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GATE | GATE-CS-2016 (Set 2) | Question 50

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The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary search tree, such that the resulting tree has height 6, is _____________ Note: The height of a tree with a single node is 0. [This question was originally a Fill-in-the-Blanks question] (A) 2 (B) 4 (C) 64 (D) 32

Answer: (C)

Explanation: To get height 6, we need to put either 1 or 7 at root. So count can be written as T(n) = 2*T(n-1) with T(1) = 1

    7
   / 
 [1..6]  

    1
      \
     [2..7] 
Therefore count is 26 = 64 Another Explanation: Consider these cases, 1 2 3 4 5 6 7 1 2 3 4 5 7 6 1 7 6 5 4 3 2 1 7 6 5 4 2 3 7 6 5 4 3 2 1 7 6 5 4 3 1 2 7 1 2 3 4 5 6 7 1 2 3 4 6 5 For height 6, we have 2 choices. Either we select the root as 1 or 7. Suppose we select 7. Now, we have 6 nodes and remaining height = 5. So, now we have 2 ways to select root for this sub-tree also. Now, we keep on repeating the same procedure till remaining height = 1 For this last case also, we have 2 ways. Therefore, total number of ways = 26= 64

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Last Updated : 28 Jun, 2021
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