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LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110)<br />
Some of the properties of binary tree :<br />
A binary tree with ‘n’ elements n>0,Has exactlyn‐1 edges.<br />
A binary tree of height ‘h’,h>0,has atleast h and atmost 2*..2 ‐1<br />
elements in it.<br />
The height of the binary tree that contains n elements ,n>0,is atmost n &<br />
atleast [log8..2(n+1)].<br />
Let i,1n, then this element has no left child. Otherwise,its left child has been<br />
assigned the number 2i.<br />
If 2i+1>n, then this element has no right child.Otherwise,its right child has been<br />
assigned the number 2i+<strong>1.</strong><br />
The number of nodes n in a perfect binary tree can be found <strong>using</strong> this formula:<br />
n = 2 h + 1 − 1 where ‘h’ is the height of the tree.<br />
The number of nodes n in a complete binary tree is minimum: n = 2 h and<br />
maximum: n = 2 h + 1 − 1 where h is the height of the tree.<br />
The number of nodes n in a perfect binary tree can also be found <strong>using</strong> this<br />
formula: n = 2L − 1 where L is the number of leaf nodes in the tree.<br />
The number of leaf nodes n in a perfect binary tree can be found <strong>using</strong> this<br />
formula: n = 2 h where h is the height of the tree.<br />
he number of NULL links in a Complete Binary Tree of n‐node is (n+1).<br />
The number of leaf node in a Complete Binary Tree of n‐node is UpperBound(n /<br />
2).<br />
Prepared By :<br />
Er. Harvinder Singh<br />
Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 178 ‐
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