Press n or j to go to the next uncovered block, b, p or k for the previous block.
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// code copied from https://levelup.gitconnected.com/building-a-b-tree-in-javascript-4482dee083cb
import { v4 as uuidv4 } from 'uuid';
export class BTreeNode {
constructor(isLeaf) {
/**
* @type {number[]} list of values in the node
*/
this.values = [];
/**
* @type {boolean} is a leaf
*/
this.leaf = isLeaf;
/**
* @type {BTreeNode[]}
*/
this.children = [];
/**
* Reference to the tree its belong.
* @type {BTree}
*/
this.tree = null;
/**
* @type {BTreeNode}
*/
this.parent = null;
this.id = 'N' + uuidv4();
}
getId() {
return this.id;
}
/**
* Number of values
* @returns {number}
*/
get n() {
return this.values.length;
}
/**
* Add value
* @param {number} value
* @param {number} pos
*/
addValue(value) {
if (!value) {
return;
}
let pos = 0;
while (pos < this.n && this.values[pos] < value) {
pos++;
}
this.values.splice(pos, 0, value);
}
/**
* Delete value and return it
* @param {number} pos position
* @return {number}
*/
removeValue(pos) {
if (pos >= this.n) {
return null;
}
return this.values.splice(pos, 1)[0];
}
/**
* Add child node at position pos
* @param {BTreeNode} node
* @param {number} pos
*/
addChild(node, pos) {
this.children.splice(pos, 0, node);
node.parent = this;
}
/**
* Delete node from position and return it
* @param {number} pos
* @return {BTreeNode}
*/
deleteChild(pos) {
return this.children.splice(pos, 1)[0];
}
}
/**
* btree namespace.
* @type {BTree}
*/
export default class BTree {
constructor(order) {
/** @type {number} */
this.order = order;
/**
* Root node of the tree.
* @type {BTreeNode}
*/
this.root = null;
}
/**
* Search a value in the Tree and return the node. O(log N)
* @param {number} value
* @param {BTreeNode} node
* @returns {BTreeNode}
*/
searchValue(node, value) {
if (node.values.includes(value)) {
return node;
}
if (node.leaf) {
// Value was not found
return null;
}
let child = 0;
while (child <= node.n && node.values[child] < parseInt(value, 10)) {
child++;
}
return this.searchValue(node.children[child]);
}
/**
* Deletes the value from the Tree. O(log N)
* @param {number} value
*/
delete(value) {
if (this.root.n === 1 && !this.root.leaf &&
this.root.children[0].n === this.order-1 && this.root.children[1].n === this.order -1) {
// Check if the root can shrink the tree into its childs
this.mergeNodes(this.root.children[1], this.root.children[0]);
this.root = this.root.children[0];
}
// Start looking for the value to delete
this.deleteFromNode(this.root, parseInt(value, 10));
}
/**
* Delete a value from a node. O(log N)
* @param {BTreeNode} node
* @param {number} value
*/
deleteFromNode(node, value) {
// Check if value is in the actual node
const index = node.values.indexOf(value);
if (index >= 0) {
// Value present in the node
if (node.leaf && node.n > this.order - 1) {
// If the node is a leaf and has more than order-1 values, just delete it
node.removeValue(node.values.indexOf(value));
return true;
}
// Check if one children has enough values to transfer
if (node.children[index].n > this.order - 1 ||
node.children[index + 1].n > this.order - 1) {
// One of the immediate children has enough values to transfer
if (node.children[index].n > this.order - 1) {
// Replace the target value for the higher of left node.
// Then delete that value from the child
const predecessor = this.getMinMaxFromSubTree(node.children[index], 1);
node.values[index] = predecessor;
return this.deleteFromNode(node.children[index], predecessor);
}
const successor = this.getMinMaxFromSubTree(node.children[index+1], 0);
node.values[index] = successor;
return this.deleteFromNode(node.children[index+1], successor);
}
// Children has not enough values to transfer. Do a merge
this.mergeNodes(node.children[index + 1], node.children[index]);
return this.deleteFromNode(node.children[index], value);
}
// Value is not present in the node
if (node.leaf) {
// Value is not in the tree
return false;
}
// Value is not present in the node, search in the children
let nextNode = 0;
while (nextNode < node.n && node.values[nextNode] < value) {
nextNode++;
}
if (node.children[nextNode].n > this.order - 1) {
// Child node has enough values to continue
return this.deleteFromNode(node.children[nextNode], value);
}
// Child node has not enough values to continue
// Before visiting next node transfer a value or merge it with a brother
if ((nextNode > 0 && node.children[nextNode - 1].n > this.order - 1) ||
(nextNode < node.n && node.children[nextNode + 1].n > this.order - 1)) {
// One of the immediate children has enough values to transfer
if (nextNode > 0 && node.children[nextNode - 1].n > this.order - 1) {
this.transferValue(node.children[nextNode - 1], node.children[nextNode]);
} else {
this.transferValue(node.children[nextNode + 1], node.children[nextNode]);
}
return this.deleteFromNode(node.children[nextNode], value);
}
// No immediate brother with enough values.
