https://leetcode.com/problems/greatest-common-divisor-traversal/description/?envType=daily-question&envId=2024-02-25

var canTraverseAllPairs = function (nums) {
    let n = nums.length, map = new Map(), uf = new UnionFind(n);

    for (let i = 0; i < n; i++) {
        let primeFactors = getPrimeFactors(nums[i]);

        for (let factor of primeFactors) {
            if (map.has(factor)) uf.union(i, map.get(factor));
            else map.set(factor, i);
        }
    }
    return uf.size === 1;
};


function getPrimeFactors(n) {
    let res = new Set();
    for (let x = 2; (x * x) <= n; x++) {
        // loop while n is divisible by x
        while (n % x === 0) {
            res.add(x);
            n /= x;
        }
    }
    if (n > 1) res.add(n);
    return res;
}

class UnionFind {
    constructor(size) {
        this.size = size;
        this.root = Array(size);
        this.rank = Array(size);
        for (let i = 0; i < size; i++) {
            this.root[i] = i;
            this.rank[i] = 1;
        }
    }
    find(x) {
        if (this.root[x] === x) return x;
        return this.root[x] = this.find(this.root[x]);
    }
    union(x, y) {
        let rootX = this.find(x), rootY = this.find(y);
        if (rootX === rootY) return false;
        if (this.rank[rootX] < this.rank[rootY]) {
            this.root[rootX] = rootY;
        } else if (this.rank[rootX] > this.rank[rootY]) {
            this.root[rootY] = rootX;
        } else {
            this.root[rootY] = rootX;
            this.rank[rootX]++;
        }
        this.size--;
        return true;
    }
    isConnected(x, y) {
        return this.find(x) === this.find(y);
    }
}