Related
I am trying to print the kth smallest element in an BST.
The first solution is using in-order traversal.
Next solution is finding the index of the current node by calculation the size of its left subtree.
Complete algo:
Find size of left subtree:
1.If size = k-1, return current node
2.If size>k return (size-k)th node in right subtree
3.If size<k return kth node in left subtree
This can be implemented using a separate count function which looks something like
public class Solution {
public int kthSmallest(TreeNode root, int k) {
//what happens if root == null
//what happens if k > total size of tree
return kthSmallestNode(root,k).val;
}
public static TreeNode kthSmallestNode(TreeNode root,int k){
if(root==null) return root;
int numberOfNodes = countNodes(root.left);
if(k == numberOfNodes ) return root;
if(k<numberOfNodes ) return kthSmallestNode(root.left,k);
else return kthSmallestNode(root.right,k-numberOfNodes );
}
private static int countNodes(TreeNode node){
if(node == null) return 0;
else return 1+countNodes(node.left)+countNodes(node.right);
}
}
But I see that we count the size for same trees multiple times, so one way is to maintain an array to store thes sizes like the DP way.
But I want to write a recursive solution for this.And here is the code I have written.
class Node {
int data;
Node left;
Node right;
public Node(int data, Node left, Node right) {
this.left = left;
this.data = data;
this.right = right;
}
}
public class KthInBST
{
public static Node createBST(int headData)
{
Node head = new Node(headData, null, null);
//System.out.println(head.data);
return head;
}
public static void insertIntoBst(Node head, int data)
{
Node newNode = new Node(data, null, null);
while(true) {
if (data > head.data) {
if (head.right == null) {
head.right = newNode;
break;
} else {
head = head.right;
}
} else {
if (head.left == null) {
head.left = newNode;
break;
} else {
head = head.left;
}
}
}
}
public static void main(String[] args)
{
Node head = createBST(5);
insertIntoBst(head, 7);
insertIntoBst(head, 6);
insertIntoBst(head, 2);
insertIntoBst(head, 1);
insertIntoBst(head, 21);
insertIntoBst(head, 11);
insertIntoBst(head, 14);
insertIntoBst(head, 3);
printKthElement(head, 3);
}
public static int printKthElement(Node head, int k)
{
if (head == null) {
return 0;
}
int leftIndex = printKthElement(head.left, k);
int index = leftIndex + 1;
if (index == k) {
System.out.println(head.data);
} else if (k > index) {
k = k - index;
printKthElement(head.right, k);
} else {
printKthElement(head.left, k);
}
return index;
}
}
This is printing the right answer but multiple times, I figured out why it is printing multiple times but not understanding how to avoid it.
And also If I want to return the node instead of just printing How do I do it?
Can anyone please help me with this?
Objective:
Recursively finding the kth smallest element in a binary search tree and returning the node corresponding to that element.
Observation:
The number of elements smaller than the current element is the size of the left subtree so instead of recursively calculating its size, we introduce a new member in class Node, that is, lsize which represents the size of the left subtree of current node.
Solution:
At each node we compare the size of left subtree with the current value of k:
if head.lsize + 1 == k: current node in our answer.
if head.lsize + 1 > k: elements in left subtree are more than k, that is, the k the smallest element lies in the left subtree. So, we go left.
if head.lsize + 1 < k: the current element alongwith all the elements in the left subtree are less than the kth element we need to find. So, we go to the right subtree but also reduce k by the amount of elements in left subtree + 1(current element). By subtracting this from k we make sure that we have already taken into account the number of elements which are smaller than k and are rooted as the left subtree of current node (including the current node itself).
Code:
class Node {
int data;
Node left;
Node right;
int lsize;
public Node(int data, Node left, Node right) {
this.left = left;
this.data = data;
this.right = right;
lsize = 0;
}
}
public static void insertIntoBst(Node head, int data) {
Node newNode = new Node(data, null, null);
while (true) {
if (data > head.data) {
if (head.right == null) {
head.right = newNode;
break;
} else {
head = head.right;
}
} else {
head.lsize++; //as we go left, size of left subtree rooted
//at current node will increase, hence the increment.
if (head.left == null) {
head.left = newNode;
break;
} else {
head = head.left;
}
}
}
}
public static Node printKthElement(Node head, int k) {
if (head == null) {
return null;
}
if (head.lsize + 1 == k) return head;
else if (head.lsize + 1 > k) return printKthElement(head.left, k);
return printKthElement(head.right, k - head.lsize - 1);
}
Changes:
A new member lsize has been introduced in class Node.
