11
In the worst case a binary search tree is linear and has a height equal to the number of nodes. so h=O(h).
largest possible number is (2^2k) - 1 nodes when every other node down to the path is red and it is complete binary tree with height 2k. smallest is (2^k) - 1 nodes
It's a set of nodes, together with edges that have directions associated with them.
Figrin D'an and the Modal Nodes.
In project management, particularly in network diagrams, "activity on node" (AON) and "activity on arrow" (AOA) represent different methods for illustrating project tasks. In AON, nodes represent activities, and the arrows indicate the relationships or dependencies between them, allowing for easier identification of slack time directly related to each activity. Conversely, in AOA, the arrows represent activities, and nodes represent events, which can complicate the identification of slack as it is associated with the events rather than the individual activities. As a result, slack management can be more straightforward in AON compared to AOA.
h+1
Minimum is h nodes (Maximum is 2h+1 - 1 nodes, if tree consisting of only one node is considered to have height of 0. if you consider a tree with one node to be a height of one, then the minimum nodes is (2^(h-1)) 1 nodes. Minimum number of nodes in a binary tree of height is 2h+1. For example, if the height of the binary tree is 3, minimum number of nodes is 2*3+1=7.
The maximum height of a binary tree with 'n' nodes is 'n-1'.
if u assign a 0th level to root of binary tree then,the minimum no. of nodes for depth K is k+1.
The height of a complete binary tree is in terms of log(n) where n is the number of nodes in the tree. The height of a complete binary tree is the maximum number of edges from the root to a leaf, and in a complete binary tree, the number of leaf nodes is equal to the number of internal nodes plus 1. Since the number of leaf nodes in a complete binary tree is equal to 2^h where h is the height of the tree, we can use log2 to find the height of a complete binary tree in terms of the number of nodes.
3
In a binary tree, each level can have a maximum of (2^n) nodes, where (n) is the level number starting from 0. For a binary tree with 3 levels (0, 1, 2), the minimum number of nodes occurs when each level has at least one node. Therefore, the minimum number of nodes is 1 (at level 0) + 1 (at level 1) + 1 (at level 2) = 3 nodes.
For the height `h' of a binary tree, for which no further attributes are given than the number `n' of nodes, holds:ceil( ld n)
For a full binary tree of height 3 there are 4 leaf nodes. E.g., 1 root, 2 children and 4 grandchildren.
8
In a binary tree with a maximum depth of ( H ), the number of leaf nodes can vary depending on the structure of the tree. However, if the tree is a complete binary tree, the maximum number of leaf nodes occurs at depth ( H ), which is ( 2^H ). For a full binary tree, the minimum number of leaf nodes at depth ( H ) is ( 1 ), occurring when all nodes except the last level are filled. Thus, the number of leaf nodes can range from ( 1 ) to ( 2^H ).
The formula to calculate the height of a binary tree is h log2(n1) - 1, where h is the height of the tree and n is the number of nodes in the tree.