Project subject: A tree application where student names are stored

The requirements and scoring are as follows.

$1-$ Inserting names into the tree $(60$ points$)$

The names entered by the user must be inserted into a tree, starting with the first letter. Each letter is stored in a node. The same prefix shared between different names are represented by the same nodes. The number of names overlapped in a node must be kept in this node.

For example, Figure $1$ shows a tree which is initially empty. Figure $2,$ Figure $3,$ Figure $4,$ Figure $5$ and Figure $6$ represent the tree after the names "Ali", $"$Ay$$e$",$ "Irfan", "Alihan" and "Alican" were inserted, respectively.

For example, considering the node $(A$:$2)$ in Figure $3,$ it is understood that this node represents the letter $"$A$"$ and it is associated with $2$ names. Similarly, considering the node $($I:$3)$ in Figure $6,$ it is understood that this node represents the letter "I" and it is associated with $3$ names.

$2.$ Updating the names $(40$ points$)$

The user may want to update a name at any stage. For example, a command such as Update$("$Alihan$",$ "Veli"$)$ means that the name "Alihan" is wanted to be updated as the name "Veli". Figure $7$ represents the tree after this update was made. If the name to be updated is not found in the tree, the user must be informed.