GATE 2018 CS – Question 56
The number of possible min-heaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is ________.
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Correct answer: 80
Explanation
Count heap orderings of the complete binary tree with 7 nodes: $N(7)=\binom{6}{3}N(3)N(3)=20\times2\times2=80$, since $N(3)=2$ and the root is fixed to be 1.