Given a modified binary search tree, find k'th smallest element

Question

Suppose in a given binary tree if each node contains number of child elements, then what is the optimal way to find k'th smallest element in the tree ?

Please note this is not regular BST. Each node is containing number of child element under it.

Absolutely not a homework. @Skizz, I would like to show you my office badge for once. :) — Ajeet Ganga, Sep 06 '11 at 13:07

Simone · Accepted Answer · 2011-09-06T13:24:39.980

4

find_element(root, k)

    if(root.left.nchildren + 1 == k - 1) 
        return root;

    if(root.left.nchildren + 1 >= k)
        return find_element(root.left, k)             

    else 
        return find_element(root.right, k - (root.left.children + 1))

edited Sep 06 '11 at 13:24

answered Sep 06 '11 at 13:04

Simone

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@ajeet, Simone: `each node contains number of child elements`. this includes the right subtree. if you are looking for the nth element in a full binary tree with n elements, this algorithm will wrongly return the root. – amit Sep 06 '11 at 13:20
@amit, Observe that Simone is counting left.nchildren not root.nchildren. And Simone is counting K starting from 0. Considering that his algo will return right result. – Ajeet Ganga Sep 06 '11 at 16:11
@ajeet: Simone edited the answer after I made the comment, and this issue was indeed solved by counting the left son size instead the root size. My comment is not relevant anymore – amit Sep 06 '11 at 17:05
@amit : Got it amit. :) Also in that case, the answer I had posted within the gap of 30second was indeed the correct one. – Ajeet Ganga Sep 07 '11 at 21:14

score 0 · Answer 2 · edited May 23 '17 at 12:08

0

Traverse BST in InOrder traverse manner and store elements to array. Your array is a sorted array.

edited May 23 '17 at 12:08

Community

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answered May 22 '13 at 19:15

Cannon

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Ajeet Ganga · Answer 3 · 2015-11-24T07:39:19.680

0

This is what I got:

find (root, k)
{
leftChildCount = root->left->n
rightChildCount = root->right->n

if (leftChildCount+1 == k)
  Print root node
else if (k< leftChildCount)
  Find(root->left,k)
else
  Find(root->right,k-leftChildCount)
}

edited Nov 24 '15 at 07:39

answered Sep 06 '11 at 13:05

Ajeet Ganga

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Given a modified binary search tree, find k'th smallest element

3 Answers3