#### Union Find

```/**
* union find data structure for javascript
*
* In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set,
* is a data structure that stores a collection of disjoint (non-overlapping) sets. Equivalently, it stores a partition
* of a set into disjoint subsets. It provides operations for adding new sets, merging sets (replacing them by their union),
* and finding a representative member of a set.
* The last operation allows to find out efficiently if any two elements are in the same or different sets.
*
* Disjoint-set data structures play a key role in Kruskal's algorithm for finding the minimum spanning tree of a graph.
* The importance of minimum spanning trees means that disjoint-set data structures underlie a wide variety of algorithms.
* In addition, disjoint-set data structures also have applications to symbolic computation, as well in compilers,
* especially for register allocation problems.
*
* you can learn more on disjoint-set / union–find data structure at https://en.wikipedia.org/wiki/Disjoint-set_data_structure
*/
function UnionFind (n, key) {
if (!(this instanceof UnionFind)) return new UnionFind(n)
if (key && typeof key !== 'function') {
throw new Error('key has to be a function or else left undefined')
}
let cnt, length
// init Union Find with number of distinct groups. Each group will be referred to as index of the array of size 'size' starting at 0.
// Provide an optional key function that maps these indices. I.e. for the groups starting with 1 provide function(a){return a-1;}. The default value is function(a){return a;}.
key = key || function (a) { return a }
cnt = length = n
const id = new Array(n)
const sz = new Array(n)
for (let i = 0; i < n; i++) {
id[i] = i
sz[i] = 1
}
// Returns the number of elements of uf object.
this.size = function () {
return length
}
// Returns the number of distinct groups left inside the object.
this.count = function () {
return cnt
}
// Return the root (value) of the group in which p is.
this.find = function (p) {
p = key(p)
while (p !== id[p]) {
id[p] = id[id[p]]
p = id[p]
}
return p
}
// Returns true if p and p are both in same group, false otherwise.
this.connected = function (p, q) {
p = key(p)
q = key(q)
ensureIndexWithinBounds(p, q)
return this.find(p) === this.find(q)
}
// Combine elements in groups p and q into a single group. In other words connect the two groups.
this.union = function (p, q) {
p = key(p)
q = key(q)
ensureIndexWithinBounds(p, q)
const i = this.find(p)
const j = this.find(q)
if (i === j) return
if (sz[i] < sz[j]) {
id[i] = j; sz[j] += sz[i]
} else {
id[j] = i; sz[i] += sz[j]
}
cnt--
}
function ensureIndexWithinBounds (args) {
for (let i = arguments.length - 1; i >= 0; i--) {
const p = arguments[i]
if (p >= length) throw new Error('Index out of bounds. The maximum index can be length-1')
}
}
}

export { UnionFind }
```  