QUESTION 20 Consider a binary tree T with 50 nodes as: 1, 2, 3, 4, ....., 26, ....., 50 If...
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QUESTION 20
Consider a binary tree T with 50 nodes as:
1, 2, 3, 4, ....., 26, ....., 50
If the above values are the nodes of an almost complete binary tree where 1 is the root node, 2 is its left child and 3 is its right child so on, then what is the Parent node, Left Child of node 17?
Show answer & explanation
In a complete binary tree with level-order numbering, for any node n: parent = ⌊n/2⌋, left child = 2n, right child = 2n+1. For node 17: parent = ⌊17/2⌋ = 8, left child = 2×17 = 34, right child = 2×17+1 = 35. All three values are ≤ 50, so all nodes exist.
Step-by-step Derivation:
Using binary tree indexing formulas for a complete binary tree stored in array/level-order form:
Parent of node 17:
parent(n) = ⌊n/2⌋ = ⌊17/2⌋ = ⌊8.5⌋ = 8Left child of node 17:
left_child(n) = 2n = 2×17 = 34
Check: 34 ≤ 50 ✓ (exists)Right child of node 17:
right_child(n) = 2n+1 = 2×17+1 = 35
Check: 35 ≤ 50 ✓ (exists)
Answer: Parent = 8, Left Child = 34, Right Child = 35