# Questions tagged [balanced-search-trees]

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### Data structure for a queue of weighted elements

Consider a queue of elements with weights $w_0, w_1 \ldots, w_{n-1}$. The queue supports two operations: Inserting one element at the back of the queue Reducing the weight of one element in the ...
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### What is the maximal difference between the depths of 2 leaves in AVL tree?

I'm wondering what's the answer of the following question: What is the maximal difference between the depths of 2 leaves in an AVL tree? Intuitively I think that it shouldn't exceed $log n$ but have ...
55 views

### Worst Case for AVL Tree Balancing after Deletion

After deleting a node in an AVL tree, self-balancing (zig-zag rotation or the left-right balancing) maintains O(logn) time that is not guaranteed in other unbalanced trees (like BST). The Balancing ...
432 views

### What is the fastest way to merge two B trees?

Given two B-trees of some order $m$ - $T_1,T_2$, such that $y > x$ for every pair $x \in T_1$ and $y \in T_2$. What is the fastest way to create a new tree that is the union of both $T_1,T_2$? My ...
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### Why do b*trees partition 2 nodes into 3?

I'm writing a b*tree library in Rust. I'm thinking it might be better to make the purposeful decision to only implement half of the b* optimizations. (And not because it is easier, although it is.) ...
50 views

### What is the name of the data structure that is a tree on the backend but has a list like API?

I'm looking for the name of a data structure. It is organized like a balanced tree. The elements need not be comparable. Instead of asking if the tree contains a thing (like you would with a ...
187 views

### Splitting a node in B+ tree with odd number of keys

This and several other resources suggest to "Always a node that gets the middle key from bottom splits, should drop one item for a new middle key". To illustrate with an example. For 5-way B+-tree, ...
37 views

### Scapegoat Trees: Why are they only loosely a-height-balanced?

From Wikipedia: Even a degenerate tree (linked list) satisfies this condition if Ī±=1, whereas an Ī±=0.5 would only match almost complete binary trees. A binary search tree that is Ī±-weight-...
35 views

### Treap union unrandomizes priorities?

The algorithm for the union of two sets represented by treaps is defined in this paper and on Wikipedia, but the algorithm seems flawed. Take for example the following loop. ...
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### What would happen if we added this rule to red-black trees?

So, I know that a normal r-b tree has a height of O(logn). What would happen is we let a red node have a red child if its parent is black? Would the height still be O(logn)? Would you have to have a ...
107 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, ...
78 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 ...
724 views

### How to prove that in an AVL tree with height h, the depth of every leaf node is at least $\lceil h/2 \rceil$

I have an AVL tree with height h. I understand how to get h $\thickapprox$ 1.440 log N. However, I can't figure out how to calculate the minimum depth of a leaf node from root. I tried constructing a ...
39 views

### Linked lists with auxiliary data

I'm trying to design a data structure that supports the following operations in $O(1)$ time: $\operatorname{query}(\ell)$: Yield some auxiliary datum associated with list $\ell$ (just a single ...
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### 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 ...
229 views

### How to find the number of intervals containing a point when given a static set of intervals?

I've seen similar questions around here but I'm trying to address this problem with a slight change and maybe it makes it easier to solve. I'm given a set of intervals $\{s_1,s_2,...,s_n\}$ where ...
252 views

### Finding an interval in a binary search tree that contains a point

I have a binary search tree where nodes are non-overlapping intervals. I'm given a point, and I need to determine which interval the point belongs to (if any). This is easy to do because I can compare ...
280 views

### How to create an AVL tree, given it's pre-order traversal?

Given the pre-order traversal, we can easily obtain the necessary Binary Search Tree(BST- not necessarily balanced). However, the problem arises when we have to decide the balancing manually(this was ...
2k views

### AVL tree worst case height proof

The worst case height of AVL tree is $1.44 \log n$. How do we prove that? I read somewhere about Fibonacci quicks but did not understand it.
480 views

### How do I know which direction I should rotate a node in an AVL Tree?

I'm studying AVL Trees in my programming class and we got this exercise dealing with right, left, left-right and right-left rotations as a way to check if we understand the theoretical concept of AVL ...
172 views

### I don't understand the case 4 of red-black tree deletion

I don't know why case 4 will resolve the issue of the double black of $x$ described in Introduction to algorithm p.329. I know case 1 is transformed into one of {2,3,4} case, and case 2 re-point $x$ ...
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### Does keeping underflowed nodes unbalance the R-tree?

When deleting nodes from an R-tree, if a branch underflows, then it's meant to be dissolved and its children are meant to be reinserted into the tree. But most R-tree implementations that I've seen ...
197 views

### Counting chords intersections in a circle

The problem is: Given 2n distinct endpoints of n chords on the unit circle, count the number of intersections between chords (if k chords intersect at one point, that point counts as $\binom{n}{2}$ ...
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### Documentation of “bin number” trees

TL;DR: I implemented a special (?) binary tree and can't find any further details on the method I used on the internet. I would like to know if there are any scientific papers discussing my ...
47 views

### Efficient data structure for multidimensional searching on intervals and keys

I am searching for a data structure that can capture a database, which is consisted of one column of intervals (like [0, 2], [4, 6]) and one/two columns of keys (...
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### Minimum finger search tree complexity

Suppose I have an AVL tree with a pointer to the minimal element. I'd like to conduct a search for some key x, which is the $k$-smallest key in the entire tree. I can do this by "climbing" up the tree'...
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### B/B+ trees without leftmost pointers

In both B-trees and B+trees, a node (a.k.a page) contains K keys and K+1 pointers: node = [ ptr_1, key_1, ... , ptr_K , key_K , ptr_(K+1) ] Now suppose that I ...
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### 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)?
4k views

### How many rotations after AVL insertion and deletion

Is it true that inserting an element to an AVL tree requires $O(1)$ rotations? How many rotations, does deletion from AVL require? I've searched for these two questions with no luck so far.
512 views

### Left-Right-Rotation of AVL-Tree

For AVL-Tree there exists the following Rotations for Balancing: Left Rotation Right Rotation Left-Right Rotation Right-Left Rotation My Question is about the Naming for the Double-Rotations. ...