Traversing a tree involves iterating over all nodes in some manner.
Because from a given node there is more than one possible next node (it is not a linear data structure), then, assuming sequential computation (not parallel), some nodes must be deferred—stored in some way for later visiting.
This is often done via a stack (LIFO) or queue (FIFO).
As a tree is a self-referential (recursively defined) data structure, traversal can be defined by recursion or, more subtly, corecursion, in a very natural and clear fashion;
in these cases the deferred nodes are stored implicitly in the call stack.
Depth-first search is easily implemented via a stack, including recursively (via the call stack), while breadth-first search is easily implemented via a queue, including corecursively.
Inorder Traversal (Practice):
Algorithm Inorder(tree)
1. Traverse the left subtree, i.e., call Inorder(left-subtree)
2. Visit the root.
3. Traverse the right subtree, i.e., call Inorder(right-subtree)
Preorder Traversal (Practice):
Algorithm Preorder(tree)
1. Visit the root.
2. Traverse the left subtree, i.e., call Preorder(left-subtree)
3. Traverse the right subtree, i.e., call Preorder(right-subtree)
Postorder Traversal (Practice):
Algorithm Postorder(tree)
1. Traverse the left subtree, i.e., call Postorder(left-subtree)
2. Traverse the right subtree, i.e., call Postorder(right-subtree)
3. Visit the root.
class Node:
def __init__(self,key):
self.left = None
self.right = None
self.val = key
# A function to do inorder tree traversal
def printInorder(root):
if root:
# First recur on left child
printInorder(root.left)
# then print the data of node
print(root.val),
# now recur on right child
printInorder(root.right)
# A function to do postorder tree traversal
def printPostorder(root):
if root:
# First recur on left child
printPostorder(root.left)
# the recur on right child
printPostorder(root.right)
# now print the data of node
print(root.val),
# A function to do preorder tree traversal
def printPreorder(root):
if root:
# First print the data of node
print(root.val),
# Then recur on left child
printPreorder(root.left)
# Finally recur on right child
printPreorder(root.right)
Preorder traversal of binary tree is
1 2 4 5 3
Inorder traversal of binary tree is
4 2 5 1 3
Postorder traversal of binary tree is
4 5 2 3 1
