Questions tagged [binary-search-trees]

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15 views

When can a (max) heap be a BST?

Cheers, let's suppose we have a MAX heap which does not allow duplicate elements. Is it possible for this heap to be a BST ? Choose the right answer(s) below: A heap can never be a BST A heap is ...
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1answer
13 views

Find two nodes in a BST such that the root's key is the average of their keys without extra space in $\theta(n)$ worst case time

We can do this in $\theta(n^2)$ time if we calculate the average of all couples of nodes in the tree and compare it to the root, but this is too much time. We can do this in linear time but with extra ...
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33 views

Calculating the expected height of a randomly built binary search tree

I need to calculate the expected height of a randomly built binary search tree, BST, with 4 different keys: $x < y < z < w$ According to Catalan numbers, there are 14 possible trees, 8 with ...
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34 views

Finding 2 nodes which sum equals twice their common ancestor in RBT in $\Theta(n\lg n)$

I have a red black tree, $T$, and I need to write an algorithm to find 2 nodes $x$ and $y$ so that $key[x] + key[y] = 2 \cdot key[p(x, y)]$, where $p(x, y)$ is the lowest common ancestor of $x$ and $y$...
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1answer
42 views

Splay Tree, repeatedly searching for the same key that´s not in the Tree

In a Splay Tree, doing $m$ sequential search operations for the same key that is in the tree has a time complexity in $O(n+m)$ where n is the number of nodes in the Tree. Since the first search has a ...
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18 views

BST deletion of node with 2 children by copying right child to predecessor

I try to delete a node, $z$, with 2 children in binary search tree by exchanging $z$'s right child and $z$'s predecessor, $y$, right child, which is NULL because $y$ has no right child, if it had then ...
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69 views

Suggest a Data Structure that support the following operations with time complexity O(log(n))

I’m looking for a data structure that supports that store the salaries of it’s employees. Insert(e) – Insert employee e into the data structure. AvgDecile(k) – Returns the average salary of the k’th ...
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39 views

Average depth BST upper bound

I have a question regarding the BST average depth upper bound. Following the proof from Data Strucutures and Algorithms in Java by Weiss (3rd edition), I was wondering if there was some kind of ...
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1answer
23 views

For a balanced binary search tree what is the worst case case time complexity for accessing all elements within a range of nodes?

I have this question which is asking for the worst case time complexity for a balanced binary search tree, assume the nodes are labeled as integers and we consider a range of ...
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1answer
23 views

Converting Binary Search Tree into Decreasing Ordered Linked List

Given a BST with n nodes, the algorithm should create a linked list that contains a decreasing order sorted array. The algorithm should have a worst case time complexity O(n). The signature of the ...
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1answer
50 views

If a key in a red-black tree has exactly one child (which isn't null) then it is always red

I have the following claim: Prove or disprove: If a key in a red-black tree has exactly one child (which isn't null) then it is always red. My attempt: Disproof. We will exhibit a counterexample: ...
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Are there any trees where Preorder$(T_1) =$ Preorder$(T_2)$ and Inorder $(T_1) = $Inorder $(T_2)$, but $T_1 \neq T_2$?

Is it possible for two binary trees $T_1 \neq T_2$ that both Preorder and Inorder traversal are equal ?
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1answer
104 views

Prove a statement about searching in binary search tree

Suppose search $n$ times in a given binary search tree $T$ with $n$ nodes. each searching have cost $C_i$, and $\sum_{i=1}^{n}C_i=O(n\log n)$. Now the problem is to find height of $T$. I think it be $...
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43 views

Finding height of binary search tree

Suppose given a binary search tree $T$ with $n$ nodes with depth $h$. We did $n$ times search with cost $c_i$ for search $i^{th}$ search on $T$ ,and $\sum_{i=1}^{n}c_i=O(n\log n)$. what we can say ...
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46 views

Check two balanced binary search trees that sub set of each other

Given two balanced binary search trees $T_1,T_2$. We want to check, are $T_1\subseteq T_1$ or not. $T_1$ have $n_1$ nodes, and $T_2$ have $n_2$ nodes. Instructor say it can be done in $O(n_1+n_2)$ ...
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56 views

Cormen problem 13-1 part d

I am going through problem 13-1 in CLRS 3rd edition. I came up with the following algorithm as a solution: ...
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108 views

prove correctness of in-order tree traversal subroutine

I'm trying to prove that in-order tree traversal prints the keys in sorted order. it's shown here, but what I want is to prove correctness using ordinary induction. Claim: For any n-node subtree, ...
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2answers
351 views

is it possible to create an avl tree given any set of numbers?

