A forest is a set of disjoint trees. Removing the root of a tree produces a forest. A forest can be transformed into a single binary tree by linking the binary tree representations of each tree in the forest through the rightChild field. Preorder, inorder, and postorder traversals of this binary tree correspond to forest preorder, inorder, and postorder traversals, which involve traversing the subtrees and trees of the forest in a specified order and visiting the roots.

1. DATA STRUCTURES
FOREST
By,
M.SHARMILA DEVI M.Sc(IT)

2. FORESTS
⮚ Definition: A forest is a set of n>=0 disjoint trees.
⮚ The concept of a forest is very close to that of a
tree because if we remove the root of a tree, we
obtain a forest.
⮚ For example, removing the root of any binary tree
produces a forest of two trees.

3. THREE-TREE FOREST

4. TRANSFORMING A FOREST INTO A
BINARY TREE
⮚ To transform a forest into a single binary tree, we
first obtain the binary tree representation of each
of the trees in the forest and then link these binary
trees together through the rightChild field of the
root nodes.

5. BINARY TREE REPRESENTATION OF
FOREST

6. We can define this transformation in a formal
way as follows:
⮚ Definition: If T1 , . . . , Tn is a forest of trees, then the
binary tree corresponding to this forest, denoted by B(T1
, . . . , Tn),
⮚ 1. is empty if n=0
⮚ 2, has root equal to root (T1); has left subtree equal to
B(T11 , T12, . . . , T1m), where T11, . . . , T1m are the
subtrees of root(T1); and has right subtree B(T2 , . . . ,
Tn).

7. FOREST TRAVERSALS
⮚ Preorder and inorder traversals of the
corresponding binary tree T of a forest F have a
natural correspondence to traversals on F.

8. ⮚ Preorder Traversal
⮚ Preorder traversal of T is equivalent to visiting
the nodes of F in forest preorder, which is defined
as follows:
1. If F is empty then return.
2. Visit the root of the first tree of F.
3. Traverse the subtrees of the first tree in forest
preorder
4. Traverse the remaining trees of F in forest
preorder.

9. InOrder Traversal
InOrder Traversal of T is equivalent to visiting the
nodes of F in forest inorder, which is defined as
follows:
1. If F is empty then return
2. Traverse the subtrees of the first tree in forest
inorder
3. Visit the root of the first tree
4. Traverse the remaining trees in forest inorder

10. Postorder Traversal
We can define the postorder traversal of a forest as
follows:
1. If F is empty then return
2. Traverse the subtrees of the first tree of F in
forest postorder.
3. Traverse the remaining trees of F in forest
postorder.
4. Visit the root of the first tree of F.