In the previous post Binary Search Tree in JavaScript we wrote our own implementation in JavaScript with a basic interface. Now we'll try to expand it.

Traversal

Unlike linear data structures (Array, Linked List, Stacks, etc.), which have only one logical way of traversing them, trees can be traversed in different ways. Ways for traversing the binary search tree:

• Inorder traversal
• Postorder traversal
• Preorder traversal

Let's focus on each in more detail.

Inorder traversal

Tree traversal algorithm:

1. Traverse the left subtree
2. Visit the root of the tree
3. Traverse the right subtree

For all examples, we'll use the binary tree from the previous part

For this binary search tree, this method should return such an array [6, 8, 11, 12, 13, 24, 29, 37, 42, 55]

inOrder() {
  if (this.root === null) return null;
  const nodeList = [];
  const traverse = function(current) {
    if (current.left) traverse(current.left);
    nodeList.push(current.data);
    if (current.right) traverse(current.right);
  };
  traverse(this.root);
  return nodeList;
};

Algorithm

1. If root property is empty then return null
2. Create the variable nodeList to store the node value
3. Create the method traverse, this method takes a node as an argument
4. The traverse method is recursively called for all elements of the tree according to the algorithm that we announced earlier
5. And as a result, we return the nodeList variable

Check the result

tree.inOrder(); // [6, 8, 11, 12, 13, 16, 24, 29, 37, 42, 55]

Postorder traversal

Tree traversal algorithm:

1. Traverse the left subtree
2. Traverse the right subtree
3. Visit the root of the tree

For the previously used binary search tree, this method should return such an array [6, 12, 11, 8, 16, 29, 24, 55, 42, 37, 13].

postOrder() {
  if (this.root === null) return null;
  const nodeList = [];
  const traverse = function(current) {
    if (current.left) traverse(current.left);
    if (current.right) traverse(current.right);
    nodeList.push(current.data);
  };
  traverse(this.root);
  return nodeList;
};

Algorithm

1. If root property is empty then return null
2. Create the variable nodeList to store the node value
3. Create the method traverse, this method takes a node as an argument
4. The traverse method is recursively called for all elements of the tree according to the algorithm that we announced earlier
5. And as a result, we return the nodeList variable

Check the result

tree.postOrder(); // [6, 12, 11, 8, 16, 29, 24, 55, 42, 37, 13]

Preorder traversal

Tree traversal algorithm:

1. Visit the root of the tree
2. Traverse the left subtree
3. Traverse the right subtree

For the previously used binary search tree, this method should return such an array [13, 8, 6, 11, 12, 37, 24, 16, 29, 42, 55].

preOrder() {
  if (this.root === null) return null;
  const nodeList = [];
  const traverse = function(current) {
    nodeList.push(current.data);
    if (current.left) traverse(current.left);
    if (current.right) traverse(current.right);
  };
  traverse(this.root);
  return nodeList;
}

Algorithm

1. If root property is empty then return null
2. Create the variable nodeList to store the node value
3. Create the method traverse, this method takes a node as an argument
4. The traverse method is recursively called for all elements of the tree according to the algorithm that we announced earlier
5. And as a result, we return the nodeList variable

Check the result

console.log(tree.preOrder()); // [13, 8, 6, 11, 12, 37, 24, 16, 29, 42, 55]

We have considered three ways to traversal a binary tree. The main idea of these three methods is visiting each node exactly once. As you can see, the implementation of these methods is very similar to each other and we visit each node only once.

Finding maximum and minimum node values

Finding the maximum or minimum node in the binary search tree is a very common task.

Let's look at our tree again

For this binary search tree, the minimum value is 6 and the maximum value is 55. I think you already see the pattern 🙂

Find maximum

Since in the binary search tree the value is already sorted to get the maximum value we need to get the value of the right child node.

findMax() {
  if (this.root === null) return null;
  let current = this.root;
  if (!current) return null;
  while (current.right) {
    current = current.right;
  }
  return current.data;
};

Algorithm

1. If root property is empty then return null
2. Create the variable current here we'll store the current node
3. While the current node has the right child we need to update the value to current
4. Return the current value

Check the result for the tree that was considered earlier.

console.log(tree.findMax()); // 55

Find minimum

Now let's do the same for the left child node and we'll get the minimum value. It's really that simple 🙂

findMin() {
  if (this.root === null) return null;
  let current = this.root;
  if (!current) return null;
  while (current.left) {
    current = current.left;
  }
  return current.data;
};

Algorithm

1. If root property is empty then return null
2. Create the variable current here we'll store the current node
3. While the current node has the left child we need to update the value to current
4. Return the current value

Check the result for the tree that was considered earlier.

console.log(tree.findMin()); // 6

To practice, you can implement your own additional methods. I'll get to the practical part. I take all tasks in LeetCode this is a great service for those who want to practice solving problems before interviews.

Same Tree

Problem

Given two binary trees, write a function to check if they're the same or not.

Two binary trees considered the same if they're structurally identical and the nodes have the same value.

