feat(book/bt): add binary tree diameter problem

Author: amejiarosario

book/D-interview-questions-solutions.asc

@@ -332,6 +332,84 @@ As you can see, we opted for using a set to trade speed for memory.
 
 
 
+:leveloffset: +1
+
+=== Solutions for Binary Tree Questions
+(((Interview Questions Solutions, Binary Tree)))
+
+:leveloffset: -1
+
+[#binary-tree-q-diameter-of-binary-tree]
+include::content/part03/tree-intro.asc[tag=binary-tree-q-diameter-of-binary-tree]
+
+We are asked to find the longest path on binary tree that might or might not pass through the root node.
+
+We can calculate the height (distance from root to farthest leaf) of a binary tree using this recursive function:
+
+[source, javascript]
+----
+function getHeight(node) {
+  if (!node) return 0;
+  const leftHeight = getHeight(node.left);
+  const rightHeight = getHeight(node.right);
+  return 1 + Math.max(leftHeight, rightHeight);
+}
+----
+
+That will give use the height from furthest leaf to root. However, the problem says that it might or might not go through the root.
+In that case, we can keep track of the maximun distance (`leftHeight + rightHeight`) seen so far.
+
+*Algorithm*:
+
+- Initialize diameter to `0`
+- Recursively find the height of the tree from root.
+- Keep track of the maximun diameter length seen so far (left + right).
+- Return the diameter.
+
+*Implementation*:
+
+[source, javascript]
+----
+include::interview-questions/diameter-of-binary-tree.js[tags=description;solution]
+----
+
+We are using `Math.max` to keep track of the longest diameter seen.
+
+*Complexity Analysis*:
+
+- Time: `O(n)`, where `n` is each one of the nodes on the tree. We visite each one once.
+- Space: `O(n)`. We use `O(1)` variables, but because we are using the `height` recursive function we are using the implicit call stack, thus `O(n)`.
+
+
+
+
+[#binary-tree-q-diameter-of-binary-tree2]
+include::content/part03/tree-intro.asc[tag=binary-tree-q-diameter-of-binary-tree]
+
+RESTATE REQUIREMENTS AND DESCRIPTIONS
+
+*Algorithm*:
+
+- STEP 1
+- STEP 2
+    - STEP 2.1
+    - STEP 2.2
+
+*Implementation*:
+
+[source, javascript]
+----
+include::interview-questions/diameter-of-binary-tree.js[tag=description]
+include::interview-questions/diameter-of-binary-tree.js[tag=solution]
+----
+
+IMPLEMENTATION NOTES
+
+*Complexity Analysis*:
+
+- Time: `O(?)`. WHY?
+- Space: `O(?)`. WHY?
+
 
 // [#linkedlist-q-FILENAME]
 // include::content/part02/linked-list.asc[tag=linkedlist-q-FILENAME]

