an infinite loop! Remember this: if you use a while-loop, the loop condition should depend on some variable that will be updated and eventually change to a value that would cause the loop to stop. For example, if we use a loop that iterates while k < 10 (assuming k is initialized to 1, for instance), we must remember to increment k on each iteration of the loop (with a statement like k = k+1) so that the loop will eventually stop.

Question 4 (Generating random integers and real numbers, indefinite iteration, function and function call)

Part (b)

• Algorithm: a single while-loop does it. Some students used a while-loop and a for-loop to keep track of the amount of water and the number of time steps, respectively. This is incorrect. Remember that when you have nested loops, at each value of the outer loop, you do all the specified iterations of the inner loop. So if you use an outer loop for water and an inner loop for time steps, then you are saying, at some current amount of water, do all the steps, then at the next amount of water, do all the steps, and so on. This is incorrect. Instead, use a single while-loop with two continuation conditions, one for the amount of water and the other for the number of steps.
• Many students got the big idea that you had to write multiple if/else conditions to check each case separately. Also, nearly all knew that they had to generate a random number in (0,1) to determine which condition is appropriate. Some, however, generated a different random number for each case which is incorrect.
• In determining the water storage at each time step, some students forgot to subtract the smaller value between the storage amount and the requested amount, which led to a negative storage amount--wrong--in vector S (if the simulation stopped because too big a water release request was made). Another common mistake was forgetting to update w, the current storage, in addition to assigning S(k).
• Finally, consider simplifying (shortening) your code in conditional statements. Instead of updating the storage amount under each condition, one could update it AFTER all branches of the if-statement.

Question 5 (nested loops and grid pattern)

The most difficult part of the problem was how to deal with a number of disks that doesn't form a full grid. A number of approaches can be used to solve the problem, the simpler (and more commonly used) approaches are

1. Loop over the full grid including the spaces where there should be no disk; keep track of how many disks have been drawn so far; draw a disk only if the number of disks so far is less than or equal to nd.
2. Use nested loops to draw a full grid of disks in all but the last column, followed by a single loop to draw just the disks that should be in the last column.

1. the calculation of the y increment, i.e., the separation between the CENTERS of two adjacent disks. This amount is 2 times the radius ra plus the gap g. Similarly you can determine the x increment.
2. the calculation of the coordinate y, which would be some multiple of the y increment determined in part 1. So in this part you focus on finding the correct multiple. Another approach is to start at some initial y value and then increase y by the y increment calculated in part 1 after drawing each disk. Again, deal wih the x value similarly. With this approach, don't forget to reinitialize at the beginning of each column (or row).

Statisics

% Given yourScore, action to take after prelim ...

if  yourScore > 88

    toDo= celebrate + later look at the solution

elseif  yourScore > 73

    toDo= redo problems + later check solution

else

    toDo= meet with course staff to go over exam ...
          + stay caught up from now on ...
          + do NOT just read the solution--must redo problems
end