Questions tagged [binary-search-trees]

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28 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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1answer
103 views

Binary Tree Node Insertion

I was trying to implement a Binary Search Tree using this article as a reference: Binary Search Tree in JavaScript. I was thinking especially about the node insertion method. Here's my ...
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0answers
9 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
40 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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34 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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1answer
179 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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1answer
14 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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3answers
18k views

What is “rank” in a binary search tree and how can it be useful?

I am having a bit of trouble wrapping my mind around what a ranked binary search tree is and why having a rank is important. I am hoping that someone can clarify a few things for me. What I have ...
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3answers
733 views

Why is the number of comparisons in a BST missing key lookup about 2 ln N?

In (An Introduction to the Analysis of Algorithms) by Philippe Flajolet and Robert Sedgewick it's written that: Insertions and search misses in a BST built from N random keys require ~ 2 ln N (about 1....
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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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1answer
146 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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77 views

Calculate number of nodes in all subtrees without using DFS

Is it possible to calculate the number of nodes using post-traversal order, instead of using DFS? Below is an illustration of the question:
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1answer
657 views

Data structure for handling intervals

I am trying to create a data structure for handling the subsets of the real line of the form $[x,y)$. That is, suppose $X \subseteq \mathbb{R}$ and the data structure supports two types of operations: ...
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0answers
13 views

Data structure for revising ordering given a (largely) ordered stream of data

I have an input stream of timestamped data that is largely sorted in ascending order by timestamp. There are occasionally out-of-order elements, at which point I need to do each of the following: ...
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136 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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0answers
29 views

How many Binary Search Trees are there which have N nodes and their height is log N

How many Binary Search Trees are there which have N nodes and their height is log N ? We need a recursive function to solve this problem. For example if n=2 the answer is 2. If n=3 answer is 1 . If n=...
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1answer
255 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
41 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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0answers
40 views

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
170 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
34 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
35 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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1answer
104 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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2answers
32 views

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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2answers
41 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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2answers
4k views

Which of the following sequences could not be the sequences of nodes examined in a binary search tree?

Suppose that we have numbers between $1$ and $1000$ in a binary search tree and want to search for the number $363$. Which of the following sequences could not be the sequences of nodes examined <...
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2answers
1k 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
334 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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1answer
51 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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0answers
30 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
26 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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1answer
159 views

All the possible inputs for a given AVL tree

Given an AVL tree,what are the possible inputs so that the same given tree is formed(please dont mention brute force technique)?
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712 views

Time complexity of creating the unique binary tree from given inorder and preorder (or postorder) traversal sequences

Given inorder and preorder (or postorder) traversal sequences of a binary tree balanced binary tree binary search tree of n nodes, what is the time complexity of creating the respective unique tree.
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1answer
209 views

how does rotation works in AVL trees and what is a good way to understand it?

If we consider this tree with T1 and T2 as subtrees, and we want to rotate on x (rotating the edge between T1 and x), what is the result? how does it work then? Does the x stay in its place and T1 ...
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3answers
899 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
70 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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0answers
34 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 ...
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2answers
1k views

If inorder traversal of a tree is in ascending order will the tree definitely be a BST?

For a binary search tree (BST) the inorder traversal is always in ascending order. Is the converse also true?
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168 views

Tracing BST Pseudocode for Insertion

I'm having real trouble tracing some pseudocode for insetion into a Binary Search Tree. I need to understand this in order to be able to teach it, but I think there are flaws in the material. For ...
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2answers
46 views

Algorithm for searching in BST with only <

How could one construct an algorithm for finding a node in a binary search tree that only requires the presence of $<$ on the key type. The ones I can easily also requires $=$.
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1answer
34 views

Augmenting a tree such that we preserve the insertion operation optimal runtime

Suppose we are given a red-black tree with $n$ vertices with distinct keys and we want to store, as addition information in each vertex $v$, the biggest key out of the keys that are smaller than $v$ (...
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1answer
181 views

Proof that a subtree of a red-black tree has no more than $\frac{3n}{4}$ nodes

I have a red-black tree with $n$ nodes, rooted at $x$. How can I prove or disprove that the number of nodes in any subtree of $x$ (including the root of the subtree) will never be greater than $\frac{...
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1answer
83 views

avl trees rotations question

As you can see in this tree its unbalanced at the root with a balanced factor of $-2$. You can also perform a Right left rotation or a Right Right rotation. Which do you have to pick in this case?
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1answer
139 views

fixing a slightly broken BST tree

I'm stuck on this question, a BST is slightly broken only if there is a node with value x in which : there is at least one value less than x on its right branch or atleast one value greater than x on ...
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1answer
645 views

AVL Tree rotations : How to balance below AVL Tree with imbalance at root node

How to balance this AVL tree after inserting node 5, using left/right rotations as indicated in the AVL tree tutorial. I have tried applying both double rotations but with no luck. Either of the ...
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2answers
131 views

BST - Sufficient condition for connecting a node to a parent

Let's assume that we have a binary search tree with node Y that hasn't a right child and for whom a successor exists in the tree. I want to prove that if I insert a node X into the tree and node X is ...
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2answers
254 views

Deriving the average depth for a randomly generated binary search tree

If $D(n)$ is the internal path length (sum of the depths of all nodes) for some tree $T$ with $n$ nodes then we have the following recurrence relation: $$D(n)=D(i)+D(n-i-1)+N-1$$ where I simply taken ...
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1answer
645 views

Binary Search Tree – Number of comparisons when element is not found

I am confused regarding Binary Search Trees (BST) when an element does not exist in the tree. For example, to search for element "6", would it take 5 comparisons to search for this element? My ...
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1answer
74 views

The validity of the potential function for splay tree

The paper "Self-Adjusting Binary Search Trees" defines (Page 658) the potential function for analyzing the amortized cost of a sequence of $m$ splay operations as the sum of the ranks of all nodes in ...