Slight modification in insertIntoBst.
Major changes in printKthElement.
Corner case:
Add a check to ensure that k is between 1 and the size of the tree otherwise a null node will be returned resulting in NullPointerException.
This is working on the test cases I have tried, so far. Any suggestions or corrections are most welcome.
:)
I am reading Binary Trees. while practicing coding problems I came across some solutions where it is asked to find Min Depth of Binary Tree.
Now as per my understanding depth is no of edges from root to node (leaf node in case of leaf nodes / binary tree)
What is the min depth of Binary tree {1,2}
As per my solution it should be 1.
My tested solution
public int minDepth(TreeNode root) {
if(root == null){
return 0;
}
int ldepth = minDepth(root.left);
int rdepth = minDepth(root.right);
if(ldepth == 0){
return 1+rdepth;
}else if(rdepth == 0){
return 1+ldepth;
}
return (1 + Math.min(rdepth, ldepth));
}
Here, we calculate ldepth (minimum left subtree depth) and rdepth (minimum right subtree depth) for a node. Then, if ldepth is zero but rdepth is not, that means current node is not a leaf node, so return 1 + rdepth. If both rdepth and ldepth are zeros then still 'if' condition works as we return 1+0 for current leaf node.
Similar logic for 'else if' branch. In 'return' statement as both 'if' conditions has been failed we return 1 (current node) + minimum value of recursive calls to both left and right branch.
Remember a leaf node has neither left nor right child.
1
/
/
2
so here 2 is the leaf node but 1 is not. so minimum depth for this case is 2 assuming depth of root node is 1.
#include<vector>
#include<iostream>
#include<climits>
using namespace std;
struct TreeNode {
int val;
TreeNode *left;
TreeNode *right;
TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};
class Solution {
public:
int minDepth(TreeNode *root) {
if(root == NULL) return 0;
return getDepth(root);
}
int getDepth(TreeNode *r ){
if(r == NULL) return INT_MAX;
if(r->left == NULL && r->right == NULL)
return 1;
return 1+ min(getDepth(r->left), getDepth(r->right));
}
};
A root node will have a depth of 0, so here depth of the given tree will be 1, refer below recursion and iterative solution to find min dept of binary tree.
Recursive solution :
public static int findMinDepth(BTNode root) {
if (root == null || (root.getLeft() == null && root.getRight() == null)) {
return 0;
}
int ldepth = findMinDepth(root.getLeft());
int rdepth = findMinDepth(root.getRight());
return (Math.min(rdepth + 1, ldepth + 1));
}
Iterative solution :
public static int minDepth(BTNode root) {
int minDepth = Integer.MAX_VALUE;
Stack<BTNode> nodes = new Stack<>();
Stack<BTNode> path = new Stack<>();
if (root == null) {
return -1;
}
nodes.push(root);
while (!nodes.empty()) {
BTNode node = nodes.peek();
if (!path.empty() && node == path.peek()) {
if (node.getLeft() == null && node.getRight() == null && path.size() <= minDepth) {
minDepth = path.size() - 1;
}
path.pop();
nodes.pop();
} else {
path.push(node);
if (node.getRight() != null) {
nodes.push(node.getRight());
}
if (node.getLeft() != null) {
nodes.push(node.getLeft());
}
}
}
return minDepth;
}
The depth o a binary tree is the length of the longest route from the root to the leaf. In my opinion the depth should be 2.
public int minDepth(TreeNode root){
if(root==null)
return 0;
else if(root.left==null && root.right==null)
return 1;
else if(root.left==null)
return 1+minDepth(root.right);
else if(root.right==null)
return 1+minDepth(root.left);
else
return 1+Math.min(minDepth(root.right), minDepth(root.left));
}
As others stated, solution should be 2... But it's semantic, you could simply take result and subtract 1 if your definition of depth is different.
Here's an iterative answer (in C#) (Rajesh Surana answer is a good Recusive answer):
public static int FindMinDepth<T>(BinarySearchTree<T> tree) where T : IComparable<T>
{
var current = tree._root;
int level = 0;
Queue<BSTNode<T>> q = new Queue<BSTNode<T>>();
if (current != null)
q.Enqueue(current);
while (q.Count > 0)
{
level++;
Queue<BSTNode<T>> nq = new Queue<BSTNode<T>>();
foreach (var element in q)
{
if (element.Left == null && element.Right == null)
return level;
if (element.Left != null) nq.Enqueue(element.Left);
if (element.Right != null) nq.Enqueue(element.Right);
}
q = nq;
}
return 0;
//throw new Exception("Min Depth not found!");
}
JavaScript Solution
Given the following Binary Tree structure:
function BT(value, left = null, right = null) {
this.value = value;
this.left = left;
this.right = right;
}
A method to find the minimum depth can be something like so:
BT.prototype.getMinDepth = function() {
if (!this.value) {
return 0;
}
if (!this.left && !this.right) {
return 1;
}
if (this.left && this.right) {
return Math.min(this.left.getMinDepth(), this.right.getMinDepth()) + 1;
}
if (this.left) {
return this.left.getMinDepth() + 1;
}
if (this.right) {
return this.right.getMinDepth() + 1;
}
}
The time complexity of the above solution is O(n) as it traverses all the tree nodes.