// Merge node with immediate one brother
this.mergeNodes(
nextNode > 0 ? node.children[nextNode - 1] : node.children[nextNode + 1],
node.children[nextNode]);
return this.deleteFromNode(node.children[nextNode], value);
}
/**
* Transfer one value from the origin to the target. O(1)
* @param {BTreeNode} origin
* @param {BTreeNode} target
*/
transferValue(origin, target) {
const indexo = origin.parent.children.indexOf(origin);
const indext = origin.parent.children.indexOf(target);
if (indexo < indext) {
target.addValue(target.parent.removeValue(indexo));
origin.parent.addValue(origin.removeValue(origin.n-1));
if (!origin.leaf) {
target.addChild(origin.deleteChild(origin.children.length-1), 0);
}
} else {
target.addValue(target.parent.removeValue(indext));
origin.parent.addValue(origin.removeValue(0));
if (!origin.leaf) {
target.addChild(origin.deleteChild(0), target.children.length);
}
}
}
/**
* Merge 2 nodes into one with the parent median value. O(1)
* @param {BTreeNode} origin
* @param {BTreeNode} target
*/
mergeNodes(origin, target) {
const indexo = origin.parent.children.indexOf(origin);
const indext = target.parent.children.indexOf(target);
target.addValue(target.parent.removeValue(Math.min(indexo, indext)));
for (let i = origin.n - 1; i >= 0; i--) {
target.addValue(origin.removeValue(i));
}
// Remove reference to origin node
target.parent.deleteChild(indexo);
// Transfer all the children from origin node to target
if (!origin.leaf) {
while (origin.children.length) {
if (indexo > indext) {
target.addChild(origin.deleteChild(0), target.children.length);
} else {
target.addChild(origin.deleteChild(origin.children.length - 1), 0);
}
}
}
}
/**
* Get the lower or higher value in a sub-tree. O(log N)
* @param {BTreeNode} node
* @param { 0 | 1 } max 1 for find max, 0 for min
* @returns {number}
*/
getMinMaxFromSubTree(node, max) {
while (!node.leaf) {
node = node.children[max ? node.n : 0];
}
return node.values[max ? node.n - 1 : 0];
}
/**
* Insert a new value in the tree O(log N)
* @param {number} value
*/
insert(value) {
const actual = this.root;
if (actual.n === 2 * this.order - 1) {
// Create a new node to become the root
// Append the old root to the new one
const temp = new BTreeNode(false);
temp.tree = this;
this.root = temp;
temp.addChild(actual, 0);
this.split(actual, temp, 1);
this.insertNonFull(temp, parseInt(value, 10));
} else {
this.insertNonFull(actual, parseInt(value, 10));
}
};
insert_(value) {
const currentNode = this.root;
while (currentNode.leaf === false) {
}
}
/**
* Divide child node from parent into parent.values[pos-1] and parent.values[pos]. O(1)
* @param {BTreeNode} child
* @param {BTreeNode} parent
* @param {number} pos
*/
split(child, parent, pos) {
const newChild = new BTreeNode(child.leaf);
newChild.tree = this.root.tree;
// Create a new child
// Pass values from the old child to the new
for (let k = 1; k < this.order; k++) {
newChild.addValue(child.removeValue(this.order));
}
// Trasspass child nodes from the old child to the new
if (!child.leaf) {
for (let k = 1; k <= this.order; k++) {
newChild.addChild(child.deleteChild(this.order), k - 1);
}
}
// Add new child to the parent
parent.addChild(newChild, pos);
// Pass value to parent
parent.addValue(child.removeValue(this.order - 1));
parent.leaf = false;
}
/**
* Insert a value in a not-full node. O(1)
* @param {BTreeNode} node
* @param {number} value
*/
insertNonFull(node, value) {
if (node.leaf) {
node.addValue(value);
return;
}
let temp = node.n;
while (temp >= 1 && value < node.values[temp - 1]) {
temp = temp - 1;
}
if (node.children[temp].n === 2 * this.order - 1) {
this.split(node.children[temp], node, temp + 1);
if (value > node.values[temp]) {
temp = temp + 1;
}
}
this.insertNonFull(node.children[temp], value);
}
}
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