How Many Regular Ternary Ordered Trees with Height 3 Exist?

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In summary, the conversation discusses the concept of ordered trees and the calculation of the total number of possibilities for a regular ternary ordered tree with a height of 3. The smallest and biggest radius for a tree with height k is also mentioned. There is also a reference to further discussion on k-ary trees for checking the answer. The participants also mention a possible calculation of the total number of possibilities for ordered trees with a height of 3, and the reasoning behind it.
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fiksx
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I’m not too familiar with ordered tree. I’m solving excercise about tree but i’m not sure it is right or wrong
Summary: I’m not too familiar with ordered tree. I’m solving excercise about tree but i’m not sure it is right or wrong

How many regular ternary ordered tree with height 3 (ordered tree means children of each vertex are assigned a fixed ordering)? What is the smallest and biggest radius for tree with height k?

Attempt: For regular ternary ordered tree with height 3 There will be 9 node that will have children 9C1 +9C2+9C3+9C4+9C4+9C5+9C6+9C7+9C8+9C9

And smallest and biggest radius for tree with height
 
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jedishrfu said:
Here's some discussion on k-ary trees that might help you check your answer:

https://cs.lmu.edu/~ray/notes/orderedtrees/

Thankyou but for ordered tree with height of 3 is the total possibility tree are 511? Because all sum possible combination of 9Ck (1<=k<=9) =511
Or other way multiplication of possibility in each subtree. First subtree will be 3C0 +3C1+3C2+3C3= 8 , because there are 3 subtree in height 1 so 8x8x8=512-1=511 , why substract 1 because 9C0 makes tree height 2 . Is this quite right?
 
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1. What is a ternary ordered tree?

A ternary ordered tree is a type of data structure in which each node can have up to three child nodes. It is similar to a binary tree, but with an additional third child node. The nodes in a ternary ordered tree are arranged in a specific order, such as left to right or top to bottom.

2. What are the advantages of using a ternary ordered tree?

One advantage of using a ternary ordered tree is that it allows for more efficient storage and retrieval of data compared to other tree structures. It also offers a more balanced structure, which can improve the performance of certain operations. Additionally, ternary ordered trees are useful for representing hierarchical data, such as file systems or mathematical expressions.

3. How is a ternary ordered tree different from a binary tree?

A ternary ordered tree differs from a binary tree in that each node can have up to three child nodes instead of just two. This allows for more flexibility in the structure and can improve the efficiency of certain operations. Additionally, the nodes in a ternary ordered tree are typically arranged in a specific order, whereas binary trees can be arranged in any order.

4. How do you insert and delete nodes in a ternary ordered tree?

To insert a node in a ternary ordered tree, you first need to find the appropriate position for the new node based on the ordering of the tree. Then, you can add the node as a child of the appropriate parent node. To delete a node, you need to first remove all of its child nodes, then remove the node itself from the tree. This may require rearranging the remaining nodes to maintain the ordering of the tree.

5. What are some common applications of ternary ordered trees?

Ternary ordered trees are commonly used in computer science for storing and organizing data, particularly in applications that involve hierarchical data or require efficient retrieval of data. Some examples of applications that use ternary ordered trees include file systems, decision trees, and mathematical expression trees. They are also used in some algorithms and data compression techniques.

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