2-3 Insertion

Introduction

Insertion in 2-3 trees is different from binary search trees. In 2-3 trees, values are only inserted at leaf nodes based on certain conditions. As discussed before, the insertion algorithm takes $O(Logn)$ time where n is the number of nodes in the tree. Searching an element is done in $Log(n)$, and then insertion takes a constant amount of time. Overall, the time complexity of the insertion algorithm is $O(Logn)$. Let’s see how it works!

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Insertion algorithm

The insertion algorithm is based on these scenarios:

• If the tree is empty, create a new leaf node and insert your value.
• If the tree is not empty, traverse through the tree to find the right leaf node where the value should be inserted.
• If the leaf node has only one value, insert your value into the node.
• If the leaf node has more than two values, split the node by moving the middle element to the top node.
• Keep forming new nodes wherever you get more than two elements.

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Example - 1

Take a look at the following example where you will build a 2-3 tree from scratch by inserting elements one by one.