# Generic Trees(N-array Trees)

The Generic trees are the n-ary trees which have the following properties:

- Many children at every node.
- The number of nodes for each node is not known in advance.

**Example:**

To represent the above tree, we have to consider the worst case, that is the node with maximum children (in above example, 6 children) and allocate that many pointers for each node.

The node representation based on this method can be written as:

`//Node declaration ` `struct` `Node{ ` ` ` `int` `data; ` ` ` `struct` `Node *firstchild; ` ` ` `struct` `Node *secondchild; ` ` ` `struct` `Node *thirdchild; ` ` ` `struct` `Node *fourthchild; ` ` ` `struct` `Node *fifthchild; ` ` ` `struct` `Node *sixthchild; ` `} ` |

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**Disadvantages of the above representation are:**

**Memory Wastage**– All the pointers are not required in all the cases. Hence, there is lot of memory wastage.**Unknown number of children**– The number of children for each node is not known in advance.

**Better Approach:** First child / Next sibling representation

In first child/next sibling representation, the steps taken are:

- At each node link the children of same parent(siblings) from left to right.
- Remove the links from parent to all children except the first child.

Since we have a link between children, we do not need extra links from parent to all the children. This representation allows us to traverse all the elements by starting at the first child of the parent.

The node declaration for first child / next sibling representation can be written as:

`//Node declaration ` `struct` `Node{ ` ` ` `int` `data; ` ` ` `struct` `Node *firstChild; ` ` ` `struct` `Node *nextSibling; ` `} ` |

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**Advantages:**

- Memory efficient – No extra links are required, hence lot of memory is saved.
- Treated as binary trees – Since we are able to convert any generic tree to binary representation, we can treat all generic trees with a first child/next sibling representation as binary trees.Instead of left and right pointers, we just use firstChild and nextSibling.

Height of generic tree from parent array

Generic tree – level order traversal

## Recommended Posts:

- Height of a generic tree from parent array
- AA Trees | Set 1 (Introduction)
- B*-Trees implementation in C++
- Disjoint Set Union on trees | Set 2
- Combinatorics on ordered trees
- Disjoint Set Union on trees | Set 1
- m-WAY Search Trees | Set-1 ( Searching )
- Check if two trees are Mirror | Set 2
- Red-Black Trees | Top-Down Insertion
- Foldable Binary Trees
- Dynamic Programming on Trees | Set-1
- Dynamic Programming on Trees | Set 2
- DP on Trees | Set-3 ( Diameter of N-ary Tree )
- Enumeration of Binary Trees
- 2-3 Trees | (Search and Insert)

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