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Updated by Matthew Van Dyke on 1/16/2020 1920 U5L3p3 Classifying Algorithms (starter file) Week 2: Algorithmic Complexity Unit 5 Lab 3: Timing Experiments Classifying AlgorithmsWhile the block is running, Snap! is doing other things, such as responding to mouse motion and clicks, and maybe running other scripts. And maybe your browser has other windows open that require updating. Those things will affect the "clock time" to run your expression. A better measure would be "processor time," which would tell you exactly how much time the computer spent on this one task. Some operating systems provide features to allow measurement of processor time for a program such as your browser, but it would be hard to get that measurement for just one Snap! thread.1.0 If it isn't already open, load the project U5L3-timer from the previous page, and experiment with time function on algorithms you've built (such as alphie way, betsy way, factorial, find in unsorted list, find in sorted list, and any others you have handy). What happens to the running time if you double the size of the input?10Here is a block to compute average running time in case you wish to utilize it.The greater the number of trials, the less the average time will vary.2.0 Use the list from [ ] to [ ] block to build the following two blocks in Snap!. Then, determine which block's algorithm can be executed in a reasonable time, and which cannot. The list of 2-digit numbers goes from 10 to 99. There's a math operations block that can give you powers of 10. 2.1 list of 1000 numbers 2.2 all N digit numbers5.3.3.2: The first block is kind of slow, because 1000 numbers is a lot, but its time doesn't depend on its input. The next thousand numbers starting from a billion take no more time to generate than the next thousand numbers starting from one. The second block, though, generates ten times as many numbers every time you add 1 to its input. When the input is 2 it generates the not-quite-100 numbers from 10 to 99, which is fast. When the input is 3, it generates not-quite-1000 numbers, so its speed is similar to that of the first block. But beyond that point it's much too slow to watch. When the input is 6, not a very big input, it generates almost a million numbers -- or it would, but Snap! will probably run out of memory first. When the input is 100, it tries to generate a googol numbers (not a Google), which would certainly fail. This running time displays exponential growth.3.0 Look at some algorithms you've built. Determine whether each algorithm runs in constant time, linear time, polynomial time, or unreasonable time.5.3.3.3: Here are some examples of algorithms that students might consider: - GRAPH DATAPOINTS from Unit 3 Lab 4: Building a Graphing App runs in linear time. - ARE THE NUMBERS OF () DISTINCT? from Unit 5 Lab 1: List Processing Algorithms runs in quadratic time. - NUMBERS FROM () TO () from Unit 5 Lab 3: Comparing Algorithms runs in linear time. - ALPHIE WAY from Unit 5 Lab 3: Timing Reporters runs in linear time. - BETSY WAY from Unit 5 Lab 3: Timing Reporters runs in constant time.4.0 For Alphie's way of adding integers, create a graph with the number of integers on the horizontal and the runtime on the vertical. Generate data for the graph by running time function with large inputs to Alphie's way (say, multiples of 100). Then use the techniques from Lab 2 to plot the graph.01000020000true5.3.3.5: Alphie's algorithm runs in linear time.5.3.3.7: If an algorithm runs in reasonable time, that means that a computer using that algorithm can solve problems big enough to be of practical importance in a short enough time to be usable. An unreasonable-time algorithm means that no matter how fast your computer is, big problems will never be usefully solved using that algorithm. Technically, the dividing line is that a polynomial time algorithm is considered reasonable, while an exponential-time or longer algorithm is considered unreasonable. (If an algorithm took time measured by a huge power of n, such as n^100, it would be unreasonable in practice, but there aren't any such algorithms that actually arise.)

Like many games, this is coded as a FOREVER loop, with a STOP THIS BLOCK to escape when we win or detect an inconsistency. It uses two global variables, one to count the number of guesses and the other for the buttons to tell us when they are pressed. There are more elegant ways to accomplish the latter, but they'd result in multiple WHEN I RECEIVE scripts, and we'd have to make LOW and HIGH global for those scripts to use. Also, we change the values of our input variables, which some people would consider bad style. But since those variables are local to this procedure, it really doesn't hurt anyone outside this script. Students will organize their code in many different ways. It might be useful to have them flag with comments where each of the five steps (or however many steps /their/ algorithm has) is carried out.

