Apply max height to SplayTree

[hackerwins]

What this PR does / why we need it?

Apply max height to splay

Related to yorkie-team/yorkie#989

Any background context you want to provide?

Before	After

What are the relevant tickets?

Address yorkie-team/yorkie#941

Checklist

• Added relevant tests or not required
• Didn't break anything

Summary by CodeRabbit

• New Features
  • Enhanced splay tree functionality with node height management and balancing logic.
  • Introduced methods to retrieve and set node heights, improving tree performance.
  • Added balancing and splay operations to maintain tree structure efficiently.

[coderabbitai]

Walkthrough

The changes involve enhancements to the SplayNode and SplayTree classes by introducing new properties and methods for managing node heights and balancing the tree. A height property is added to SplayNode, along with methods to retrieve and set this height. The SplayTree class now includes a nodeCount property and methods for balancing the tree and updating node weights and heights. These modifications aim to improve the overall functionality of the splay tree.

Changes

File Path	Change Summary
packages/sdk/src/util/splay_tree.ts	- Added methods for height management in SplayNode: getHeight, getLeftHeight, getRightHeight, setHeight. - Introduced nodeCount property in SplayTree. - Added balance, splayMaxHeight, and updateWeightAndHeight methods in SplayTree. - Added updateHeight method in SplayTree.

Sequence Diagram(s)

sequenceDiagram
    participant User
    participant SplayTree
    participant SplayNode

    User->>SplayTree: insert(node)
    SplayTree->>SplayNode: create new node
    SplayTree->>SplayNode: setHeight()
    SplayTree->>SplayTree: updateWeightAndHeight(node)
    SplayTree->>SplayTree: balance()
    SplayTree->>User: confirm insertion

Loading

Poem

In the forest where trees sway,
A splay tree found a new way.
With heights now tall and nodes so bright,
It dances in the moonlight.
Hopping with joy, the rabbit sings,
For balance and heights are wondrous things! 🐇✨

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Recent review details

Configuration used: CodeRabbit UI
Review profile: CHILL

Commits

Files that changed from the base of the PR and between 4d5416f and 14501ba.

Files selected for processing (1)

• packages/sdk/src/util/splay_tree.ts (11 hunks)

Additional comments not posted (14)

packages/sdk/src/util/splay_tree.ts (14)

29-29: LGTM!

The new height property is correctly initialized to 1 in the constructor.

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95-100: LGTM!

The getHeight method correctly returns the height of the node.

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174-179: LGTM!

The getLeftHeight method correctly returns the height of the left child node or 0 if it doesn't exist.

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181-186: LGTM!

The getRightHeight method correctly returns the height of the right child node or 0 if it doesn't exist.

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188-193: LGTM!

The setHeight method correctly updates the height of the node.

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203-203: LGTM!

The new nodeCount property is correctly initialized to 0 in the constructor.

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249-268: LGTM!

The balance method correctly balances the tree based on the height of the root node and the total node count. It calls the splayMaxHeight method if the height of the root node exceeds a calculated threshold.

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270-285: LGTM!

The splayMaxHeight method correctly splays the node with the maximum height by traversing the tree and selecting the child node with the maximum height at each level.

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357-363: LGTM!

The updateWeightAndHeight method correctly updates both the weight and height of a node by calling the updateWeight and updateHeight methods.

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365-379: LGTM!

The updateHeight method correctly recalculates the height of a node by comparing its current height with the height of its left and right child nodes plus 1.

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351-352: LGTM!

The updateWeightAndHeight method is correctly called on both the target node and the new node after inserting a node.

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476-476: LGTM!

The updateWeightAndHeight method is correctly called on the root node after deleting a node.

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601-602: LGTM!

The updateWeightAndHeight method is correctly called on both the root node and the pivot node after rotating the tree.

Also applies to: 626-627

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340-340: Verify the impact of calling balance after inserting a node.

Calling balance after inserting a node ensures that the tree remains balanced. However, it's important to verify that this doesn't have any unintended side effects on the tree structure or the order of the nodes.

Run the following script to verify the tree structure and node order after inserting a node and calling balance:

Verification successful

---

Verification successful: The balance method maintains tree balance as intended. The balance method, through its calls to splayMaxHeight and splayNode, performs standard splay tree operations to maintain balance without unintended side effects on the tree structure or node order.

Scripts executed

The following scripts were executed for the analysis:

Script:

#!/bin/bash
# Description: Verify the tree structure and node order after inserting a node and calling `balance`.

# Test: Search for the `insertAfter` method and check if `balance` is called after inserting a node.
# Expect: `balance` is called after inserting a node.
rg --type typescript -A 10 $'insertAfter'

# Test: Search for the `balance` method and check if it modifies the tree structure or node order.
# Expect: The tree structure and node order are not modified by `balance`.
rg --type typescript -A 20 $'balance\(\)'

Length of output: 153

---

Script:

#!/bin/bash
# Description: Verify the tree structure and node order after inserting a node and calling `balance`.

# Test: Search for the `insertAfter` method and check if `balance` is called after inserting a node.
# Expect: `balance` is called after inserting a node.
rg --glob '*.ts' -A 10 'insertAfter'

# Test: Search for the `balance` method and check if it modifies the tree structure or node order.
# Expect: The tree structure and node order are not modified by `balance`.
rg --glob '*.ts' -A 20 'balance\(\)'

Length of output: 35288

---

Script:

#!/bin/bash
# Description: Verify the impact of the `splayMaxHeight` method on the tree structure and node order.

# Test: Search for the `splayMaxHeight` method to understand its implementation.
rg --glob '*.ts' -A 20 'splayMaxHeight'

# Test: Search for any other methods called within `balance` that might affect the tree structure.
rg --glob '*.ts' -A 20 'splayNode'

Length of output: 15728

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[hackerwins]

Adding both weight and height to each node increases memory usage, and the cost of re-computation becomes higher. Additionally, when splaying based on height, it seems that more splay operations are performed than anticipated. Therefore, @m4ushold and I have decided to close this PR for now.