L

A

```
/**
* Author: Adrito Mukherjee
* Binary Lifting implementation in Javascript
* Binary Lifting is a technique that is used to find the kth ancestor of a node in a rooted tree with N nodes
* The technique requires preprocessing the tree in O(N log N) using dynamic programming
* The technique can answer Q queries about kth ancestor of any node in O(Q log N)
* It is faster than the naive algorithm that answers Q queries with complexity O(Q K)
* It can be used to find Lowest Common Ancestor of two nodes in O(log N)
* Tutorial on Binary Lifting: https://codeforces.com/blog/entry/100826
*/
export class BinaryLifting {
constructor (root, tree) {
this.root = root
this.connections = new Map()
this.up = new Map() // up[node][i] stores the 2^i-th parent of node
for (const [i, j] of tree) {
this.addEdge(i, j)
}
this.log = Math.ceil(Math.log2(this.connections.size))
this.dfs(root, root)
}
addNode (node) {
// Function to add a node to the tree (connection represented by set)
this.connections.set(node, new Set())
}
addEdge (node1, node2) {
// Function to add an edge (adds the node too if they are not present in the tree)
if (!this.connections.has(node1)) {
this.addNode(node1)
}
if (!this.connections.has(node2)) {
this.addNode(node2)
}
this.connections.get(node1).add(node2)
this.connections.get(node2).add(node1)
}
dfs (node, parent) {
// The dfs function calculates 2^i-th ancestor of all nodes for i ranging from 0 to this.log
// We make use of the fact the two consecutive jumps of length 2^(i-1) make the total jump length 2^i
this.up.set(node, new Map())
this.up.get(node).set(0, parent)
for (let i = 1; i < this.log; i++) {
this.up
.get(node)
.set(i, this.up.get(this.up.get(node).get(i - 1)).get(i - 1))
}
for (const child of this.connections.get(node)) {
if (child !== parent) this.dfs(child, node)
}
}
kthAncestor (node, k) {
// if value of k is more than or equal to the number of total nodes, we return the root of the graph
if (k >= this.connections.size) {
return this.root
}
// if i-th bit is set in the binary representation of k, we jump from a node to its 2^i-th ancestor
// so after checking all bits of k, we will have made jumps of total length k, in just log k steps
for (let i = 0; i < this.log; i++) {
if (k & (1 << i)) {
node = this.up.get(node).get(i)
}
}
return node
}
}
function binaryLifting (root, tree, queries) {
const graphObject = new BinaryLifting(root, tree)
const ancestors = []
for (const [node, k] of queries) {
const ancestor = graphObject.kthAncestor(node, k)
ancestors.push(ancestor)
}
return ancestors
}
export default binaryLifting
```