Recursion becomes much easier once students have the right mental model. Visualization will help get them there.

Take the Tower of Hanoi problem. The recursive solution is beautifully short, to move n disks we:

• first remove n-1 disks from the largest disk
• then move the largest disk
• and then move the n-1 disks back on top

But when students try to implement recursion, they often get stuck, and adding debug prints only adds to the confusion. That is where visualization can help to bring the right mental model. Here is the Tower of Hanoi problem solved recursively, visualized with 𝗶𝗻𝘃𝗼𝗰𝗮𝘁𝗶𝗼𝗻_𝘁𝗿𝗲𝗲: https://www.invocation-tree.com/#codeurl=https%3A%2F%2Fraw.githubusercontent.com%2Fbterwijn%2Fmemory_graph_examples%2Frefs%2Fheads%2Fmain%2Ftowers_of_hanoi.py&timestep=0.5&play=

Instead of thinking about “a function calling itself again and again” students can now see the depth-first execution of a tree of subproblems showing the divide-and-conquer strategy in action. Once a student can think in terms of a tree of subproblems, recursion becomes much easier to understand, explain, and debug.

#Python #invocation_tree #Recursion

The difference in Python OOP between:

• instance method
• class method
• static method

visually explained using 𝗺𝗲𝗺𝗼𝗿𝘆_𝗴𝗿𝗮𝗽𝗵:

An exercise to help build the right mental model for Python data.

• Solution: https://memory-graph.com/#codeurl=https%3A%2F%2Fraw.githubusercontent.com%2Fbterwijn%2Fmemory_graph_videos%2Frefs%2Fheads%2Fmain%2Fexercises%2Fexercise9.py&play=
• Explanation: https://github.com/bterwijn/memory_graph?tab=readme-ov-file#python-data-model

The “Solution” link visualizes execution and reveals what’s actually happening using 𝗺𝗲𝗺𝗼𝗿𝘆_𝗴𝗿𝗮𝗽𝗵: https://github.com/bterwijn/memory_graph

Data structures like Trie can in Python be easier understood and debugged after visualization using the memory_graph package.

A Trie is a tree of dictionaries and can be used for things like word completion.

Data structures become much easier to understand when students can see the structure of their data visualized using memory_graph. A data structure is no longer an abstract idea but concrete, clear and debuggable. Here’s a live demo of a Linear Linked List: https://memory-graph.com/#codeurl=https%3A%2F%2Fraw.githubusercontent.com%2Fbterwijn%2Fmemory_graph%2Frefs%2Fheads%2Fmain%2Fsrc%2Flinked_list_lin.py&breakpoints=27&continues=1&timestep=0.2&play=

An exercise to help build the right mental model for Python data. The “Solution” link uses memory_graph to visualize execution and reveals what’s actually happening:

• Solution: https://memory-graph.com/#codeurl=https%3A%2F%2Fraw.githubusercontent.com%2Fbterwijn%2Fmemory_graph_videos%2Frefs%2Fheads%2Fmain%2Fexercises%2Fexercise19.py&play=
• Explanation: https://github.com/bterwijn/memory_graph?tab=readme-ov-file#python-data-model

Understanding and debugging Python data structures gets easier with memory_graph visualization. Here's a Multiway Tree example. A Multiway Tree is similar to a Binary Tree but has an arbitrary number of children making the tree less deep and more efficient.

An exercise to help build the right mental model for Python data. The “Solution” link uses memory_graph to visualize execution and reveals what’s actually happening:

• Solution
• Explanation

An exercise to help build the right mental model for Python data. The “Solution” link uses memory_graph to visualize execution and reveals what’s actually happening:

• Solution
• Explanation

Teaching and learning Python bitwise operators gets much easier after showing the binary representations of integers using memory_graph: bitwise operators in Memory Graph Web Debugger

Understanding of the inverse ~ operator is helped by showing the two’s complement representation.

An exercise to help build the right mental model for Python data. The “Solution” link uses memory_graph to visualize execution and reveals what’s actually happening:

• Solution
• Explanation

Some struggle with recursion, but as package invocation_tree visualizes the Python call tree in real time, it gets easy to understand what is going on and to debug any remaining issues.

See this one-click Quick Sort demo in the Invocation Tree Web Debugger.