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Tree traversal in MATLAB (#690)
* adding matlab implementation to tree traversal * adding matlab implementation to tree traversal algorithm * replaced length truth comparison with not empty comparison for better performance * finishing replacements Co-authored-by: James Schloss <jrs.schloss@gmail.com>
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‎contents/tree_traversal/code/matlab/tree.m

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main()
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%% Functions
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function root = create_tree()
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node = @(k,v) containers.Map(k,v);
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node2 = node(2, {{}}); node3 = node(3, {{}}); node4 = node(4, {{}});
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node6 = node(6, {{}}); node7 = node(7, {{}}); node8 = node(8, {{}});
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node10 = node(10, {{}}); node11 = node(11, {{}}); node12 = node(12, {{}});
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node1 = node(1, {node2, node3, node4});
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node5 = node(5, {node6, node7, node8});
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node9 = node(9, {node10, node11, node12});
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root = node(0, {node1, node5, node9});
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end
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function root = create_btree()
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node = @(k,v) containers.Map(k,v);
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node2 = node(2, {{}}); node3 = node(3, {{}});
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node5 = node(5, {{}}); node6 = node(6, {{}});
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node1 = node(1, {node2, node3});
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node4 = node(4, {node5, node6});
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root = node(0, {node1, node4});
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end
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function DFS_recursive(n)
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cell_index = @(a, b) a{b};
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ID = cell_index(keys(n), 1);
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fprintf('%u ', ID);
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children = cell_index(values(n), 1);
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for i = children
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child = i{1};
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if ~isempty(child)
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DFS_recursive(child);
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end
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end
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end
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function DFS_recursive_postorder(n)
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cell_index = @(a, b) a{b};
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children = cell_index(values(n), 1);
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for i = children
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child = i{1};
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if ~isempty(child)
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DFS_recursive_postorder(child);
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end
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end
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ID = cell_index(keys(n), 1);
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fprintf('%u ', ID);
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end
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function DFS_recursive_inorder_btree(n)
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cell_index = @(a, b) a{b};
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ID = cell_index(keys(n), 1);
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children = cell_index(values(n), 1);
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if length(children) == 2
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DFS_recursive_inorder_btree(children{1})
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fprintf('%u ', ID)
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DFS_recursive_inorder_btree(children{2})
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elseif length(children) == 1
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if ~isempty(children{1})
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DFS_recursive_inorder_btree(children{1})
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end
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fprintf('%u ', ID)
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else
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fprintf("Not a binary tree!")
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end
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end
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function DFS_stack(n)
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cell_index = @(a, b) a{b};
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node_stack = {n};
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while ~isempty(node_stack)
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parent = node_stack{end};
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node_stack(end) = [];
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ID = cell_index(keys(parent), 1);
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fprintf('%u ', ID);
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children = cell_index(values(parent), 1);
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for i = flip(children)
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child = i{1};
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if ~isempty(child)
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node_stack = {node_stack{:} child};
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end
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end
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end
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end
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function BFS_queue(n)
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cell_index = @(a, b) a{b};
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node_queue = {n};
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while ~isempty(node_queue)
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next_nodes = {};
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for parent_cell = node_queue
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parent = parent_cell{1};
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ID = cell_index(keys(parent), 1);
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fprintf('%u ', ID);
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children = cell_index(values(parent), 1);
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for i = children
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child = i{1};
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if ~isempty(child)
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next_nodes = {next_nodes{:}, child};
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end
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end
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end
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node_queue = next_nodes;
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end
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end
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function main()
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root = create_tree();
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rootb = create_btree();
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fprintf('\nDFS Recursive\n')
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DFS_recursive(root)
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fprintf('\nDFS Recursive Postorder\n')
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DFS_recursive_postorder(root)
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fprintf('\nDFS Recursive Inorder Binary Tree\n')
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DFS_recursive_inorder_btree(rootb)
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fprintf('\nDFS Stack\n')
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DFS_stack(root)
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fprintf('\nBFS Queue\n')
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BFS_queue(root)
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fprintf('\n')
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end

‎contents/tree_traversal/tree_traversal.md

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@@ -38,6 +38,8 @@ As a note, a `node` struct is not necessary in javascript, so this is an example
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[import:24-27, lang:"asm-x64"](code/asm-x64/tree_traversal.s)
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{% sample lang="emojic" %}
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[import:1-3, lang:"emojicode"](code/emojicode/tree_traversal.emojic)
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{% sample lang="m" %}
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[import:6-6, lang:"matlab"](code/matlab/tree.m)
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{% endmethod %}
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Because of this, the most straightforward way to traverse the tree might be recursive. This naturally leads us to the Depth-First Search (DFS) method:
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[import:290-314, lang:"asm-x64"](code/asm-x64/tree_traversal.s)
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{% sample lang="emojic" %}
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[import:27-34, lang:"emojicode"](code/emojicode/tree_traversal.emojic)
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{% sample lang="m" %}
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[import:31-45, lang:"matlab"](code/matlab/tree.m)
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{% endmethod %}
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At least to me, this makes a lot of sense. We fight recursion with recursion! First, we first output the node we are on and then we call `DFS_recursive(...)` on each of its children nodes. This method of tree traversal does what its name implies: it goes to the depths of the tree first before going through the rest of the branches. In this case, the ordering looks like:
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[import:316-344, lang:"asm-x64"](code/asm-x64/tree_traversal.s)
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{% sample lang="emojic" %}
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[import:36-43, lang:"emojicode"](code/emojicode/tree_traversal.emojic)
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{% sample lang="m" %}
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[import:47-62, lang:"matlab"](code/matlab/tree.m)
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{% endmethod %}
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<p>
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[import:346-396, lang:"asm-x64"](code/asm-x64/tree_traversal.s)
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{% sample lang="emojic" %}
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[import:45-62, lang:"emojicode"](code/emojicode/tree_traversal.emojic)
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{% sample lang="m" %}
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[import:64-82, lang:"matlab"](code/matlab/tree.m)
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{% endmethod %}
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<p>
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<img class="center" src="res/DFS_in.png" style="width:70%" />
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</p>
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<p>
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<img class="center" src="res/DFS_in.png" width="500" />
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</p>
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The order here seems to be some mix of the other 2 methods and works through the binary tree from left to right.
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[import:398-445, lang:"asm-x64"](code/asm-x64/tree_traversal.s)
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{% sample lang="emojic" %}
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[import:64-79, lang:"emojicode"](code/emojicode/tree_traversal.emojic)
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{% sample lang="m" %}
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[import:84-106, lang:"matlab"](code/matlab/tree.m)
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{% endmethod %}
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All this said, there are a few details about DFS that might not be ideal, depending on the situation. For example, if we use DFS on an incredibly long tree, we will spend a lot of time going further and further down a single branch without searching the rest of the data structure. In addition, it is not the natural way humans would order a tree if asked to number all the nodes from top to bottom. I would argue a more natural traversal order would look something like this:
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[import:447-498, lang:"asm-x64"](code/asm-x64/tree_traversal.s)
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{% sample lang="emojic" %}
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[import:81-96, lang:"emojicode"](code/emojicode/tree_traversal.emojic)
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{% sample lang="m" %}
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[import:108-129, lang:"matlab"](code/matlab/tree.m)
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{% endmethod %}
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## Video Explanation
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[import, lang:"asm-x64"](code/asm-x64/tree_traversal.s)
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{% sample lang="emojic" %}
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[import, lang:"emojicode"](code/emojicode/tree_traversal.emojic)
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{% sample lang="m" %}
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[import, lang:"matlab"](code/matlab/tree.m)
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{% endmethod %}
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