data_structures_mental_model

TreeMap and TreeSet both are part of the Java Collections Framework, and both rely on red–black trees (a self-balancing binary search tree).

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🌳 TreeMap • A Map where keys are stored in sorted order (based on natural ordering or a custom Comparator). • Internally backed by a red–black tree → guarantees O(log n) for insert, search, delete.

Mental model

Think of a dictionary (like in a book): • Words (keys) are alphabetically sorted. • Each word points to its definition (value).

TreeMap<String, Integer> treeMap = new TreeMap<>();
treeMap.put("dog", 1);
treeMap.put("cat", 2);
treeMap.put("apple", 3);

System.out.println(treeMap);

Output (keys sorted):

{apple=3, cat=2, dog=1}

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🌳 TreeSet • A Set implementation backed by a TreeMap. • Stores unique elements, in sorted order. • Guarantees O(log n) for add, remove, contains.

Mental model

Think of a sorted shelf of unique books: • You can quickly see if a book exists (binary search in tree). • Books are kept in sorted order automatically.

TreeSet<String> treeSet = new TreeSet<>();
treeSet.add("dog");
treeSet.add("cat");
treeSet.add("apple");

System.out.println(treeSet);

Output (sorted, no duplicates):

[apple, cat, dog]

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🧠 Key Intuition (Mental Model) • Imagine every time you insert a key/value (TreeMap) or element (TreeSet), it gets placed into a balanced binary search tree. • The tree automatically rearranges (rotates) itself to remain balanced. • Because it’s balanced, the height is ~log n, so searches, inserts, deletes are efficient.

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⚖️ Comparison vs Other Maps/Sets

Feature HashMap / HashSet LinkedHashMap TreeMap / TreeSet Ordering None (random) Insertion order Sorted (natural or comparator) Complexity O(1) avg. O(1) avg. O(log n) Use Case Fast lookup Preserve order Always keep sorted

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🏗️ Mental Pictures • TreeMap = 📖 Dictionary → words sorted, each with a definition. • TreeSet = 📚 Sorted bookshelf → unique books in order.

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