I am studying balanced trees, especially AVL trees. My question is whether is it possible to create an avl tree given any set of numbers. is it possible to prove the following statement? Let $A$ be ...
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1answer
328 views

Find amount of elements greater then number k in a BST

I am trying to find an Algorithm to find the amount of elements in a BST which are greater than a certain number K. I found it problematic as there are elements which might be greater then K but wont ...
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22 views

Probability that BST has exact height

Consider keys $[ 1 \ldots n]$. We want to calculate probability that BST tree has height = $h$. (We assume that distribution is uniform over all $C_{n}$ trees, where $C_n$ - n-th Catalan number). ...
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1answer
456 views

What exactly is the difference between a Balanced Binary Search Tree and an AVL tree?

I'm learning some Data Structures and I cannot figure out the difference between the Balanced BST and the AVL Tree. From my understanding, an AVL tree is a balanced tree with the height difference <...
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1answer
166 views

Recurrence formula for optimal binary search tree

This question is from Section 15.5 of Introduction to Algorithms (third edition). We are given sequence of keys, $ k = \{ k_{1},k_{2},\dots,k_{n} \}$, where $k_{1}<k_{2} <\dots<k_{n} $. For ...
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62 views

Understanding the Transition points of a BST

I'm trying to understand the definition of Transition point of a BST, as given in Demaine, Erik D., et al. "Dynamic optimality-almost." SIAM Journal on Computing 37.1 (2007): 240-251 ...
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1answer
38 views

What factors of the integer dataset being sorted can I change, in order to compare two sorting algorithms?

I am comparing two comparison and binary data structure based sorting algorithms, the Tree Sort, and the Heap Sort. I am measuring the time taken for both algorithms to sort an increasing size of an ...
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0answers
26 views

Splay tree amortized analysis cost using Access Lemma

Currently studying for an algorithms exam and I came across this question and solution, but I can't understand the solution where it references nodes of depth less than $4\log n$ and not restructuring....
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2answers
38 views

Call stack is hard to maintain in my brain. What should I?

When I study Binary Search Tree, I try to use a pencil and paper to scratch the process of in-order traversal. However, I find that it is hard to maintain the call stack in my brain without paper and ...
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1answer
15 views

Maintaining balanced BSTs in order to get $\frac{n}{2}$ largest elements in constant time

I wonder what is the best data structure I can use in order to achieve the following: Given a data structure based on a balanced BST, I would like to get a tree with the $\lfloor\frac{n}{2}\rfloor$ ...
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1answer
46 views

How many different (full/complete) in-order binary-trees do exist?

Given be a binary tree whose elements printed in-order results in [1,2,3,4]. Q1: How many different binary-trees do exist? Q2: How many different complete binary-...
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14 views

Parent Node in BST

Is it a good idea to store a pointer to the parent node in a binary search rather than to find the parent node several times? ...
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263 views

Remove range of keys from Binary Search Tree in O(s+h)

I have a binary search tree with integer keys. I have to remove a range (m, n]eZ of keys from the BST in O(s + h) where s is the number of keys to remove and h is the height of the tree. Attempted ...
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543 views

Algorithm to delete BST nodes with duplicated values

In a binary search tree the following must hold: Greater keys are in the right-subtree Smaller or EQUAL keys belong to the left-subtree All the algorithms I found to delete a node start by finding ...
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1answer
790 views

How to find time complexity of this pseudocode

Recently, I came across a question about finding sum of all values in range $[low, high]$ in BST $T$. Then I formulated following algorithm to carry out that task: We do inorder traversal of ...
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2answers
45 views

Inorder tree tranversal on binary search tree doesn't give the elements in order?

