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# DS-Trees -Q11

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+1 vote
Consider an array  which contains 9 distinct positive integers in some order.  Total number of ordering possible with those 9 elements  such that  array   represents a max heap  is ________.?
reshown Jul 20, 2020

Maximum element will be the first element in all such orderings.

Remaining 8 elements will be placed such that 3 elements will be in right subtree and 5 elements will be in left subtree.

So, for right subtree, select 3 elements from 8 elements and then we can place those 3 elements in the right subtree in 2 ways.

Similarly remaining 5 elements can be put in 4C1*2 ways in the left subtree.

So, total orderings possible = 8C3 * 2 * 4C1 * 2 = 896
answered Jul 24, 2020 by (226,240 points)
can you elaborate for the left subtree. why 4C1*2 ways...
in it, root will be fixed to the largest element, then how do you arrange the remaining 4 elements
In remaining 4 elements, One will go in the RST(right sub tree) , so, for that 4C1. And remaining 3 will go to LST, for that 2 ways.
sir entire result is multiply with 2 because i will take first 5 elments in right and 3 elements in left as you have take 5 in left and right in 3 it is 2 ways is it correct or  not