ducmod said:Homework Statement
Hello!
Typical binary search tree has a number of nodes equal to 2^(n+1) - 1.
I don't understand why we add 1 to the n?
For example: a tree has a height 4.
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# # # #
# # # # # # # #
each level has 2^i nodes; i = 0, 2^0 = 1 for the first row, etc.
If the height is 4 then total amount of nodes is 15, which is 2^4 - 1,
and not 2^(4+1) - 1.
I would be grateful for your help!
I see now. Thank you!Ray Vickson said:The formula works perfectly well if you regard the depth as n=3, rather than n=4. Four is the number of nodes in a path from root to tip, but three is the number of "steps". It is the same as saying that your first year of life has two endpoints, t = 0 and t = 1, but it is still just one year.
The number of nodes in a binary search tree can be calculated using the formula N = 2^(h+1) - 1, where N is the number of nodes and h is the height of the tree.
The number of nodes in a binary search tree is important because it gives us an idea of the size and complexity of the tree. It also helps us determine the efficiency of operations such as searching and inserting in the tree.
No, the number of nodes in a binary search tree can vary depending on the structure of the tree. However, for a given height h, the number of nodes will always be the same.
Yes, the number of nodes in a binary search tree can impact its performance. A larger number of nodes can result in slower search and insert operations, while a smaller number of nodes can lead to a more efficient tree.
No, the number of nodes in a binary search tree cannot be negative as it represents the actual number of nodes present in the tree. If the tree is empty, the number of nodes would be zero.