I have been told that inorder tree tranversal of binary search trees returns the tree elements in order. I came up with this binary search tree: ...
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Reasoning for awkward style of TreeMap.getHigherEntry

Consider a binary search tree (AVL, red-black, whatever). The goal "find the least key strictly greater than the specified one" ("upper_bound" in C++ STL, higherEntry//higherKey in Java, etc.) can be ...
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1answer
498 views

Constructing preorder traversal from postorder of a Binary Search Tree in O(n)

We are given postorder traversal of a Binary "SEARCH" Tree (in an array) and we want to find (print) its preorder traversal. A very naive solution is to check from end until we find element less than ...
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1answer
45 views

question about the construction of BSTs using a repeated sequence of rotations

How can I show that any binary search tree can be balanced with at most O(n log n) rotations (“balanced” here means that the lengths of any two paths from root to leaf differ by at most 1).
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50 views

How to construct a perfect BST from an unbalanced BST with n elements (assuming that n=(2^i)-1, i is natural)

How do I construct a perfect BST from an unbalanced BST with $n$ elements (assuming that $n=2^i-1$, $i$ is natural). ** At the worst case of $O(n)$**.
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1answer
112 views

Height of epsilon-balanced binary search tree

In Balanced Binary Search Trees on the basis of size of left and right child subtrees, Hannes says: For example, one can say, a BST is balanced, if each subtree has at most epsilon * n nodes, ...
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426 views

Leaf nodes of B+ Tree

I have a b+ tree and i want to find the record associated with a specific key Ki. So i run the b+ tree search algorithm. If a certain node in the search path is a leaf and K=Ki, then the record exists ...
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61 views

creating a binary search tree (manual)

I've been given the following values to add to a binary search tree (in the order given) 56, 35, 55, 58, 29, 15, 16, 5, 71, 92, 69, 95 and this is what my tree ended up like: but apparently it's ...
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post order for binary search tree

I got this as the post order sequence but the answer says it is wrong. I do get a bit confused with the post order logic as well. 8 11 10 9 13 16 18 15
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1answer
37 views

in order of binary search tree

This is what I got for the in-order of the bst but it's wrong because I'm answering some questions about some successors of some of the letters and I got them wrong. so I'm wondering where in this in-...
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1answer
1k views

How is the right, root, left order traversal called in a binary search tree?

In a Binary Search Tree you have the following orders for traversal: Left, Root, Right is called Inorder (or ascending order). Root, Left, Right is called Preorder. Left, Right, Root is called ...
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3k views

Time complexity for balancing an unbalanced binary tree

The question here is that: There is an unbalanced binary tree with n-nodes. What is the time complexity to balance the tree? The solution I thought of involved solving using Recursion where for the ...
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1answer
131 views

Is the tree shown a valid red-black tree?

I have made a red-black tree and I think that it is not valid. Could someone please verify? As far as I know, in red-black tree we also consider the leaf nodes at the NULLS of the visible leaf nodes ...
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35 views

RB trees from any balanced BST?

Given any perfectly balanced binary search tree, is it always possible to assign a coloring to the nodes so that it becomes a Red-Black tree? If so, how do you prove this, and if false, what would be ...
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1answer
41 views

AVL tree balance property states for the two subtrees of a node, their height can differ at most one. Why can't it be zero?

I was thinking that if they were equal, say they are required to be zero this would be enforce the balance property more effectively. Can anyone explain why 1 is a satisfactory rather than just them ...
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3answers
2k views

Why is Binary Heap never unbalanced?

My professor asks this question: Binary Search tree has Rotation Method to prevent it from degenerating into a linear structure (unbalanced tree). Why is there no need for such method for Binary Heaps?...
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1answer
79 views

Which binary search trees have constant time rebalancing time at min/max?

Given that I'm already at either the min or the max node of a binary search tree, which balanced variant would require only constant time bottom-up rebalancing after an update (add new min/max, or ...
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43 views

Finding Binary Search Tree Height, What happens to duplicates?

I'm going over past exam papers with this question: The answer to a). will be (height of 5): For b.): I assume the height function will be to find the height of the tree. So, I will have to compare ...