Revisit the English version (#1885)

* Update giscus scroller.

* Refine English docs and landing page

* Sync the headings.

* Update landing pages.

* Update the avatar

* Update Acknowledgements

* Update landing pages.

* Update contributors.

* Update

* Fix the formula formatting.

* Fix the glossary.

* Chapter 6. Hashing

* Remove Chinese chars.

* Fix headings.

* Update giscus themes.

* fallback to default giscus theme to solve 429 many requests error.

* Add borders for callouts.

* docs: sync character encoding translations

* Update landing page media layout and i18n

en/docs/chapter_data_structure/character_encoding.md

@@ -2,7 +2,7 @@
 
 In computers, all data is stored in binary form, and character `char` is no exception. To represent characters, we need to establish a "character set" that defines a one-to-one correspondence between each character and binary numbers. With a character set, computers can convert binary numbers to characters by looking up the table.
 
-## Ascii Character Set
+## ASCII Character Set
 
 <u>ASCII code</u> is the earliest character set, with the full name American Standard Code for Information Interchange. It uses 7 binary bits (the lower 7 bits of one byte) to represent a character, and can represent a maximum of 128 different characters. As shown in the figure below, ASCII code includes uppercase and lowercase English letters, numbers 0 ~ 9, some punctuation marks, and some control characters (such as newline and tab).
 
@@ -12,9 +12,9 @@ However, **ASCII code can only represent English**. With the globalization of co
 
 Worldwide, a batch of EASCII character sets suitable for different regions have appeared successively. The first 128 characters of these character sets are unified as ASCII code, and the last 128 characters are defined differently to adapt to the needs of different languages.
 
-## Gbk Character Set
+## GBK Character Set
 
-Later, people found that **EASCII code still cannot meet the character quantity requirements of many languages**. For example, there are nearly one hundred thousand Chinese characters, and several thousand are used daily. In 1980, the China National Standardization Administration released the <u>GB2312</u> character set, which included 6,763 Chinese characters, basically meeting the needs for computer processing of Chinese characters.
+Later, people found that **EASCII still could not provide enough characters for many languages**. For example, there are nearly one hundred thousand Chinese characters, and several thousand are used in everyday life. In 1980, the China National Standardization Administration released the <u>GB2312</u> character set, which included 6,763 Chinese characters, basically meeting the needs of computer processing for Chinese.
 
 However, GB2312 cannot handle some rare characters and traditional Chinese characters. The <u>GBK</u> character set is an extension based on GB2312, which includes a total of 21,886 Chinese characters. In the GBK encoding scheme, ASCII characters are represented using one byte, and Chinese characters are represented using two bytes.
 
@@ -22,13 +22,11 @@ However, GB2312 cannot handle some rare characters and traditional Chinese chara
 
 With the vigorous development of computer technology, character sets and encoding standards flourished, which brought many problems. On the one hand, these character sets generally only define characters for specific languages and cannot work normally in multilingual environments. On the other hand, multiple character set standards exist for the same language, and if two computers use different encoding standards, garbled characters will appear during information transmission.
 
-Researchers of that era thought: **If a sufficiently complete character set is released that includes all languages and symbols in the world, wouldn't it be possible to solve cross-language environment and garbled character problems**? Driven by this idea, a large and comprehensive character set, Unicode, was born.
+Researchers of that era thought: **If a sufficiently complete character set were released to include all languages and symbols in the world, wouldn't that solve problems in cross-language environments and eliminate garbled text**? Driven by this idea, a large and comprehensive character set, Unicode, was born.
 
-<u>Unicode</u> is called "统一码" (Unified Code) in Chinese and can theoretically accommodate over one million characters. It is committed to including characters from around the world into a unified character set, providing a universal character set to handle and display various language texts, reducing garbled character problems caused by different encoding standards.
+<u>Unicode</u>, or Unified Code, can theoretically accommodate over one million characters. It is committed to including characters from around the world into a unified character set, providing a universal character set to handle and display various language texts, reducing garbled character problems caused by different encoding standards. Since its release in 1991, Unicode has continuously expanded to include new languages and characters. As of September 2022, Unicode has included 149,186 characters, including characters, symbols, and even emojis from various languages.
 
