8.6 KiB
8.6 KiB
id | title | challengeType | forumTopicId |
---|---|---|---|
587d8257367417b2b2512c7d | Find the Minimum and Maximum Height of a Binary Search Tree | 1 | 301641 |
Description
Instructions
findMinHeight
and findMaxHeight
. These methods should return an integer value for the minimum and maximum height within a given binary tree, respectively. If the node is empty let's assign it a height of -1
(that's the base case). Finally, add a third method isBalanced
which returns true
or false
depending on whether the tree is balanced or not. You can use the first two methods you just wrote to determine this.
Tests
tests:
- text: The <code>BinarySearchTree</code> data structure should exist.
testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() }; return (typeof test == 'object')})());
- text: The binary search tree should have a method called <code>findMinHeight</code>.
testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; return (typeof test.findMinHeight == 'function')})());
- text: The binary search tree should have a method called <code>findMaxHeight</code>.
testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; return (typeof test.findMaxHeight == 'function')})());
- text: The binary search tree should have a method called <code>isBalanced</code>.
testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; return (typeof test.isBalanced == 'function')})());
- text: The <code>findMinHeight</code> method should return the minimum height of the tree.
testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.findMinHeight !== 'function') { return false; }; test.add(4); test.add(1); test.add(7); test.add(87); test.add(34); test.add(45); test.add(73); test.add(8); return (test.findMinHeight() == 1); })());
- text: The <code>findMaxHeight</code> method should return the maximum height of the tree.
testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.findMaxHeight !== 'function') { return false; }; test.add(4); test.add(1); test.add(7); test.add(87); test.add(34); test.add(45); test.add(73); test.add(8); return (test.findMaxHeight() == 5); })());
- text: An empty tree should return a height of <code>-1</code>.
testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.findMaxHeight !== 'function') { return false; }; return (test.findMaxHeight() == -1); })());
- text: The <code>isBalanced</code> method should return <code>false</code> if the tree is an unbalanced binary search tree.
testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.isBalanced !== 'function') { return false; }; test.add(4); test.add(1); test.add(7); test.add(87); test.add(34); test.add(45); test.add(73); test.add(8); return test.isBalanced() === false; })());
- text: The <code>isBalanced</code> method should return <code>true</code> if the tree is a balanced binary search tree.
testString: assert((function() { var test = false; if (typeof BinarySearchTree !== 'undefined') { test = new BinarySearchTree() } else { return false; }; if (typeof test.isBalanced !== 'function') { return false; }; test.add(10); test.add(3); test.add(22); test.add(1); test.add(4); test.add(17); test.add(32); return test.isBalanced() === true; })());
Challenge Seed
var displayTree = tree => console.log(JSON.stringify(tree, null, 2));
function Node(value) {
this.value = value;
this.left = null;
this.right = null;
}
function BinarySearchTree() {
this.root = null;
// Only change code below this line
// Only change code above this line
}
After Test
BinarySearchTree.prototype = Object.assign(
BinarySearchTree.prototype,
{
add: function(value) {
function searchTree(node) {
if (value < node.value) {
if (node.left == null) {
node.left = new Node(value);
return;
} else if (node.left != null) {
return searchTree(node.left);
}
} else if (value > node.value) {
if (node.right == null) {
node.right = new Node(value);
return;
} else if (node.right != null) {
return searchTree(node.right);
}
} else {
return null;
}
}
var node = this.root;
if (node == null) {
this.root = new Node(value);
return;
} else {
return searchTree(node);
}
}
}
);
Solution
var displayTree = tree => console.log(JSON.stringify(tree, null, 2));
function Node(value) {
this.value = value;
this.left = null;
this.right = null;
}
function BinarySearchTree() {
this.root = null;
// Only change code below this line
// Only change code above this line
this.findMinHeight = function(root = this.root) {
// empty tree.
if (root === null) {
return -1;
}
// leaf node.
if (root.left === null && root.right === null) {
return 0;
}
if (root.left === null) {
return this.findMinHeight(root.right) + 1;
}
if (root.right === null) {
return this.findMinHeight(root.left) + 1;
}
const lHeight = this.findMinHeight(root.left);
const rHeight = this.findMinHeight(root.right);
return Math.min(lHeight, rHeight) + 1;
};
this.findMaxHeight = function(root = this.root) {
// empty tree.
if (root === null) {
return -1;
}
// leaf node.
if (root.left === null && root.right === null) {
return 0;
}
if (root.left === null) {
return this.findMaxHeight(root.right) + 1;
}
if (root.right === null) {
return this.findMaxHeight(root.left) + 1;
}
const lHeight = this.findMaxHeight(root.left);
const rHeight = this.findMaxHeight(root.right);
return Math.max(lHeight, rHeight) + 1;
};
this.isBalanced = function(root = this.root) {
if (root === null) {
return true;
}
if (root.left === null && root.right === null) {
return true;
}
if (root.left === null) {
return this.findMaxHeight(root.right) <= 0;
}
if (root.right === null) {
return this.findMaxHeight(root.left) <= 0;
}
const lHeight = this.findMaxHeight(root.left);
const rHeight = this.findMaxHeight(root.right);
if (Math.abs(lHeight - rHeight) > 1) {
return false;
}
return this.isBalanced(root.left) && this.isBalanced(root.right);
};
}