**No** this is not a Binary Search Tree,Because right of 14,13 not come, it violate the Property of BST.

1 vote

Consider an empty binary search tree of height $-1.$We need to fill the following sequence of numbers in it $: 11, 12, 13, 14, 15, 16, 17.$The number of ways in which the numbers can be inserted in an empty binary search tree, such that the resulting tree has height $6,$ is _____________

$A)2$ $B)4$ $C)32$ $D)64$

$A)2$ $B)4$ $C)32$ $D)64$

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**No** this is not a Binary Search Tree,Because right of 14,13 not come, it violate the Property of BST.

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I think it will work like this -

Take 1 from 11 or 17 suppose taken 11 then for next level take one from 17 or 12 let say 12 taken then for next 17 or 13,13 or 16 if 17 taken then 14 or 16 then 16 or 15 and lastly if 16 taken then 15...Please comment if I'm going in wrong direction

Take 1 from 11 or 17 suppose taken 11 then for next level take one from 17 or 12 let say 12 taken then for next 17 or 13,13 or 16 if 17 taken then 14 or 16 then 16 or 15 and lastly if 16 taken then 15...Please comment if I'm going in wrong direction

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In Binary Search Tree all Sorted elements in ascending order like $11,12,13,14,15,16,17$ gives always INORDER TRAVERSAL of the BST.

With $7$ nodes Number of unlabeled BST Possible are $429$.To get Inorder so we can assign the number in the all BST and get $429$ BST with In order $11,12,13,14,15,16,17$, But some tree doesn't have a height $6$, So we can subtract these BST and get the answer, but I'm not able to find the BST, which doesn't have height $6.$

can anyone help me?