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/**

* Author: Adrito Mukherjee

* Finding Lowest Common Ancestor By Binary Lifting implementation in JavaScript

* The technique requires preprocessing the tree in O(N log N) using dynamic programming)

* It can be used to find Lowest Common Ancestor of two nodes in O(log N)

* Tutorial on Lowest Common Ancestor: https://www.geeksforgeeks.org/lca-in-a-tree-using-binary-lifting-technique

*/

import { BinaryLifting } from './BinaryLifting'

class LCABinaryLifting extends BinaryLifting {

constructor (root, tree) {

super(root, tree)

this.depth = new Map() // depth[node] stores the depth of node from root

this.depth.set(root, 1)

this.dfsDepth(root, root)

}

dfsDepth (node, parent) {

// DFS to find depth of every node in the tree

for (const child of this.connections.get(node)) {

if (child !== parent) {

this.depth.set(child, this.depth.get(node) + 1)

this.dfsDepth(child, node)

}

}

}

getLCA (node1, node2) {

// We make sure that node1 is the deeper node among node1 and node2

if (this.depth.get(node1) < this.depth.get(node2)) {

[node1, node2] = [node2, node1]

}

// We check if node1 is the ancestor of node2, and if so, then return node1

const k = this.depth.get(node1) - this.depth.get(node2)

node1 = this.kthAncestor(node1, k)

if (node1 === node2) {

return node1

}

for (let i = this.log - 1; i >= 0; i--) {

if (this.up.get(node1).get(i) !== this.up.get(node2).get(i)) {

node1 = this.up.get(node1).get(i)

node2 = this.up.get(node2).get(i)

}

}

return this.up.get(node1).get(0)

}

}

function lcaBinaryLifting (root, tree, queries) {

const graphObject = new LCABinaryLifting(root, tree)

const lowestCommonAncestors = []

for (const [node1, node2] of queries) {

const lca = graphObject.getLCA(node1, node2)

lowestCommonAncestors.push(lca)

}

return lowestCommonAncestors

}

export default lcaBinaryLifting