# Learning Lua Step-By-Step (Part 13)

This entry is part 13 of 25 in the series Learning Lua Step-By-Step

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## Tree and Trie Applications

In this part of our Lua learning series, we'll explore two tree-based data structures: a tree used for sorting item depth in a 3D game, and a trie for efficient word searching.

## Tree for 3D Item Depth Sorting

In 3D games, it's important to render objects in the correct order to ensure proper visibility and avoid visual artifacts. One way to achieve this is by using a quadtree, a specialized tree data structure that can efficiently sort and store 3D objects based on their depth.

Here's an example implementation of a quadtree in Lua:

-- Quadtree node
return {
bounds = bounds,
objects = objects or {},
children = {}
}
end

-- Recursive function to insert an object into the quadtree
local function insert_object(node, obj)
-- Check if the object is within the node's bounds
if not node.bounds:contains(obj.position) then
return
end

-- If the node has no children and the object count is less than 4, add the object to the node
if #node.children == 0 and #node.objects < 4 then
table.insert(node.objects, obj)
return
end

-- Otherwise, create child nodes and recursively insert the object
if #node.children == 0 then
local bounds = node.bounds:split()
for _, child_bounds in ipairs(bounds) do
end
end

for _, child in ipairs(node.children) do
insert_object(child, obj)
end
end

In this example, we define a create_quadtree_node function that creates a new node in the quadtree, with a bounding box and a list of objects. The insert_object function recursively inserts an object into the appropriate node of the quadtree, based on the object's position and the node's bounds.

By using a quadtree, you can efficiently sort and store 3D objects, allowing you to render them in the correct order and improve the overall visual quality of your 3D game.

## Trie for Word Search

A trie, also known as a prefix tree, is a tree-based data structure that is particularly useful for efficient word searching and autocompletion. In a trie, each node represents a character in a word, and the path from the root to a leaf node represents a complete word.

Here's an example implementation of a trie in Lua:

-- Trie node
local function create_trie_node()
return {
children = {},
is_end_of_word = false
}
end

-- Insert a word into the trie
function trie:insert(word)
local node = self
for char in word:gmatch(".") do
if not node.children[char] then
node.children[char] = create_trie_node()
end
node = node.children[char]
end
node.is_end_of_word = true
end

-- Search for a word in the trie
function trie:search(word)
local node = self
for char in word:gmatch(".") do
if not node.children[char] then
return false
end
node = node.children[char]
end
return node.is_end_of_word
end

In this example, we define a create_trie_node function that creates a new node in the trie, with a table of child nodes and a flag to indicate if the node represents the end of a word. We also define two functions: insert to add a word to the trie, and search to check if a word is present in the trie.

Tries are particularly useful for applications that require efficient word searching, such as spell checkers, autocomplete features, and database indexing. By leveraging the tree-like structure, tries can quickly determine if a word is present in the data structure, without the need for complex string comparisons.

## Exercises

1. Modify the quadtree implementation to also store the depth (or z-coordinate) of each object, and implement a function to render the objects in the correct order.
2. Implement a function to find all words in the trie that start with a given prefix.
3. Implement a function to remove a word from the trie.

## Conclusion

In this article, we've explored two tree-based data structures: a quadtree for sorting 3D objects based on depth, and a trie for efficient word searching. These data structures demonstrate the power and versatility of trees, and how they can be applied to solve real-world problems in game development and text processing.

Remember to practice the exercises and refer to the resources below to further your understanding of these concepts. In the next article, we'll dive into graphs and pathfinding algorithms.

## Resources

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