Example

Input:     1         1
          / \       / \
         2   3     2   3

        [1,2,3],   [1,2,3]

Output: true

Example 2

Input:     1       1
          /         \
         2           2

        [1,2],   [1,null,2]

Output: false

Example 3

Input:     1         1
          / \       / \
         2   1     1   2

        [1,2,1],   [1,1,2]

Output: false

Solution

The easiest strategy to solve this problem is to use recursion. We need to compare each node of two trees and if they are equal return true.

/**
 * @param {TreeNode} tree1
 * @param {TreeNode} tree2
 * @returns {boolean}
 **/
const isSameTree = (tree1, tree2) => {
  if (!tree1 && !tree2) return true;
  if (!tree1 || !tree2) return false;
  return (
    tree1.data === tree2.data &&
    isSameTree(tree1.left, tree2.left) &&
    isSameTree(tree1.right, tree2.right)
  );
};

Congratulations, we solved the first problem 🙂

• Link to LeetCode Note: the binary tree interface in our implementation and on the site is different
• Link to Jsfiddle
• Link to GitHub

Merge Two Binary Trees

Problem

Given two binary trees and imagine that when you put one of them to cover the other, some nodes of the two trees are overlapped while the others are not.

You need to merge them into a new binary tree. The merge rule is that if two nodes overlap, then sum node values up as the new value of the merged node. Otherwise, the NOT null node will be used as the node of new tree.

Example 1

Input:
    Tree 1           Tree 2
          1               2
         / \             / \
        3   2           1   3
       /                 \   \
      5                   4   7
Output:
Merged tree:
         3
        / \
       4   5
      / \   \
     5   4   7

Solution

To solve the problem, we need to completely traverse both binary trees. At each iteration, we'll create a new node and check if there are nodes of each of the trees tree1 and tree2. If this is true, we add a new value (the sum of two nodes) to the current node. Then, for the left and right nodes, we call the mergeTrees function. If at any step one of the trees turns out to be empty, we'll return the child node of the other tree. After all nodes of both trees are completely traversed, we return a new binary tree.

/**
 * @param {TreeNode} tree1
 * @param {TreeNode} tree2
 * @returns {TreeNode}
 **/
const mergeTrees = (tree1, tree2) => {
  if (!tree1) return tree2;
  if (!tree2) return tree1;
  const root = new Node(tree1.data + tree2.data);
  root.left = mergeTrees(tree1 ? tree1.left : null, tree2 ? tree2.left : null);
  root.right = mergeTrees(
    tree1 ? tree1.right : null,
    tree2 ? tree2.right : null
  );
  return root;
};

Note: all the conditions of the tasks have been completed and LeetCode accepts this decision, but the merge result has a problem. When merge two trees break the logic of the right child node. If one tree contained the right child node and the other did not, after the merge, the right child node may become smaller than the parent node. As a practice, you can solve this problem 😉

• Link to LeetCode
• Link to Jsfiddle
• Link to GitHub

Diameter of Binary Tree

Problem

Given a binary tree, you need to compute the length of the diameter of the tree. The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root.

Example 1

Given a binary tree

       4
      / \
     2   5
    / \
   1   3

Return 3, which is the length of the path [1, 2, 4, 5] or [3, 2, 4, 5].

Note: The length of the path between two nodes is represented by the number of edges between them.

Solution

In the example, the longest path goes through the root. To calculate the length of such a path, just look at the maximum length of the right and left branches. To do this, we create the countDiameter function. This function will be called recursively and count the length of each path. But the longest path may not go through the center, for example:

       9
      /
     8
    / \
   4   6
  /     \
 3       7
  \
    5

Here the longest path [5, 3, 4, 8, 6, 7] doesn't go through the center. To do this, we will recursively call the diameterOfBinaryTree method for each element of the tree and then find the longest path using Math.max. This isn't the best option since we will have to go through each node a large number of times, but I think it's intuitive.

/**
 * Calculate diameter with center `root`
 * @param {TreeNode} root
 * @returns {number}
 */
const countDiameter = root => {
  if (!root) return 0;

  return 1 + Math.max(countDiameter(root.left), countDiameter(root.right));
};

/**
 * @param {TreeNode} root
 * @returns {number}
 */
const diameterOfBinaryTree = root => {
  if (!root) return 0;

  const center = countDiameter(root.left) + countDiameter(root.right);
  const left = diameterOfBinaryTree(root.left);
  const right = diameterOfBinaryTree(root.right);

  return Math.max(center, left, right);
};

Implementation is ready, you can test it 👏

• Link to LeetCode
• Link to Jsfiddle
• Link to GitHub

We have analyzed several problems, I hope you understand how to work with binary search trees and how to solve similar problems. On the site LeetCode and Hackerrank you can find ever more interesting challenges on various topics. And I made a small list of tasks that will help you remember information about trees:

• Binary Tree Inorder Traversal
• Symmetric Tree
• Univalued Binary Tree
• Balanced Binary Tree

You can share your decision or question in the comments 😀

Thank you for your attention and have a nice day 👋