A better runtime solution will be to use a breadth traversal method that ends when reaching the first leaf node:
BT.prototype.getMinDepth = function(depth = 0) {
if (!this.value) {
return depth;
}
depth++;
if (!this.left || !this.right) {
return depth;
}
return Math.min(this.left.getMinDepth(depth), this.right.getMinDepth(depth));
}
Given the depth of a path is the number of nodes from the root to the leaf node along this path. The minimum is the path with minimum number of nodes from the root to the LEAF node. In this case, the only leaf node is 2. (A leaf node is defined as a node with no children) Therefore, the only depth and also min depth is 2.
A sample code in Java:
public class Solution {
public int minDepth(TreeNode root) {
if (root==null) return 0;
if ((root.left==null) || (root.right==null)) {
return 1+Math.max(minDepth(root.left),minDepth(root.right));
}
return 1+Math.min(minDepth(root.left),minDepth(root.right));
}
}
Minimum depth is the minimum of the depth of leftsubtree and rightsubtree.
public static int maxDepth(TreeNode root) {
if(root == null) {
return 0;
}
return getDepth(root);
}
private static int getDepth(TreeNode a) {
if(a.left == null & a.right == null) {
return 1;
}
int leftDepth = 0;
int rightDepth = 0;
if(a.left != null) {
leftDepth = getDepth(a.left);
}
if(a.right != null) {
rightDepth = getDepth(a.right);
}
return (Math.min(leftDepth, rightDepth)+1);
}
The minDepth of a binary tree means the shortest distance from the root to a leaf node. Though it is arguable whether the minDepth of your binary tree is 1 or 2, depending on whether you want the shortest distance to a null node, in which case the answer would be 1 OR the shortest distance to a null node whose sibling is ALSO a null node, in which case the answer to Binary tree{1,2} would be 2. Generally, the former is asked, and following the algorithm mentioned in Cracking the Coding Interview , we have the solution as
int minDepth(TreeNode root) {
if (root == null) { return 0;}
return 1 + Math.min(minDepth(root.left), minDepth(root.right));
}
The right pointer can be made to point to the right sibling by performing a level order traversal and changing accordingly. However, i don't know the procedure to do this simultaneously. Any suggestions?
Just do a BFS and remember the level and parent. The following a c++ code for that
void BSTRightSibling(BSTNode *root)
{
queue<BSTNode*> q;
map<BSTNode*, BSTNode*> m;
BSTNode* levelNode = root;
q.push(root);
while(! q.empty()) {
BSTNode* n = q.front();
if (n->left) {
q.push(n->left);
m[n->left] = n;
if (n == levelNode) {
levelNode = n->left;
}
}
if (n->right) {
q.push(n.right);
m[n->right] = n;
if (n == levelNode) {
levelNode = n->right;
}
}
q.pop();
if ((!q.empty()) && (n != levelNode)) {
n->right = q.front();
} else {
n->right = NULL;
}
n->left = m[n];
}
}
In tournament problem you can use a gray-code to decide when its a left or right node. Another method is also if the value is less or equal then the parent value then its a right node.
I need to implement a non-recursive function to determine if a binary tree is balanced or not.
Anyone?
Thanks!!!
Assuming that by "balanced", you mean "height-balanced" in the AVL-tree sense, and you can store arbitrary information for each node,
For each node in post-order,
if either child doesn't exist, assume its respective height is 0.
if the height of both children differs by more than one, the tree is not balanced.
otherwise, this node's height is the larger of both children's heights.
If this point is reached, the tree is balanced.
One way to perform post-order traversal:
start at the root
loop
if this node's left child exists and does not have its height computed, visit its left child next.
else if this node's right child exists and does not have its height computed, visit its right child next.
else
compute this node's height, possibly returning early
if this node is not the root, visit its parent next.
If this point is reached, the tree is balanced.
