The number of nodes in a typical binary search tree (BST) is calculated using the formula 2^(n+1) - 1, where n represents the depth of the tree. In this context, depth refers to the number of edges from the root to the deepest leaf, which is one less than the total number of nodes. For example, a BST with a height of 4 has a depth of 3, resulting in 15 nodes, as calculated by 2^(3+1) - 1. Understanding this distinction between height and depth is crucial for accurately applying the formula.
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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.