10 clarifications #47

justinmeiners · 2021-12-14T06:21:18Z

Includes PR some clarifications and typos in chapter 10 #45

- Informed by Alastair's work in PR #45 and issue #46

justinmeiners · 2021-12-14T06:37:48Z

@aharrison24 Here is an initial pass which mostly fixes typos and footnotes with your recommendations. I am still working on the larger reorg!

Please bring them up if you think things should be different. I think everything we talked about, but I did remove some details from the Dirichlet proof footnote.

05_swap.md

10_binary_counter.md

aharrison24 · 2021-12-14T22:30:22Z

I've gone ahead and read chapter 11 and had a good think about the algorithm. I think I have a reasonable understanding of what's going on now. There are certainly some things I would have appreciated knowing sooner. I've mentioned most of them in my in-line comments.

A couple of minor extra things: In the add_to_counter algorithm it would be helpful to clarify that carry is the element to be inserted and op is a binary operation such as min or max that returns one of its two inputs.

I also think it would be very valuable to have a slightly extended example of how the counter works, where multiple elements are inserted. You could do an example where the elements are characters and the binary operator is min, for instance. 'zero' could be a space character. You could push in 8 letters in an order that causes multiple slots to be occupied at the end. You can use that to show that the counter only needs log2(8) = 3 slots. You can also show that after all the elements have been inserted, the job isn't yet finished. This justifies the need for the reduce_counter operation, which performs all the remaining comparisons to get to a single 'winner'. I think that's important, because with the text as it is currently, the reduction step is never really justified. It's just presented as something that is necessary.

aharrison24 · 2021-12-14T22:46:09Z

I also realised that nowhere is it explicitly stated that the counter starts out empty and has elements pushed in to it one at a time.

Co-authored-by: Alastair Harrison <aharrison24@gmail.com>

justinmeiners · 2021-12-15T04:34:01Z

11_min_1_2.md

+I pick this algorithm because it allows us to learn how to do decomposition
+and learn these components like `list_pool` and `binary_counter` along the way.
+
+Let me sketch the grand plan of the whole alogorithm.


This information was completely missing before. This explains that we will use the linked list to store histories, and that it doesn't effect the binary_counter implementation.

This is really good!

justinmeiners · 2021-12-15T04:42:51Z

10_binary_counter.md

+
+Let us assume we have elements of type `T` that need to be paired or combined in some way,
+whether with `min`, `+`, `merge`, or any other assocative operation on `T`.
+What we can do is create an array called a "counter".


This information now reinforces that we are talking about generic element T with generic operation.

justinmeiners · 2021-12-15T04:43:14Z

10_binary_counter.md

+If there is a guy in slot 2 he has won 2 games, and so on.
+This structure will help us to only pair up elements that have the same power.
+
+The following example using `min` as the operation should make this clear.


This specific example uses the min operation so we can more clearly talk about winners and losers.

justinmeiners · 2021-12-15T04:43:40Z

10_binary_counter.md

+ 0 1 ... 31 0 1 ... 31
+ x 0 ... 0 --> 0 y ... 0
+
+Otherwise `x` wins:


Example corrected.

justinmeiners · 2021-12-15T04:44:01Z

10_binary_counter.md

- y 0 ... 0 --> x 0 ... 0
+What if the counter is full, and has no zero slots?
+That's called an an **overflow**.
+There is a close analogy between our counter and binary integer counting:


Analogy between the two stated more clearly.

justinmeiners · 2021-12-15T04:45:00Z

10_binary_counter.md

+**Exercise:** If you want to implement [merge sort][merge-sort] you can use exactly the same device, since merge is associative. The idea with merge sort, is you only want to merge lists if they are roughly the same length and this helps you do it (see Chapter 12).
+ Write the associtative binary operation `merge` which can combine two sorted arrays into a sorted array.
+
+**Exercise:** When we become grownups we learn about advanced data structures, such as [binomial forest][binomial]. They use the same idea. Learn about this data structure and try to figure out where


These other examples have been moved to exercises.

justinmeiners · 2021-12-15T04:54:16Z

I just finished the "big" revision and I think I have been able to address most of your comments. I went back to the videos to review this section and found some helpful comments I missed which address many of your concerns.

I have added comments to this code here indicating specific resolutions to concerns.
Once again, I really appreciate you working through this with me.

justinmeiners · 2021-12-15T04:55:19Z

it would be very valuable to have a slightly extended example of how the counter works

I think that's a great idea, and added it to issue #48 .

justinmeiners · 2021-12-15T05:04:10Z

10_binary_counter.md


-The second function applies the operation
-to all the elements left sitting in the counter.
+After we finish adding all our elements to the counter, they might not all be reduced to one element.


This justifies the need for the reduce_counter operation and is a quote from Alex.

aharrison24

This is all looking really good! I haven't had a chance to re-read both chapters from beginning to end. Will try to do that soon.

10_binary_counter.md

aharrison24 · 2021-12-15T23:05:36Z

11_min_1_2.md

+I pick this algorithm because it allows us to learn how to do decomposition
+and learn these components like `list_pool` and `binary_counter` along the way.
+
+Let me sketch the grand plan of the whole alogorithm.


This is really good!

11_min_1_2.md

Co-authored-by: Alastair Harrison <aharrison24@gmail.com>

justinmeiners · 2021-12-30T03:33:12Z

I have resolved those comments you left. I am going to merge this in for now as it is a significant improvement. Let's start a new PR for additional fixes if needed. (I will review your issue again.)

justinmeiners added 5 commits December 13, 2021 23:18

expand and move footnote about abstract algebra

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corrections, footnotes, clarifications

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- Informed by Alastair's work in PR #45 and issue #46

typos

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minor footnote fix

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Merge branch 'master' into 10-clarifications

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aharrison24 reviewed Dec 14, 2021

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justinmeiners and others added 6 commits December 14, 2021 18:52

Update 05_swap.md

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Co-authored-by: Alastair Harrison <aharrison24@gmail.com>

Update 05_swap.md

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Update 05_swap.md

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Update 10_binary_counter.md

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Co-authored-by: Alastair Harrison <aharrison24@gmail.com>

typos

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major revisions to 10 and intro to 11

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justinmeiners commented Dec 15, 2021

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10_binary_counter.md

0 1 ... 31 0 1 ... 31

x 0 ... 0 --> 0 y ... 0

Otherwise `x` wins:

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Example corrected.

justinmeiners commented Dec 15, 2021

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additional typos and information

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additional typos and clarifications

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typo

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justinmeiners and others added 2 commits December 29, 2021 19:12

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additional fixes based on review comments

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justinmeiners merged commit ffbc54f into master Dec 30, 2021

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10 clarifications #47

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