More integer encoding, git objects, floor/ceiling.

2024-03-08 13:50:13 -07:00 · 2024-03-08 13:50:13 -07:00 · cdb916c2b4
parent 1651c9d6c3
commit cdb916c2b4
10 changed files with 356 additions and 34 deletions
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@ -91,7 +91,11 @@
    "ordering-n-repetition-n.jpg",
    "triangular-gnomon.png",
    "pascals-triangle.webp",
-    "square-gnomon.png"
+    "square-gnomon.png",
+    "floor-negative.png",
+    "floor-positive.png",
+    "ceil-positive.png",
+    "ceil-negative.png"
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--- a/notes/_journal/2024-03-08.md
+++ b/notes/_journal/2024-03-08.md
@ -1,13 +1,19 @@
 ---
-title: "2024-03-06"
+title: "2024-03-08"
 ---

 - [x] Anki Flashcards
 - [x] KoL
 - [ ] Sheet Music (10 min.)
- [ ] Go (1 Life & Death Problem)
+- [x] Go (1 Life & Death Problem)
 - [ ] Korean (Read 1 Story)
 - [ ] Interview Prep (1 Practice Problem)
 - [ ] Log Work Hours (Max 3 hours)

-* Added notes on how asymptotic notation relates to one another.
+* 101weiqi (serial numbers)
+	* Q-8118
+	* Q-56273
+	* Q-220867
+	* Q-141879
+	* Q-12638
+	* Q-242062
--- a/notes/_journal/2024-03/2024-03-06.md
+++ b/notes/_journal/2024-03/2024-03-06.md
@ -0,0 +1,23 @@
+---
+title: "2024-03-06"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [ ] Sheet Music (10 min.)
+- [x] Go (1 Life & Death Problem)
+- [ ] Korean (Read 1 Story)
+- [x] Interview Prep (1 Practice Problem)
+- [x] Log Work Hours (Max 3 hours)
+
+* Added notes on how asymptotic notation relates to one another.
+* Leetcode Problems
+	* [Search In Rotated Sorted Array](https://leetcode.com/problems/search-in-rotated-sorted-array/)
+	* [Find First and Last Position of Element in Sorted Array](https://leetcode.com/problems/find-first-and-last-position-of-element-in-sorted-array/)
+	* [Search Input Position](https://leetcode.com/problems/search-insert-position/)
+	* [Valid Sudoku](https://leetcode.com/problems/valid-sudoku/)
+* 101weiqi (serial numbers)
+	* Q-151618
+	* Q-20227
+	* Q-215640
+* Began reading chapter 3 of "Designing Data-Intensive Applications". Up to and including in-memory hash indices.
--- a/notes/_journal/2024-03/2024-03-07.md
+++ b/notes/_journal/2024-03/2024-03-07.md
@ -0,0 +1,20 @@
+---
+title: "2024-03-07"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [ ] Sheet Music (10 min.)
+- [ ] Go (1 Life & Death Problem)
+- [ ] Korean (Read 1 Story)
+- [x] Interview Prep (1 Practice Problem)
+- [ ] Log Work Hours (Max 3 hours)
+
+* Spent a while thinking through floor/ceiling identities. Want to return to two's-complement division (rounding up) after I dive into the division algorithm more.
+	* In particular, I want to explore the relationship between floors and `mq + r` as well as ceilings and `mq - r`.
+* Read chapter 3 of "Designing Data-Intensive Applications".
+* Transcribed hard-copy soft skills notes to Google document.
+* Leetcode Problems
+	* [Count and Say](https://leetcode.com/problems/count-and-say/)
+	* [Combination Sum](https://leetcode.com/problems/combination-sum/)
+	* [Multiply Strings](https://leetcode.com/problems/multiply-strings/)
--- a/notes/algebra/floor-ceiling.md
+++ b/notes/algebra/floor-ceiling.md
@ -60,7 +60,7 @@ END%%

