Question

a)
i) Maximum number of nodes of symmetric binary tree with depth of 7 is ---
15
a) 125
b) 127 c) 128
d) 124
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Answer 1

Answer:

Level of a node is distance from root to that node. For example, level of root is 1 and levels of left and right children of root is 2. The maximum number of nodes on level i of a binary tree is : if level is 3 then there will be maximum 7 nodes in the binary tree.

and the answer is 127

Answer 2

A level number is assigned to each node in a tree. The level number of the tree's root R is usually zero, and every subsequent node is given a level number that is one higher than the level number of its parent. It is the distance from the root.

Depth of a binary tree: The greatest level of any node in the tree is defined as the depth of a binary tree.

The binary tree's depth is equal to 1+ the highest level number.

A symmetric binary tree with depth n has a maximum of $2^{n}$ -1 nodes.

∴ Given that, depth = n =7

∴ Maximum number of nodes = $2^{n}$ - 1

∴ Maximum number of nodes = $2^{7}$ - 1

∴ Maximum number of nodes = 128 - 1

∴ Maximum number of nodes = 127

∴ (b) 127