Add Gap Buffer post

content/posts/2024-07-06-gap-buffer/index.md

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+---
+title: "Gap Buffer"
+date: 2024-07-06T21:27:19+01:00
+draft: false # I don't care for draft mode, git has branches for that
+description: "As featured in GNU Emacs"
+tags:
+- algorithms
+- data structures
+- python
+categories:
+- programming
+series:
+- Cool algorithms
+favorite: false
+disable_feed: false
+---
+
+The [_Gap Buffer_][wiki] is a popular data structure for text editors to
+represent files and editable buffers. The most famous of them probably being
+[GNU Emacs][emacs].
+
+[wiki]: https://en.wikipedia.org/wiki/Gap_buffer
+[emacs]: https://www.gnu.org/software/emacs/manual/html_node/elisp/Buffer-Gap.html
+
+<!--more-->
+
+## What does it do?
+
+A _Gap Buffer_ is simply a list of characters, similar to a normal string, with
+the added twist of splitting it into two side: the prefix and suffix, on either
+side of the cursor. In between them, a gap is left to allow for quick
+insertion at the cursor.
+
+Moving the cursor moves the gap around the buffer, the prefix and suffix getting
+shorter/longer as required.
+
+## Implementation
+
+I'll be writing a sample implementation in Python, as with the rest of the
+series. I don't think it showcases the elegance of the _Gap Buffer_ in action
+like a C implementation full of `memmove`s would, but it does makes it short and
+sweet.
+
+### Representation
+
+We'll be representing the gap buffer as an actual list of characters.
+
+Given that Python doesn't _have_ characters, let's settle for a list of strings,
+each representing a single character...
+
+```python
+Char = str
+
+class GapBuffer:
+    # List of characters, contains prefix and suffix of string with gap in the middle
+    _buf: list[Char]
+    # The gap is contained between [start, end) (i.e: buf[start:end])
+    _gap_start: int
+    _gap_end: int
+
+    # Visual representation of the gap buffer:
+    # This is a very  [                     ]long string.
+    # |<----------------------------------------------->| capacity
+    # |<------------>|                       |<-------->| string
+    #                 |<------------------->|             gap
+    # |<------------>|                                    prefix
+    #                                        |<-------->| suffix
+    def __init__(self, initial_capacity: int = 16) -> None:
+        assert initial_capacity > 0
+        # Initialize an empty gap buffer
+        self._buf = [""] * initial_capacity
+        self._gap_start = 0
+        self._gap_end = initial_capacity
+```
+
+### Accessors
+
+I'm mostly adding these for exposition, and making it easier to write `assert`s
+later.
+
+```python
+@property
+def capacity(self) -> int:
+  return len(self._buf)
+
+@property
+def gap_length(self) -> int:
+  return self._gap_end - self._gap_start
+
+@property
+def string_length(self) -> int:
+  return self.capacity - self.gap_length
+
+@property
+def prefix_length(self) -> int:
+  return self._gap_start
+
+@property
+def suffix_length(self) -> int:
+  return self.capacity - self._gap_end
+```
+
+### Growing the buffer
+
+I've written this method in a somewhat non-idiomatic manner, to make it closer
+to how it would look in C using `realloc` instead.
+
+It would be more efficient to use slicing to insert the needed extra capacity
+directly, instead of making a new buffer and copying characters over.
+
+```python
+def grow(self, capacity: int) -> None:
+    assert capacity >= self.capacity
+    # Create a new buffer with the new capacity
+    new_buf = [""] * capacity
+    # Move the prefix/suffix to their place in the new buffer
+    added_capacity = capacity - len(self._buf)
+    new_buf[: self._gap_start] = self._buf[: self._gap_start]
+    new_buf[self._gap_end + added_capacity :] = self._buf[self._gap_end :]
+    # Use the new buffer, account for added capacity
+    self._buf = new_buf
+    self._gap_end += added_capacity
+```
+
+### Insertion
+
+Inserting text at the cursor's position means filling up the gap in the middle
+of the buffer. To do so we must first make sure that the gap is big enough, or
+grow the buffer accordingly.
+
+Then inserting the text is simply a matter of copying its characters in place,
+and moving the start of the gap further right.
+
+```python
+def insert(self, val: str) -> None:
+    # Ensure we have enouh space to insert the whole string
+    if len(val) > self.gap_length:
+        self.grow(max(self.capacity * 2, self.string_length + len(val)))
+    # Fill the gap with the given string
+    self._buf[self._gap_start : self._gap_start + len(val)] = val
+    self._gap_start += len(val)
+```
+
+### Deletion
+
+Removing text from the buffer simply expands the gap in the corresponding
+direction, shortening the string's prefix/suffix. This makes it very cheap.
+
+The methods are named after the `backspace` and `delete` keys on the keyboard.
+
+```python
+def backspace(self, dist: int = 1) -> None:
+    assert dist <= self.prefix_length
+    # Extend gap to the left
+    self._gap_start -= dist
+
+def delete(self, dist: int = 1) -> None:
+    assert dist <= self.suffix_length
+    # Extend gap to the right
+    self._gap_end += dist
+```
+
+### Moving the cursor
+
+Moving the cursor along the buffer will shift letters from one side of the gap
+to the other, moving them accross from prefix to suffix and back.
+
+I find Python's list slicing not quite as elegant to read as a `memmove`, though
+it does make for a very small and efficient implementation.
+
+```python
+def left(self, dist: int = 1) -> None:
+    assert dist <= self.prefix_length
+    # Shift the needed number of characters from end of prefix to start of suffix
+    self._buf[self._gap_end - dist : self._gap_end] = self._buf[
+        self._gap_start - dist : self._gap_start
+    ]
+    # Adjust indices accordingly
+    self._gap_start -= dist
+    self._gap_end -= dist
+
+def right(self, dist: int = 1) -> None:
+    assert dist <= self.suffix_length
+    # Shift the needed number of characters from start of suffix to end of prefix
+    self._buf[self._gap_start : self._gap_start + dist] = self._buf[
+        self._gap_end : self._gap_end + dist
+    ]
+    # Adjust indices accordingly
+    self._gap_start += dist
+    self._gap_end += dist
+```