 %%ANKI
 Basic
-What does $\lceil x \rceil - \lfloor x \rceil$ equal?
+What does $\lceil x \rceil - \lfloor x \rfloor$ equal?
 Back: Either $0$ or $1$.
 Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
 <!--ID: 1708110779681-->
@ -69,7 +69,7 @@ END%%
 %%ANKI
 Basic
 What can be said about $x$ if $\lceil x \rceil - \lfloor x \rfloor = 0$?
-Back: $x$ is even.
+Back: $x$ is an integer.
 Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
 <!--ID: 1708110779687-->
 END%%
@ -77,11 +77,51 @@ END%%
 %%ANKI
 Basic
 What can be said about $x$ if $\lceil x \rceil - \lfloor x \rfloor = 1$?
-Back: $x$ is odd.
+Back: $x$ is not an integer.
 Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
 <!--ID: 1708110779693-->
 END%%

+%%ANKI
+Basic
+What values of $x$ satisfy $\lfloor x \rfloor = \lceil x \rceil - 1$?
+Back: Non-integral values.
+Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
+<!--ID: 1709831032489-->
+END%%
+
+%%ANKI
+Basic
+What values of $x$ satisfy $\lceil x \rceil = \lfloor x \rfloor + 1$?
+Back: Non-integral values.
+Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
+<!--ID: 1709831032496-->
+END%%
+
+%%ANKI
+Basic
+What values of $x$ satisfy $\lfloor x \rfloor = \lceil x \rceil + 1$?
+Back: None.
+Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
+<!--ID: 1709831032505-->
+END%%
+
+%%ANKI
+Basic
+What values of $x$ satisfy $\lceil x \rceil = \lfloor x \rfloor - 1$?
+Back: None.
+Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
+<!--ID: 1709831032513-->
+END%%
+
+%%ANKI
+Basic
+For what values $k$ is horizontal and vertical shifting of $\lfloor x \rfloor$ the same?
+Back: Integral values.
+Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
+<!--ID: 1709831032519-->
+END%%
+
 %%ANKI
 Basic
 What C operator corresponds to floor division?
@ -90,6 +130,14 @@ Reference: Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete M
 <!--ID: 1708110779699-->
 END%%

+%%ANKI
+Basic
+What C operator corresponds to integer division?
+Back: `/`
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1709831032524-->
+END%%
+
 %%ANKI
 Basic
 When does C operator `/` behave like floor division?
@ -306,5 +354,6 @@ END%%

 ## References

+* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
 * Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
 * Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
--- a/notes/algebra/sequences/index.md
+++ b/notes/algebra/sequences/index.md
@ -29,7 +29,7 @@ END%%

 %%ANKI
 Basic
-How is sequence $a_1, a_2, \ldots$ denoted?
+How is sequence $a_1, a_2, \ldots$ more compactly denoted?
 Back: $(a_n)_{n \geq 1}$
 Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
 <!--ID: 1709302343201-->
--- a/notes/encoding/integer.md
+++ b/notes/encoding/integer.md
@ -940,7 +940,7 @@ Addition of two unsigned or two two's-complement numbers operate in much the sam

 %%ANKI
 Basic
-*Why* is adding $w$-bit integral types equal to $w$-bit truncation?
+*Why* is addition overflow of $w$-bit integral types equivalent to $w$-bit truncation?
 Back: The underlying bit adder discards any final carry bit.
 Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
 <!--ID: 1708799678721-->
@ -1648,7 +1648,7 @@ END%%

 %%ANKI
 Basic
-How is `unsigned x` equivalently modified without using multiplication?
+How is `unsigned x` equivalently modified using bitwise operations?
 ```c
 x = x * pow(2, k);
 ```
@ -1661,6 +1661,21 @@ Tags: c17
 <!--ID: 1709570428818-->
 END%%

+%%ANKI
+Basic
+How is `unsigned x` equivalently modified using arithmetic operations?
+```c
+x = (x << k);
+```
+Back:
+```c
+x = x * pow(2, k);
+```
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17
+<!--ID: 1709831032382-->
+END%%
+
 Similarly, two's-complement multiplication is defined as follows: $$x *_w^t y = U2T_w((x \cdot y) \bmod 2^w)$$

 %%ANKI
@ -1771,7 +1786,7 @@ END%%

 %%ANKI
 Basic
-Assuming two's-complement encoding, how is `int x` equivalently modified without using multiplication?
+In two's-complement, how is `x` equivalently modified using bitwise operators?
 ```c
 x = x * pow(2, k);
 ```
@ -1784,6 +1799,21 @@ Tags: c17
 <!--ID: 1709570428828-->
 END%%

+%%ANKI
+Basic
+In two's-complement, how is `x` equivalently modified using arithmetic operations?
+```c
+x = (x << k);
+```
+Back:
+```c
+x = x * pow(2, k);
+```
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17
+<!--ID: 1709831032386-->
+END%%
+
 %%ANKI
 Basic
 How can we rewrite $x \cdot 1101_2$ as an expression of *only* `<<` and `+`?
@ -1837,7 +1867,171 @@ END%%

 ### Division

+Integer division divides the result and discards any fractional result. This has the same effect as rounding toward zero.