Try this,
public class BalancedBinaryTree {
public static class TreeNode {
int val;
TreeNode left;
TreeNode right;
TreeNode() {}
TreeNode(int val) { this.val = val; }
TreeNode(int val, TreeNode left, TreeNode right) {
this.val = val;
this.left = left;
this.right = right;
}
}
public boolean isBalanced(TreeNode root) {
if (root==null) {
return true;
}
Stack<TreeNode> stack = new Stack<>();
Map<TreeNode, Integer> map = new HashMap<>();
stack.push(root);
while(!stack.isEmpty()) {
TreeNode node = stack.pop();
if ((node.left==null || (node.left!=null && map.containsKey(node.left))) && (node.right==null || (node.right!=null && map.containsKey(node.right)))) {
int right = (node.right==null) ? 0 : map.get(node.right);
int left = (node.left==null) ? 0 : map.get(node.left);
if (Math.abs(right-left)>1) {
return false;
} else {
map.put(node, Math.max(right, left)+1);
}
} else {
if (node.left!=null && !map.containsKey(node.left)) {
stack.push(node);
stack.push(node.left);
} else {
stack.push(node);
stack.push(node.right);
}
}
}
return true;
}
public static void main(String[] args) {
BalancedBinaryTree b = new BalancedBinaryTree();
boolean v = b.isBalanced(new TreeNode(3, new TreeNode(9), new TreeNode(20, new TreeNode(15), new TreeNode(7))));
System.out.println(v);
v = b.isBalanced(new TreeNode(1, new TreeNode(2, new TreeNode(3, new TreeNode(4), new TreeNode(4)), new TreeNode(3)), new TreeNode(2)));
System.out.println(v);
v = b.isBalanced(new TreeNode(1, new TreeNode(2, new TreeNode(4, new TreeNode(8), null), new TreeNode(5)), new TreeNode(3, new TreeNode(6), null)));
System.out.println(v);
}
}
Here is a c++ code that works, inspired by the postorder traversal. The code is not commented because i do not think a simple comment is enough to explain the whole algorithm. You can execute this code manually with the example below and then you will understand everything.
bool IsBalance(const Node *head)
{
std::stack<const Node *> s;
std::stack<int> sV;
const Node *curr = head, *lastVisit = nullptr;
int deep = 0;
while (curr || !s.empty())
{
while (curr)
{
s.push(curr);
sV.push(-1);
curr = curr->m_pLeft;
}
curr = s.top();
if (sV.top() == -1)
{
sV.top() = deep;
}
if (!curr->m_pRight || curr->m_pRight == lastVisit)
{
if (!curr->m_pRight)
{
deep = 0;
}
if (std::abs(sV.top() - deep) > 1)
{
return false;
}
deep = std::max(sV.top(), deep) + 1;
lastVisit = curr;
s.pop();
sV.pop();
curr = nullptr;
}
else
{
deep = 0;
curr = curr->m_pRight;
}
}
return true;
}
examples:
(1) 21,10,3,1,#,#,5,#,6,#,#,15,12,#,#,18,16,#,#,20,#,#,35,30,22,#,#,#,40,36,#,#,42,#,45,#,#
(2) 1,2,#,4,#,5,#,#,3,6,8,#,#,#,7,#,#
(3) 3,1,#,2,#,#,#
Where nodes are arranged by PreOrder, separated by commas, and # indicates an empty node.
Find the height of left subtree and right subtree for a node of the tree, using Level order traversal and check if that node is balanced.
Repeat this for every node of the tree. For traversing all the nodes we can use level order traversal to avoid recursion.
int height(TreeNode* root){
if(!root){
return 0;
}
queue<TreeNode*> q;
q.push(root);
int count=0;
while(!q.empty()){
int size=q.size();
for(int i=0;i<size;++i){
TreeNode* temp=q.front();
q.pop();
if(temp->left){
q.push(temp->left);
}
if(temp->right){
q.push(temp->right);
}
}
count++;
}
return count;
}
bool checkEveryNode(TreeNode* root){
if(!root){
return true;
}
queue<TreeNode*> q;
q.push(root);
while(!q.empty()){
int count=q.size();
for(int i=0;i<count;++i){
TreeNode* temp=q.front();
q.pop();
int left=height(temp->left);
int right=height(temp->right);
if(abs(left-right)>1){
return false;
}
if(temp->left){
q.push(temp->left);
}
if(temp->right){
q.push(temp->right);
}
}
}
return true;
}
bool isBalanced(TreeNode* root) {
return checkEveryNode(root);
}
Time complexity of this approach is O(n^2), as we need to traverse all the descendant nodes for finding the height of a node(N) and we need to do this for all the nodes(N)
I was wondering if anybody could help me rework this method to find the height of a binary search tree. So far, my code looks like this. However, the answer I'm getting is larger than the actual height by 1. But when I remove the +1 from my return statements, it's less than the actual height by 1. I'm still trying to wrap my head around recursion with these BST. Any help would be much appreciated.
