2-3 Insertion

This lesson will explain the how insertion is done in 2-3 Trees based on multiple scenarios which are explained in the insertion algorithm.


Insertion in 2-3 Trees is a lot 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)O(Logn) time where n is the number of nodes in the tree. Searching an element is done in Log(n)Log(n), and then insertion takes a constant amount of time. So overall, the time complexity of the insertion algorithm is O(Logn)O(Logn). Let’s see how it works.

Insertion Algorithm:

The insertion algorithm is based on these scenarios:

  • Initially 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

Example -1

Let’s take a look at the following example where we will build a 2-3 Tree from scratch by inserting elements one by one.

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