+%%ANKI
+Basic
+What is integer division?
+Back: Division of two numbers that returns the integer part of the result.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1709831032392-->
+END%%
+
+%%ANKI
+Cloze
+Integer division $x / y$ is $\lfloor x / y \rfloor$ when $x \geq 0$ and {1:$y > 0$} or $x \leq 0$ and {1:$y < 0$}.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1709831032396-->
+END%%
+
+%%ANKI
+Cloze
+Integer division $x / y$ is $\lceil x / y \rceil$ when $x \geq 0$ and {1:$y < 0$} or $x \leq 0$ and {1:$y > 0$}.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1709831032399-->
+END%%
+
+%%ANKI
+Basic
+What distinguishes integer division from floor division?
+Back: The latter does not round towards $0$ with negative results.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1709831032402-->
+END%%
+
+%%ANKI
+Basic
+What distinguishes integer division from ceiling division?
+Back: The latter does not round towards $0$ with positive results.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1709831032406-->
+END%%
+
+%%ANKI
+Cloze
+Integer division is often called "truncation {toward zero}".
+Reference: dirkgently, “Answer to ‘What Is the Behavior of Integer Division?,’” _Stack Overflow_, August 30, 2010, [https://stackoverflow.com/a/3602857](https://stackoverflow.com/a/3602857).
+<!--ID: 1709831032412-->
+END%%
+
+%%ANKI
+Cloze
+Unsigned division is to {logical} right shifts. Two's-complement division is to {arithmetic} right shifts.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1709831032417-->
+END%%
+
+%%ANKI
+Basic
+What is the result of logical right-shifting unsigned $x$ by $k$ bits?
+Back: $\lfloor x / 2^k \rfloor$
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1709831032421-->
+END%%
+
+%%ANKI
+Basic
+In unsigned encoding, *why* is floor a part of expression $x \mathop{\texttt{>>}} k = \lfloor x / 2^k \rfloor$?
+Back: Because the least significant bit, which may have value `1`, is dropped.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17
+<!--ID: 1709831032424-->
+END%%
+
+%%ANKI
+Basic
+In unsigned encoding, how is `x` equivalently modified using bitwise operators?
+```c
+x = floor(x / pow(2, k));
+```
+Back:
+```c
+x = (x >> k);
+```
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17
+<!--ID: 1709831032428-->
+END%%
+
+%%ANKI
+Basic
+In unsigned encoding, how is `x` equivalently modified using arithmetic operations?
+```c
+x = (x >> k);
+```
+Back:
+```c
+x = floor(x / pow(2, k));
+```
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17
+<!--ID: 1709831032432-->
+END%%
+
+%%ANKI
+Basic
+What is the result of arithmetic right-shifting two's-complement $x$ by $k$ bits?
+Back: $\lfloor x / 2^k \rfloor$
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1709831032435-->
+END%%
+
+%%ANKI
+Basic
+In two's-complement, *why* is floor a part of expression $x \mathop{\texttt{>>}} k = \lfloor x / 2^k \rfloor$?
+Back: Because the least significant bit, which may have value `1`, is dropped.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17
+<!--ID: 1709831032440-->
+END%%
+
+%%ANKI
+Basic
+In two's-complement, what is `-1 >> 1`?
+Back: `-1`
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17
+<!--ID: 1709831032444-->
+END%%
+
+%%ANKI
+Basic
+Why is division by a power of two using arithmetic right-shift `x >> k` considered incorrect?
+Back: This right shift performs floor division, not integer division.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17
+<!--ID: 1709831032449-->
+END%%
+
+%%ANKI
+Basic
+In two's-complement, how is `x` equivalently modified using bitwise operators?
+```c
+x = floor(x / pow(2, k));
+```
+Back:
+```c
+x = (x >> k);
+```
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17
+<!--ID: 1709831032455-->
+END%%
+
+%%ANKI
+Basic
+In two's-complement, how is `x` equivalently modified using arithmetic operations?
+```c
+x = (x >> k);
+```
+Back:
+```c
+x = floor(x / pow(2, k));
+```
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+Tags: c17
+<!--ID: 1709831032461-->
+END%%

