Editing 2–3 tree (section)

===Searching===
Searching for an item in a 2–3 tree is similar to searching for an item in a [[binary search tree]]. Since the data elements in each node are ordered, a search function will be directed to the correct subtree and eventually to the correct node which contains the item.

# Let {{mvar|T}} be a 2–3 tree and {{mvar|d}} be the data element we want to find. If {{mvar|T}} is empty, then {{mvar|d}} is not in {{mvar|T}} and we're done.
# Let {{mvar|t}} be the root of {{mvar|T}}.
# Suppose {{mvar|t}} is a leaf.
#* If {{mvar|d}} is not in {{mvar|t}}, then {{mvar|d}} is not in {{mvar|T}}. Otherwise, {{mvar|d}} is in {{mvar|T}}. We need no further steps and we're done.
# Suppose {{mvar|t}} is a 2-node with left child {{mvar|p}} and right child {{mvar|q}}. Let {{mvar|a}} be the data element in {{mvar|t}}. There are three cases:
#* If {{mvar|d}} is equal to {{mvar|a}}, then we've found {{mvar|d}} in {{mvar|T}} and we're done. 
#* If <math>d < a</math>, then set {{mvar|T}} to {{mvar|p}}, which by definition is a 2–3 tree, and go back to step 2.
#* If <math>d > a</math>, then set {{mvar|T}} to {{mvar|q}} and go back to step 2.
# Suppose {{mvar|t}} is a 3-node with left child {{mvar|p}}, middle child {{mvar|q}}, and right child {{mvar|r}}. Let {{mvar|a}} and {{mvar|b}} be the two data elements of {{mvar|t}}, where <math>a < b</math>. There are four cases:
#* If {{mvar|d}} is equal to {{mvar|a}} or {{mvar|b}}, then {{mvar|d}} is in {{mvar|T}} and we're done.
#* If <math>d < a</math>, then set {{mvar|T}} to {{mvar|p}} and go back to step 2.
#* If <math>a < d < b</math>, then set {{mvar|T}} to {{mvar|q}} and go back to step 2.
#* If <math>d > b</math>, then set {{mvar|T}} to {{mvar|r}} and go back to step 2.