<<< Binary Tree

1. Properties of Binary Tree: e.g. 

1. Three parts partitioned: e.g.

1. Root

2. Left subtree

3. Right subtree 

2. Node degree: 0/1/2

3. height 'h', Max nodes number: (2^(h+1)) - 1

4. level 'l', Max nodes number: (2^l)-1

5. depth 'd', Max nodes number: (2^d) - 1

6. n2, Terminal nodes number: n2 + 1

2. Level vs Node relation: e.g. 

1. if level 'l' = 3, then nodes = (2^l)-1 = (2^3)-1 = 7

as nodes, n = (2^l)-1

=> log2 (n) = log2((2^l)-1)

  =>  log2 (n + 1) = log2(2^l)

  =>  log2 (n + 1) = l log2(2)

  =>  log2 (n + 1) = l

  =>  l = ceil (log2 (n + 1))

as, n = 7,

now,   l = ceil (log2 (7 + 1)) 

3. Binary Tree Traversing methods: e.g. 

1. Three parts contain: e.g.

1. V - root

2. L - Left subtree

3. R - Right subtree 

2. Ordering

1. Pre-order: (V, L, R)   e.g.   6  3  1  2  4  9  8  11

2. In-order: (L, V, R)   e.g.  1  2  3  4  6  8  9  11

3. Post-order: (L, R, V)   e.g.  2  1  4  3  8  11  9  6

#Programming #Algorithm #CodeAnalysis #BinaryTree #AbdurRahimRatulAliKhan

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