book/config

@@ -109,3 +109,106 @@ image::image35.png[image,width=258,height=169]
 Heap is better at finding max or min values in constant time *O(1)*, while a balanced BST is good a finding any element in *O(log n)*. Heaps are often used to implement priority queues while BST is used when you need every value sorted.
 ****
 indexterm:[Runtime, Logarithmic]
+
+
+==== Practice Questions
+(((Interview Questions, Binary Tree)))
+
+
+// tag::binary-tree-q-diameter-of-binary-tree[]
+===== Binary Tree Diameter
+
+*BT-1*) _Find the diameter of a binary tree. The diameter of a tree is defined as the longest possible path from two nodes (it doesn't need to include the root). The lenth of diameter is calculated by couting the number of edges on the path._
+
+// end::binary-tree-q-diameter-of-binary-tree[]
+
+_Seen in interviews at: Facebook, Amazon, Google_
+
+Example 1:
+
+[graphviz, tree-diameter-example-1, png]
+....
+graph G {
+    1 -- 2 [color=red]
+    1 -- 3 [color=red]
+
+    2 -- 4
+    2 -- 5 [color=red]
+}
+....
+
+[source, javascript]
+----
+diameterOfBinaryTree(toBinaryTree([1,2,3,4,5])); // 3 (the path 3-1-2-5 or 3-1-2-4)
+----
+
+Example 2:
+
+[graphviz, tree-diameter-example-2, png]
+....
+graph G {
+    1
+    2
+    3
+    4
+    5
+    6
+    "null" [color=white, fontcolor = white]
+    "null." [color=white, fontcolor = white]
+    7
+    8
+    "null.." [color=white, fontcolor = white]
+    "null..." [color=white, fontcolor = white]
+    9
+
+    1 -- 2
+    1 -- 3
+
+    3 -- 4 [color=red]
+    3 -- 5 [color=red]
+
+    4 -- 6 [color=red]
+    4 -- "null." [color=white]
+
+    5 -- "null" [color=white]
+    5 -- 7 [color=red]
+
+    6 -- 8 [color=red]
+    6 -- "null.." [color=white]
+
+    7 -- "null..." [color=white]
+    7 -- 9 [color=red]
+}
+....
+
+[source, javascript]
+----
+diameterOfBinaryTree(toBinaryTree([1,2,3,null,null,4,5,6,null,null,7,8,null,null,9])); // 6 (the path 8-6-4-3-5-7-9)
+----
+
+Starter code:
+
+[source, javascript]
+----
+include::../../interview-questions/diameter-of-binary-tree.js[tags=description;placeholder]
+----
+
+
+_Solution: <<binary-tree-q-diameter-of-binary-tree>>_
+
+
+
+// tag::binary-tree-q-FILENAME[]
+===== Recent Counter
+
+*BT-2*) _._
+
+Example:
+
+[source, javascript]
+----
+
+----
+
+_Seen in interviews at: X_
+// end::binary-tree-q-FILENAME[]

book/content/part03/tree-intro.asc

@@ -0,0 +1,31 @@
+// tag::description[]
+/**
+ * Find the length of the binary tree diameter.
+ *
+ * @param {BinaryTreeNode | null} root - Binary Tree's root.
+ * @returns {number} tree's diameter (longest possible path on the tree)
+ */
+function diameterOfBinaryTree(root) {
+  // end::description[]
+  // tag::placeholder[]
+  // write your code here...
+  // end::placeholder[]
+  // tag::solution[]
+  let diameter = 0;
+
+  const height = (node) => {
+    if (!node) return 0;
+    const left = height(node.left);
+    const right = height(node.right);
+    diameter = Math.max(diameter, left + right);
+    return 1 + Math.max(left, right);
+  };
+
+  height(root);
+  return diameter;
+  // end::solution[]
+  // tag::description[]
+}
+// end::description[]
+
+module.exports = { diameterOfBinaryTree };

book/images/tree-diameter-example-1.png

@@ -0,0 +1,21 @@
+const { diameterOfBinaryTree } = require('./diameter-of-binary-tree');
+const { BinaryTreeNode } = require('../../src/index');
+
+describe('Binary Tree: Diameter', () => {
+  function toBinaryTree(array, index = 0) {
+    if (index >= array.length) return null;
+    const node = new BinaryTreeNode(array[index]);
+    node.left = toBinaryTree(array, index * 2 + 1);
+    node.right = toBinaryTree(array, index * 2 + 2);
+    return node;
+  }
+
+  it('should find the diameter', () => {
+    expect(diameterOfBinaryTree(toBinaryTree([1, 2, 3, 4, 5]))).toEqual(3);
+  });
+
+  it('should find the diameter when does not pass through the root node', () => {
+    const tree = [1, 2, 3, null, null, 4, 5, 6, null, null, 7, 8, null, null, 9];
+    expect(diameterOfBinaryTree(toBinaryTree(tree))).toEqual(6);
+  });
+});