Questions tagged [red-black-trees]

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Tight upper bound for forming an $n$ element Red-Black Tree from scratch

I learnt that in a order-statistic tree (augmented Red-Black Tree, in which each node $x$ contains an extra field denoting the number of nodes in the sub-tree rooted at $x$) finding the $i$ th order ...
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28 views

Prove that a red-black tree with $n$ internal nodes has height at most $2\lg(n+1)$

I cannot understand the first paragraph of the proof, which comes from the known book Introduction to Algorithms, third-edition, and I consider it has some errors, could anyone help me check about it? ...
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20 views

Red-Black Tree Height Proof

I know that the height of a red-black tree is at most 2 lg(n + 1). However, what is the mathematical proof of this? I searched various sites, however I couldn't find a good proof. I already know the ...
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13 views

Confusion with “every path from a given node to any of the leaves goes through the same number of black nodes” property of RB trees

One of the properties of Red Black trees is: "every path from a given node/vertex to any of the leaves goes through the same number of black nodes" Two related questions about this property: 1) is ...
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0answers
74 views

Is the internal structure of a red-black-tree dependent on the insertion order?

Is the internal structure of a red-black tree (which nodes are red or black, the disposition of the branches, the location of each value...) dependent on the order in which the elements were inserted? ...
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85 views

Red-Black tree with index

I want to create a Red-Black Tree, with 2 values, (index, value) and I want to insert into the RB_tree based on the index. So if I have the function: $\text{insert}(root, value, index)$ it will ...
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1answer
47 views

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 ...
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1answer
53 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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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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0answers
115 views

Red-black tree trinode restructuring after insertion and deletion

When performing an insertion/deletion on a red-black tree, how can be argued or proved that it requires at most one/two trinode restructuring(s) respectively? My thoughts so far were: after inserting ...
1
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1answer
99 views

Introduction To Algorithms 3rd Edition MIT Press: Red Black Tree insertion error in pseudo-code?

I'm implementing the algorithm on page 316 of the book Introduction to Algorithms. When I look at the pseudo-code, I feel that there is something wrong between line 10 to 14. I feel it's missing a ...
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37 views

Red Black Tree Property

Although it may sound trivial... I was going trough the definitions for Red Black Tree in the book "Introduction to Algorithms" and I still cannot understand, why this is not a RBT? ...
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1k views

Why use heap over red-black tree?

Heap supports insert operation in $O(\log n)$ time. And while heap supports remove min/max in $O(\log n)$ time, to remove any element (non min/max) heap takes $O(n)$ time. However, red-black tree ...
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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
190 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{...