The solutions this time around are fantastic. Really. I mean Ryan Leavengood is back. Enough said. No matter which solution I select I'll be doing you a disservice, so you are all honor-bound to read through the code I don't show. Since I must choose one though, I'm going with Christian N.'s solution this time around. It's a trivial 48 lines with comments and whitespace, it solves the quiz, and it even hits two of the extra credit suggestions. Beyond that, I just thought the code was pretty without even building any classes. Let's dive in: # My straight-forward solution. require 'enumerator' # How much can the time differ? FUZZ = 0 POS = { ?1 => [0,0], ?2 => [1,0], ?3 => [2,0], ?4 => [0,1], ?5 => [1,1], ?6 => [2,1], ?7 => [0,2], ?8 => [1,2], ?9 => [2,2], ?0 => [1,3], ?* => [2,3] } # ... You can see that enumerator is pulled in here for some fancy iteration tricks we will see very soon. The FUZZ constant is actually a control for the first extra credit point. You can set it to the number of seconds the suggested keystrokes can differ from the requested time. The default, zero, disables any number fudging. POS holds the column and row coordinates of each button on the keypad. We will see this used in the distance calculation routine. In fact, that's the next bit of code: # ... def metric(string) string.enum_for(:each_byte).map { |b| POS[b] }. enum_for(:each_cons, 2).inject(0) { |sum, ((x1,y1), (x2, y2))| # 1-norm # sum + (x1-x2).abs + (y1-y2).abs # 2-norm sum + Math.sqrt((x1-x2)**2 + (y1-y2)**2) } end # ... This code takes a String of keystrokes and returns the total distance of all the button traveling needed to enter it. Here are some examples of usage: >> metric("9*") => 1.0 >> metric("6*") => 2.0 >> metric("313*") => 7.0 >> metric("1*") => 3.60555127546399 The iterators are the trickiest part of this code, so let's work through them. First, String's default iteration is by lines of the String, so map() would normally transform each line. Christian wants to work with each character though and there isn't a map_byte(). So he made one. In other words, you can think of enum_for(:each_byte).map { |b| ... } as map_byte { |b| ... }. Once you understand that, it's easy to see that each character is just translated into the coordinates for that key. The next iterator, enum_for(:each_cons, 2), allows you group adjacent keys and iterate over the pairs. This is easier to see than explain, so here's another example: >> [1, 2, 3].enum_for(:each_cons, 2).to_a => [[1, 2], [2, 3]] I used simple Integers instead of the coordinate tuples the code is actually looping through, but see how they are perfectly grouped for calculating distance? That leads us to the final iterator in this chain. The inject() iterator is just a hand-rolled sum() method. The tricky part is how the parentheses are used are used to unwrap the nested Arrays. The outer set separates the two points we are comparing, joined by each_cons(). The inner sets divide the points themselves which are then assigned to local variables. There's quite a bit of wrapping and unwrapping in there. The actual body of all this iteration is easy stuff: it does a running sum of the euclidean distance between all of the buttons. Well, that's the uncommented version. If you switch the comments, the other line does the Manhattan distance, which covers the second extra credit point. Now that we have a way to get the distance, we just need a way to generate the keystroke combinations. Here's that code: # ... def entries(time) return [] if time <= 0 min, sec = time.divmod(60) entries = [] # seconds only entries << "%d*" % [time] if time < 100 # usual time format entries << "%d%02d*" % [min, sec] # more than 60 seconds entries << ("%d%02d*" % [min-1, sec+60]) if min > 1 && sec < 40 entries end # ... This method is very straightforward. An Array is constructed, all the possible keystroke entries for the passed time are added to the Array, and the Array is returned. There are only three possible choices for reasonable keystroke entries. The standard case is the one in the middle, a traditional minutes and seconds entry. Now for low second counts that's going to give us keystrokes like "040*" which is pointless. The first condition handles that, by adding manual entry of the seconds. This is set to work for all times below 100 seconds though, just in case "80*" turns out to be a better choice than "120*". Finally, the third option covers any case where we have at least one minute and 39 seconds or less. In those cases, we could drop the time by a minute and add that back as extra seconds. For example, "230*" can also be entered as "190*". Now we just need a little more code to tie these two methods together. Christian choose to show all mappings between one and 999 seconds. Here's the code for that: # ... 1.upto(999) { |time| entries = (-FUZZ..FUZZ).map { |offset| entries(time + offset) }.flatten # Sort by movement length, then by keypresses. quickest = entries.sort_by { |s| [metric(s), s.size] }.first puts "%3d (%02d:%02d): %s" % [time, time.divmod(60), quickest].flatten } The upto() iterator is just the range of solutions I described. The first line inside there pulls all possible entries() for the selected time, remembering to account for fudging of the numbers. Entries are then sorted using the metric() method and a keystroke count for tie-breaking. The pattern that sorts to top is selected. Then the last line just prints the results. My thanks to all who spend a lot more quality time with their microwave than I do. I enjoyed the discussion of edge cases and I really did learn something cool from every single solution. Tomorrow we'll tackle a question Gavin K. captured off the radio for us...

on 2007-04-05 16:23

on 2007-04-05 20:43

```
Ruby Q. <removed_email_address@domain.invalid> writes:
> I'm going with Christian N.'s solution this time around.
Yay, thanks!
```

on 2007-04-05 22:32

I haven't read through all the solutions yet, but I will. But what I learned most about this quiz is how not to propose the problem. Had I requested that the microwave function take a string such as "MM:SS" and return a similar string, and worded the quiz description with that in mind, I think it would have eliminated much of the initial confusion. I figured that people would want to focus on the core problem and less on string parsing and formatting, so I requested that the function accept and return integers. But that caused more problems to save on parsing a time string, which in retrospect is not that difficult (and actually might have been a bit interesting).