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null(nil) = true // nil refer for empty tree
null(fork(e, T, T'))= false // e : element , T and T are two sub tree leaf(fork(e, nil, nil)) = true
leaf(fork(e, T, T')) = false if not null(T) or not null(T')
leaf(nil) = error
left(fork(e, T, T')) = T
left(nil) = error
right(fork(e, T, T')) = T' right(nil) = error
Contents (fork (e, T, T')) = e contents (nil) = error
Consider the definition of Tree (ADT). A way to think of a binary tree is that this is either empty (nil) or have an element and two sub trees that are themselves binary trees. Fork operation joins two sub trees along a parent node and generates another Binary tree. It might be noted that a tree containing a single leaf is described to be of height 1.
Definition: A tree is connected, acyclic graph
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Q. Draw a B-tree of order 3 for the sequence of keys written below: 2, 4, 9, 8, 7, 6, 3, 1, 5, 10
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Q. Prove the hypothesis that "A tree having 'm' nodes has exactly (m-1) branches". Ans: A tree having m number of nodes has exactly (m-1) branches Proof: A root
explanation with algorithm
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