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Heaps And Maps

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Why treemaps / heaps

In the trees topic, we explore what trees are.

We also explore that in a balanced BST, we can do the following :

        1. Insert in O(log n)
        2. Delete in O(log n)
        3. Search for an element in O(log n)
        4. Find Min in O(log n)
        5. Find Max in O(log n)
        6. Get all the elements in sorted order in O(n) - Inorder traversal.
        7. Find an element closest in value to x O(log n)

We also explored hashing in a previous topic along with hashmaps.
While hashmaps are really good for tracking whether an element is present or not, or the number of occurrences, it fails to answer :

        1. the min / max query in reasonable time
        2. Iterating through the element in sorted order in linear time
        3. Find an element closes to x in logarithmic time.

With that in mind, we explore treemap which helps us address all of those queries.
Treemaps are implemented internally using balanced trees ( They mostly use red black trees, but going into the implementation details of red black tree might be out of scope here ).

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