Question: In a complete binary tree, what is the maximum number of nodes at level \'h\'?
Options:
2^h
2^(h+1) - 1
h^2
h!
Correct Answer: 2^h
Solution:
In a complete binary tree, the maximum number of nodes at level \'h\' is 2^h.
In a complete binary tree, what is the maximum number of nodes at level 'h'?
Practice Questions
Q1
In a complete binary tree, what is the maximum number of nodes at level 'h'?
2^h
2^(h+1) - 1
h^2
h!
Questions & Step-by-Step Solutions
In a complete binary tree, what is the maximum number of nodes at level 'h'?
Step 1: Understand what a complete binary tree is. A complete binary tree is a type of binary tree where every level, except possibly the last, is fully filled.
Step 2: Identify what 'level h' means. The levels in a tree start counting from 0. So, level 0 is the root, level 1 is the next level down, and so on.
Step 3: Recognize that at each level in a binary tree, the number of nodes can double compared to the previous level. For example, level 0 has 1 node, level 1 has 2 nodes, level 2 has 4 nodes, and so forth.
Step 4: Realize that the pattern for the number of nodes at level h is 2 raised to the power of h. This means if you want to find the maximum number of nodes at level h, you calculate 2^h.
Step 5: Conclude that the maximum number of nodes at level h in a complete binary tree is given by the formula 2^h.
Complete Binary Tree – A complete binary tree is a type of binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible.
Levels in a Tree – In a binary tree, the level of a node is defined by the number of edges on the path from the root node to the node.
Node Count Formula – The maximum number of nodes at any level 'h' in a complete binary tree is given by the formula 2^h.
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