CS2201 DATA STRUCTURES LECTURE NOTES PDF

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One natural way to define a tree is recursively. A tree is a collection of nodes. The collection can be empty, which is sometimes denoted as A. Otherwise, a tree consists of a distinguished node r, called the root, and zero or more sub trees T1, T2,. Figure 4. From the recursive definition, we find that a tree is a collection of n nodes, one of which is the root, and n - 1 edges. That there are n - 1 edges follows from the fact that each edge connects some node to its parent and every node except the root has one parent.

Each node may children, possibly zero. Nodes with no the leaves in the tree above are B, C, A. For any node ni. For the tree in Figure 4. The length of this path is the number of edges on the path. Nodes with the same parent are siblings. E is at depth 1 and height 2. Thus all leaves are at height 0. The height of ni is the longest path from ni to a leaf.

F is at depth 1 and height 1. If there is a path from n1 to n2. There is a path of length zero from every node to itself. The depth of a tree is equal to the depth of the deepest leaf. Grandparent and grandchild relations can be defined in a similar manner. Notice that in a tree there is exactly one path from the root to each node. Tree traversal is a method for visiting all the nodes in the tree exactly once. Inorder Traversal -traverse the left subtree inorder -visit the root -traverse the right subtree in inorder.

Preorder traversal -visit the root. The declaration in Figure is typical. The solution is simple: Keep the children of each node in a linked list of tree nodes. Figure shows that a binary tree consists of a root and two subtrees. Tl and Tr. A property of a binary tree that is sometimes important is that the depth of an average binary tree is considerably smaller than n.

One of the principal uses of binary trees is in the area of compiler design. Many of the rules that apply to linked lists will apply to trees as well. Binary trees have many important uses not associated with searching. Nodes can be freed after deletion by calling free. In particular. We also do not explicitly draw NULL pointers when referring to trees.

We could draw the binary trees using the rectangular boxes that are customary for linked lists. Constructing an Expression Tree As an example.

This particular tree happens to be binary. We can evaluate an expression tree. It is also possible for a node to have only one child. Some programmers prefer to initialize the first element as a one-node tree. Sets and Maps and other associative containers. Trees and Board Games — Trees are often used in implementinggames.

It is also possible to discover the parent of a node from a threaded binary tree. To see how this is possible. Then the left pointer of r must be either a child or a thread back to k. In the case that r has a left child. So by following the chain of left pointers from r. A threaded tree. This can be useful where stack space is limited. Report "Cs Unit2 Notes" Please fill this form, we will try to respond as soon as possible.

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Cs2201 Unit2 Notes

One natural way to define a tree is recursively. A tree is a collection of nodes. The collection can be empty, which is sometimes denoted as A. Otherwise, a tree consists of a distinguished node r, called the root, and zero or more sub trees T1, T2,.

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Do not merge trees as srtuctures as possible Structure:. Cs data structures lecture notes pdf. Your email address will not be published. Construct a Ntoes and MAX heap for the following values.

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