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?
**MCQ
Show answer & explanation
In a complete binary tree with level-order numbering (1 as root), for any node n: parent = floor(n/2), left child = 2n, right child = 2n+1. For node 17: parent = floor(17/2) = 8, left child = 2×17 = 34, right child = 2×17+1 = 35. All three children exist within the 50-node constraint.
Step-by-step Derivation:
Using the standard binary tree indexing formulas for a complete binary tree stored in array form:
Parent of node 17:
parent = ⌊17/2⌋ = ⌊8.5⌋ = 8 ✓Left Child of node 17:
left_child = 2 × 17 = 34 ✓
(34 ≤ 50, so it exists)Right Child of node 17:
right_child = 2 × 17 + 1 = 35 ✓
(35 ≤ 50, so it exists)
Tree structure visualization (partial):
1 (root)
/ \
2 3
/ \ / \
4 5 6 7
...
8
/ \
16 17 ← node in question
/| /|
32 33 34 35
Node 17 has parent 8, left child 34, and right child 35.