110i

1

cont

catchtag

cont

catchtag

Sprite

Sprite

Not In ListThis will be the most common student solution. There are many other ways it could be done. For example, here's a recursive solution:EMPTY? is in the Tools library.11The last line says that the position of VALUE is one more than its position in the list without its first item. For example, if the DATA list is {3,4,5,6} and we want to know the position of 5, first find its position in {4,5,6} (namely, 2) and add 1 to get 3, which is the position of 5 in {3,4,5,6}.

guess22This is essentially the game program, but with the user interface parts removed. I also replaced the FOREVER loop with a REPEAT UNTIL. I think FOREVER is okay for games, but in a serious program the stopping condition for the loop should be self-documenting. (There's still an early stop if the error condition LOW>HIGH occurs. In this case it means that the supposedly sorted list given as input isn't sorted, or if the desired item isn't in the list.)

guess2This is exactly the code from the previous problem, but with REPORT instead of SAY.

10

LABEL will stamp text on the stage at the given font size. The direction of the text is the direction the sprite is facing, and color will match the pen color.

Hello!12

1datamapmany1data lists

1

1

Each item of DATA is a list of two numbers, the x and y coordinates of a point. The ITEM blocks extract the two numbers. An item from DATA is substituted into the empty list slots. (If you prefer you could drag the ITEM orange block from the FOR EACH into those slots -- the meaning is the same.)

We go to the first point with the pen up, so we won't see an extra line from wherever the sprite happened to be. After that, we put the pen down for each point if the value of PENDOWN is TRUE.

The block ANNOUNCE AXES POSITION does /almost/ what we want, except that it leaves the coordinates on the stage permanently, instead of having the sprite say them. So I opened its definition and copied all the green stuff above from it to here.

This is straightforward apart from the two points brought out on the lab page: 1. How to declare an input of type Reporter. 2. How to call that function and give it an input. Otherwise it's just figuring out the WAIT UNTIL / REPEAT UNTIL structure, and remembering from two pages back to put the PEN DOWN /after/ moving to the first point.

The above is probably how most students will write this. It can also be done recursively:

i11truedatatrueThis so much calls out for a recursive solution that I couldn't help putting that first. CONTAINS is a primitive block. Students who remember that will have a much easier time writing this procedure than those who don't remember it. The other thing that will complicate the solution is if the students have programmed before in one of those other languages and therefore insist on using index variables to find their way through the list instead of ALL BUT FIRST OF. Here are a few examples of possible correct solutions:datatrue

This has the same structure as ARE THERE ANY DUPLICATES (5.3.2.1), but with lists as the reported values instead of Booleans. Similarly, the alternate solutions to 5.3.2.1 work here too:i11datadataThe timing experiment in the previous problem would be easier with this procedure because it has to examine every pair of items even if a duplicate is found early on.

The versions of DUPLICATES IN that use CONTAINS are easy to turn into a remove-duplicates (REMDUP) function: Just put a NOT around the CONTAINS in the script. (The recursive version could be written without NOT by swapping the then part and else part of the IF/ELSE block, but I did it this way to make the relationship clearer.) The versions of DUPLICATES IN that essentially reimplement CONTAINS with a FOR loop are harder, because you don't want to keep an item in the result just because /one/ other item is different from it. You have to test /all/ the items. One way is with a flag variable:i11data1dataAnother solution uses a feature we haven't taught yet: nonlocal exit, like BREAK in some other languages. The CATCH and THROW blocks are in the Tools library. Don't teach this to the class; it'll be a distraction. But if a student asks "is there something like BREAK?" you can show it to them:But neither of these last two solutions is exactly elegant. If I had to do this problem and I'd forgotten about CONTAINS, I'd start by writing my own CONTAINS as a helper procedure for REMDUP.

This isn't the most efficient solution, because it makes that list of numbers, only to have a list of length TIMES so that we can run EXPRESSION that many times! But it took me way less thinking time and coding time than making a loop. "Use what you have to get what you need." -- Võ Nguyên Giáp

5equal010000.480200000.0181351470.5833333333333334