149 lines
6.3 KiB
Markdown
149 lines
6.3 KiB
Markdown
---
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id: 587d8258367417b2b2512c7f
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title: Use Breadth First Search in a Binary Search Tree
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challengeType: 1
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forumTopicId: 301718
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---
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## Description
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<section id='description'>
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Here we will introduce another tree traversal method: breadth-first search. In contrast to the depth-first search methods from the last challenge, breadth-first search explores all the nodes in a given level within a tree before continuing on to the next level. Typically, queues are utilized as helper data structures in the design of breadth-first search algorithms.
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In this method, we start by adding the root node to a queue. Then we begin a loop where we dequeue the first item in the queue, add it to a new array, and then inspect both its child subtrees. If its children are not null, they are each enqueued. This process continues until the queue is empty.
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</section>
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## Instructions
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<section id='instructions'>
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Let's create a breadth-first search method in our tree called <code>levelOrder</code>. This method should return an array containing the values of all the tree nodes, explored in a breadth-first manner. Be sure to return the values in the array, not the nodes themselves. A level should be traversed from left to right. Next, let's write a similar method called <code>reverseLevelOrder</code> which performs the same search but in the reverse direction (right to left) at each level.
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: The <code>BinarySearchTree</code> data structure should exist.
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() }; return (typeof test == 'object')})());
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- text: The binary search tree should have a method called <code>levelOrder</code>.
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; return (typeof test.levelOrder == 'function')})());
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- text: The binary search tree should have a method called <code>reverseLevelOrder</code>.
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; return (typeof test.reverseLevelOrder == 'function')})());
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- text: The <code>levelOrder</code> method should return an array of the tree node values explored in level order.
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.levelOrder !== 'function') { return false; }; test.add(7); test.add(1); test.add(9); test.add(0); test.add(3); test.add(8); test.add(10); test.add(2); test.add(5); test.add(4); test.add(6); return (test.levelOrder().join('') == '719038102546'); })());
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- text: The <code>reverseLevelOrder</code> method should return an array of the tree node values explored in reverse level order.
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.reverseLevelOrder !== 'function') { return false; }; test.add(7); test.add(1); test.add(9); test.add(0); test.add(3); test.add(8); test.add(10); test.add(2); test.add(5); test.add(4); test.add(6); return (test.reverseLevelOrder().join('') == '791108305264'); })());
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- text: The <code>levelOrder</code> method should return <code>null</code> for an empty tree.
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.levelOrder !== 'function') { return false; }; return (test.levelOrder() == null); })());
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- text: The <code>reverseLevelOrder</code> method should return <code>null</code> for an empty tree.
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testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.reverseLevelOrder !== 'function') { return false; }; return (test.reverseLevelOrder() == null); })());
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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var displayTree = tree => console.log(JSON.stringify(tree, null, 2));
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function Node(value) {
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this.value = value;
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this.left = null;
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this.right = null;
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}
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function BinarySearchTree() {
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this.root = null;
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// Only change code below this line
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// Only change code above this line
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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BinarySearchTree.prototype = Object.assign(
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BinarySearchTree.prototype,
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{
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add: function(value) {
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function searchTree(node) {
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if (value < node.value) {
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if (node.left == null) {
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node.left = new Node(value);
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return;
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} else if (node.left != null) {
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return searchTree(node.left);
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}
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} else if (value > node.value) {
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if (node.right == null) {
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node.right = new Node(value);
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return;
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} else if (node.right != null) {
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return searchTree(node.right);
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}
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} else {
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return null;
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}
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}
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var node = this.root;
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if (node == null) {
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this.root = new Node(value);
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return;
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} else {
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return searchTree(node);
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}
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}
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}
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);
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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var displayTree = tree => console.log(JSON.stringify(tree, null, 2));
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function Node(value) {
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this.value = value;
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this.left = null;
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this.right = null;
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}
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function BinarySearchTree() {
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this.root = null;
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// Only change code below this line
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this.levelOrder = (root = this.root) => {
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if(!root) return null;
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let queue = [root];
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let results = [];
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while(queue.length > 0) {
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let node = queue.shift();
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results.push(node.value);
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if(node.left) queue.push(node.left);
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if(node.right) queue.push(node.right);
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}
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return results;
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}
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this.reverseLevelOrder = (root = this.root) => {
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if(!root) return null;
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let queue = [root];
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let results = [] ;
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while ( queue.length > 0) {
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let node = queue.shift();
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results.push(node.value);
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if(node.right) queue.push(node.right);
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if(node.left ) queue.push(node.left);
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}
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return results;
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}
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// Only change code above this line
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}
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```
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</section>
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