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LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110)<br />
The minimum and maximum height of a binary tree can be related to the<br />
number of nodes. Hmin = [log2 N] + 1<br />
H max = N<br />
Given the height of a binary tree, the minimum and maximum number of nodes<br />
in the tree can be calculated as Nmin = H; Nmax = 2 H ‐ 1<br />
A null tree is a tree with no nodes. The nodes at level 2 of a tree can all be<br />
accessed by following only two branches from the root. It stands to reason ,<br />
that the shorter we can make the tree, the easier it is to locate the desired node<br />
in the tree.<br />
This leads us to a very important characteristic of a binary tree, its balance. To<br />
determine if a tree is balanced, we calculate its balance factor. The balance<br />
factor of a binary tree is the difference in height between its left and right<br />
subtrees.<br />
B= Hleft – Hright<br />
A tree is balanced if its balance factor is zero and its subtrees are also balanced.<br />
A binary tree is balanced if the height of its subtrees differs by no more than<br />
one (its balanced factor is –1,0, or +1) and its subtrees are also balanced.<br />
A binary tree traversal requires that each node of the tree be processed once<br />
and only once in a predetermined sequence. There are two general approaches<br />
to the depth first and breadth first.<br />
The depth first traversal, the processing proceeds along a path from the root<br />
through one child to the most distant descendent of that first child before<br />
processing a second child. All of the descendents of a child are processed<br />
before the next child.<br />
Prepared By :<br />
Er. Harvinder Singh<br />
Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 181 ‐
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