 ## References

--- a/notes/git/objects.md
+++ b/notes/git/objects.md
@ -79,7 +79,7 @@ END%%

 %%ANKI
 Cloze
-Interpreted as a key-value store, {oids} are to keys as {objects} are to values.
+When interpreting git as a key-value store, {oids} are to keys as {objects} are to values.
 Reference: Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Software Development (New York, NY: Apress, 2014).
 Tags: fs::cas
 <!--ID: 1709177255607-->
@ -118,7 +118,7 @@ END%%

 %%ANKI
 Cloze
-The {object database} refers to the {`.git/objects`} directory.
+The term "{object database}" refers to the {`.git/objects`} directory.
 Reference: Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Software Development (New York, NY: Apress, 2014).
 <!--ID: 1709177255644-->
 END%%
@ -240,7 +240,7 @@ What is the decompressed text of the blob generated by the following?
 ```bash
 $ echo -n "abcd" | git hash-object -w --stdin
 ```
-Back: `blob 4\0abcd`
+Back: `blob 4<NUL>abcd`
 Reference: Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Software Development (New York, NY: Apress, 2014).
 <!--ID: 1709345254733-->
 END%%
--- a/notes/posix/regexp.md
+++ b/notes/posix/regexp.md
@ -281,20 +281,20 @@ Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 202
 <!--ID: 1707050923724-->
 END%%

-Class        | Similar To      | Meaning
------------ | --------------- | ------------------------------------------------
-`[:alnum:]`  | `[A-Za-z0-9]`   | Alphanumeric characters
-`[:alpha:]`  | `[A-Za-z]`      | Alphabetic characters
-`[:blank:]`  | `[ \t]`         | `' '` and `TAB` characters
-`[:cntrl:]`  |                 | Control characters
-`[:digit:]`  | `[0-9]`         | Numeric characters
-`[:graph:]`  | `[^ [:cntrl:]]` | Printable and visible characters
-`[:lower:]`  | `[a-z]`         | Lowercase alphabetic characters
-`[:print:]`  | `[ [:graph:]]`  | Printable characters
-`[:punct:]`  |                 | All graphic characters except letters and digits
-`[:space:]`  | `[ \t\n\r\f\v]` | Whitespace characters
-`[:upper:]`  | `[A-Z]`         | Uppercase alphabetic characters
-`[:xdigit:]` | `[0-9A-Fa-f]`   | [[radices#Hexadecimal\|Hexadecimal]] digits
+| Class        | Similar To      | Meaning                                          |
+| ------------ | --------------- | ------------------------------------------------ |
+| `[:alnum:]`  | `[A-Za-z0-9]`   | Alphanumeric characters                          |
+| `[:alpha:]`  | `[A-Za-z]`      | Alphabetic characters                            |
+| `[:blank:]`  | `[ \t]`         | `' '` and `TAB` characters                       |
+| `[:cntrl:]`  |                 | Control characters                               |
+| `[:digit:]`  | `[0-9]`         | Numeric characters                               |
+| `[:graph:]`  | `[^ [:cntrl:]]` | Printable and visible characters                 |
+| `[:lower:]`  | `[a-z]`         | Lowercase alphabetic characters                  |
+| `[:print:]`  | `[ [:graph:]]`  | Printable characters                             |
+| `[:punct:]`  |                 | All graphic characters except letters and digits |
+| `[:space:]`  | `[ \t\n\r\f\v]` | Whitespace characters                            |
+| `[:upper:]`  | `[A-Z]`         | Uppercase alphabetic characters                  |
+| `[:xdigit:]` | `[0-9A-Fa-f]`   | [[radices#Hexadecimal\|Hexadecimal]] digits      |

 %%ANKI
 Basic