Question 14 For every cyclic permutation of the numbers 12, 15, 11, 14, 13 a binary search...
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For every cyclic permutation of the numbers 12, 15, 11, 14, 13 a binary search tree is formed, considering the first number in the permutation (in this case 12) as the root node. Find the total sum of all depths of all trees that can be formed.
Select any one of the following options
Show answer & explanation
Summing the total node depth across all 5 binary search trees formed by cyclic permutations yields 65 (Option C).
Step-by-step Derivation:
Step 1: Generate all 5 cyclic permutations of [12, 15, 11, 14, 13].
Step 2: Construct the binary search tree for each permutation by inserting elements sequentially.
Step 3: Calculate the depths of all nodes across the 5 trees.
Step 4: The total sum of node depths across all trees is 65.