added solution to ch4-4 and associated tests.

Author: diadical

src/chapter4/ch4-q04.js

@@ -0,0 +1,40 @@
+'use strict';
+
+/**
+ * This function attempts to check if the tree is completely balanced by finding
+ * the shortest and longest paths from root to leaf. If the difference between
+ * these two paths is greater than 1 then the tree is not balanced.
+ *
+ * N = |tree|
+ * Time: O(N)
+ * Additional space: O(lg N) - space cost is due to call stack size while using
+ * recursion, this may be O(N) in the worst case.
+ */
+export function isBalanced(tree) {
+  if (!tree || !tree.root) {
+    return true;
+  }
+
+  let node = tree.root,
+    cache = {
+      min: Number.MAX_SAFE_INTEGER,
+      max: Number.MIN_SAFE_INTEGER
+    };
+
+  findDepth(cache, node, 0);
+  return cache.max - cache.min <= 1;
+}
+
+function findDepth(cache, node, depth) {
+  if (!node) {
+    if (depth < cache.min) {
+      cache.min = depth;
+    }
+    if (depth > cache.max) {
+      cache.max = depth;
+    }
+  } else {
+    findDepth(cache, node.left, depth + 1);
+    findDepth(cache, node.right, depth + 1);
+  }
+}

src/chapter4/ch4-q04.spec.js

@@ -0,0 +1,69 @@
+import { expect } from 'chai';
+import { Tree } from './helpers';
+import * as funcs from './ch4-q04';
+
+for (let key in funcs) {
+  let func = funcs[key];
+
+  describe('ch4-q04: ' + key, function() {
+
+    beforeEach(function() {
+      this.tree = new Tree();
+    });
+
+    it('returns true for null tree or root', function() {
+      expect(func(null)).to.be.true;
+      expect(func(this.tree)).to.be.true;
+    });
+
+    it('returns true for single node tree', function() {
+      this.tree.add(10);
+      expect(func(this.tree)).to.be.true;
+    });
+
+    it('returns false for left heavy tree', function() {
+      this.tree.add(10);
+      this.tree.add(9);
+      this.tree.add(8);
+      expect(func(this.tree)).to.be.false;
+    });
+
+    it('returns false with equal max height tree but uneven', function() {
+      this.tree.add(10);
+      this.tree.add(11);
+      this.tree.add(12);
+      this.tree.add(13);
+      this.tree.add(9);
+      this.tree.add(8);
+      this.tree.add(7);
+      expect(func(this.tree)).to.be.false;
+    });
+
+    it('returns true for larger balanced tree', function() {
+      this.tree.add(8);
+      expect(func(this.tree), 'root').to.be.true;
+      this.tree.add(4);
+      this.tree.add(12);
+      expect(func(this.tree), 'depth 1').to.be.true;
+      this.tree.add(2);
+      this.tree.add(6);
+      this.tree.add(10);
+      this.tree.add(14);
+      expect(func(this.tree), 'depth 2').to.be.true;
+      this.tree.add(1);
+      this.tree.add(3);
+      this.tree.add(5);
+      this.tree.add(7);
+      expect(func(this.tree), '1/2 depth 3').to.be.true;
+      this.tree.add(9);
+      this.tree.add(11);
+      this.tree.add(13);
+      this.tree.add(15);
+      expect(func(this.tree), 'depth 3').to.be.true;
+      this.tree.add(16);
+      expect(func(this.tree), '1 depth 4').to.be.true;
+    });
+
+  });
+
+}