add UnionFind.js plus tests

Search/UnionFind.js

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+/**
+ * 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 }

Search/test/UnionFind.test.js

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+import { UnionFind } from '../UnionFind'
+
+const uf = new UnionFind(5)
+
+test('should expose .size():', () => {
+  const size = uf.size()
+  expect(size).toBe(5)
+})
+
+test('should do .union(num1, num2):', () => {
+  uf.union(1, 2)
+  uf.union(3, 4)
+  uf.union(0, 4)
+  expect(uf.connected(1, 2)).toBe(true)
+  expect(uf.connected(1, 2)).toBe(true)
+
+  expect(uf.connected(3, 4)).toBe(true)
+  expect(uf.connected(3, 0)).toBe(true)
+  expect(uf.connected(4, 0)).toBe(true)
+
+  expect(uf.connected(1, 3)).toBe(false)
+  expect(uf.connected(1, 4)).toBe(false)
+  expect(uf.connected(1, 0)).toBe(false)
+  expect(uf.connected(2, 3)).toBe(false)
+  expect(uf.connected(2, 4)).toBe(false)
+  expect(uf.connected(2, 0)).toBe(false)
+})
+
+test('.count(), should return the number of disparate groups:', () => {
+  expect(uf.count()).toBe(2)
+})
+
+test('should check if two components are connected, .connected(num1, num2):', () => {
+  expect(uf.connected(1, 2)).toBe(true)
+  expect(uf.connected(1, 3)).toBe(false)
+})
+
+test('should find the root of the tree in which the given element lives, .find(num):', () => {
+  expect(uf.find(1)).toBe(1)
+  expect(uf.find(2)).toBe(1)
+  expect(uf.find(3)).toBe(3)
+  expect(uf.find(4)).toBe(3)
+  expect(uf.find(0)).toBe(3)
+})
+
+test('should always change the id of the smaller tree and preserve the id of the larger one', () => {
+  uf.union(2, 3)
+  expect(uf.count()).toBe(1)
+  expect(uf.find(0)).toBe(3)
+  expect(uf.find(1)).toBe(3)
+  expect(uf.find(2)).toBe(3)
+  expect(uf.find(3)).toBe(3)
+  expect(uf.find(4)).toBe(3)
+})