-Since its release in 1991, Unicode has continuously expanded to include new languages and characters. As of September 2022, Unicode has included 149,186 characters, including characters, symbols, and even emojis from various languages. Unicode maps each character to a code point (a character identifier), whose values range from 0 to 1114111 (that is, U+0000 to U+10FFFF), forming a unified character numbering space.
-
-Unicode is a universal character set that essentially assigns a number (called a "code point") to each character, **but it does not specify how to store these character code points in computers**. We can't help but ask: when Unicode code points of multiple lengths appear simultaneously in a text, how does the system parse the characters? For example, given an encoding with a length of 2 bytes, how does the system determine whether it is one 2-byte character or two 1-byte characters?
+As a universal character set, Unicode essentially assigns each character a unique "code point" (character identifier), whose range is U+0000 to U+10FFFF, forming a unified character numbering space. However, **Unicode does not specify how to store these character code points in computers**. We can't help but ask: when Unicode code points of multiple lengths appear simultaneously in a text, how does the system parse the characters? For example, given an encoding with a length of 2 bytes, how does the system determine whether it is one 2-byte character or two 1-byte characters?
 
 For the above problem, **a straightforward solution is to store all characters as equal-length encodings**. As shown in the figure below, each character in "Hello" occupies 1 byte, and each character in "算法" (algorithm) occupies 2 bytes. We can encode all characters in "Hello 算法" as 2 bytes in length by padding the high bits with 0. In this way, the system can parse one character every 2 bytes and restore the content of this phrase.
 
@@ -36,7 +34,7 @@ For the above problem, **a straightforward solution is to store all characters a
 
 However, ASCII code has already proven to us that encoding English only requires 1 byte. If the above scheme is adopted, the size of English text will be twice that under ASCII encoding, which is very wasteful of memory space. Therefore, we need a more efficient Unicode encoding method.
 
-## Utf-8 Encoding
+## UTF-8 Encoding
 
 Currently, UTF-8 has become the most widely used Unicode encoding method internationally. **It is a variable-length encoding** that uses 1 to 4 bytes to represent a character, depending on the complexity of the character. ASCII characters only require 1 byte, Latin and Greek letters require 2 bytes, commonly used Chinese characters require 3 bytes, and some other rare characters require 4 bytes.
 
@@ -45,7 +43,7 @@ The encoding rules of UTF-8 are not complicated and can be divided into the foll
 - For 1-byte characters, set the highest bit to $0$, and set the remaining 7 bits to the Unicode code point. It is worth noting that ASCII characters occupy the first 128 code points in the Unicode character set. That is to say, **UTF-8 encoding is backward compatible with ASCII code**. This means we can use UTF-8 to parse very old ASCII code text.
 - For characters with a length of $n$ bytes (where $n > 1$), set the highest $n$ bits of the first byte to $1$, and set the $(n + 1)$-th bit to $0$; starting from the second byte, set the highest 2 bits of each byte to $10$; use all remaining bits to fill in the Unicode code point of the character.
 
-The figure below shows the UTF-8 encoding corresponding to "Hello算法". It can be observed that since the highest $n$ bits are all set to $1$, the system can parse the length of the character as $n$ by reading the number of highest bits that are $1$.
+The figure below shows the UTF-8 encoding corresponding to "Hello 算法". It can be observed that since the highest $n$ bits are all set to $1$, the system can determine that the character length is $n$ by counting the leading $1$ bits.
 
 But why set the highest 2 bits of all other bytes to $10$? In fact, this $10$ can serve as a check symbol. Assuming the system starts parsing text from an incorrect byte, the $10$ at the beginning of the byte can help the system quickly determine an anomaly.
 
@@ -64,7 +62,7 @@ From a compatibility perspective, UTF-8 has the best universality, and many tool
 
 ## Character Encoding in Programming Languages
 
-For most past programming languages, strings during program execution use fixed-length encodings such as UTF-16 or UTF-32. Under fixed-length encoding, we can treat strings as arrays for processing, and this approach has the following advantages.
+For many programming languages in the past, strings during program execution used internal encodings such as UTF-16 or UTF-32. Under these representations, we can often treat strings like arrays during processing, and this approach has the following advantages.
 
 - **Random access**: UTF-16 encoded strings can be easily accessed randomly. UTF-8 is a variable-length encoding. To find the $i$-th character, we need to traverse from the beginning of the string to the $i$-th character, which requires $O(n)$ time.
 - **Character counting**: Similar to random access, calculating the length of a UTF-16 encoded string is also an $O(1)$ operation. However, calculating the length of a UTF-8 encoded string requires traversing the entire string.