public int findHeight(){
if(this.isEmpty()){
return 0;
}
else{
TreeNode<T> node = root;
return findHeight(node);
}
}
private int findHeight(TreeNode<T> aNode){
int heightLeft = 0;
int heightRight = 0;
if(aNode.left!=null)
heightLeft = findHeight(aNode.left);
if(aNode.right!=null)
heightRight = findHeight(aNode.right);
if(heightLeft > heightRight){
return heightLeft+1;
}
else{
return heightRight+1;
}
}
The problem lies in your base case.
"The height of a tree is the length of the path from the root to the deepest node in the tree. A (rooted) tree with only a node (the root) has a height of zero." - Wikipedia
If there is no node, you want to return -1 not 0. This is because you are adding 1 at the end.
So if there isn't a node, you return -1 which cancels out the +1.
int findHeight(TreeNode<T> aNode) {
if (aNode == null) {
return -1;
}
int lefth = findHeight(aNode.left);
int righth = findHeight(aNode.right);
if (lefth > righth) {
return lefth + 1;
} else {
return righth + 1;
}
}
The height of a binary search tree is equal to number of layers - 1.
See the diagram at http://en.wikipedia.org/wiki/Binary_tree
Your recursion is good, so just subtract one at the root level.
Also note, you can clean up the function a bit by handling null nodes:
int findHeight(node) {
if (node == null) return 0;
return 1 + max(findHeight(node.left), findHeight(node.right));
}
int getHeight(Node node) {
if (node == null) return -1;
return 1 + Math.max(getHeight(node.left), getHeight(node.right));
}
In my opinion, your code would benefit from being simplified a bit. Rather than attempting to end the recursion when a child pointer is null, only end it when the current pointer is null. That makes the code a lot simpler to write. In pseudo-code, it looks something like this:
if (node = null)
return 0;
else
left = height(node->left);
right = height(node->right);
return 1 + max(left, right);
class Solution{
public static int getHeight(Node root) {
int height = -1;
if (root == null) {
return height;
} else {
height = 1 + Math.max(getHeight(root.left), getHeight(root.right));
}
return height;
}
For people like me who like one line solutions:
public int getHeight(Node root) {
return Math.max(root.left != null ? getHeight(root.left) : -1,
root.right != null ? getHeight(root.right) : -1)
+ 1;
}
Here's a concise and hopefully correct way to express it:
private int findHeight(TreeNode<T> aNode){
if(aNode == null || (aNode.left == null && aNode.right == null))
return 0;
return Math.max(findHeight(aNode.left), findHeight(aNode.right)) + 1;
}
If the current node is null, there's no tree. If both children are, there's a single layer, which means 0 height. This uses the definition of height (mentioned by Stephen) as # of layers - 1
This is untested, but fairly obviously correct:
private int findHeight(Treenode<T> aNode) {
if (aNode.left == null && aNode.right == null) {
return 0; // was 1; apparently a node with no children has a height of 0.
} else if (aNode.left == null) {
return 1 + findHeight(aNode.right);
} else if (aNode.right == null) {
return 1 + findHeight(aNode.left);
} else {
return 1 + max(findHeight(aNode.left), findHeight(aNode.right));
}
}
Often simplifying your code is easier than figuring out why it's off by one. This code is easy to understand: the four possible cases are clearly handled in an obviously correct manner:
If both the left and right trees are null, return 0, since a single node by definition has a height of 0. (was 1)
If either the left or right trees (but not both!) are null, return the height of the non-null tree, plus 1 to account for the added height of the current node.
If neither tree is null, return the height of the taller subtree, again plus one for the current node.
public void HeightRecursive()
{
Console.WriteLine( HeightHelper(root) );
}
private int HeightHelper(TreeNode node)
{
if (node == null)
{
return -1;
}
else
{
return 1 + Math.Max(HeightHelper(node.LeftNode),HeightHelper(node.RightNode));
}
}
C# code.
Include these two methods in your BST class. you need two method to calculate height of tree. HeightHelper calculate it, & HeightRecursive print it in main().
The definition given above of the height is incorrect. That is the definition of the depth.
"The depth of a node M in a tree is the length of the path from the root of the tree to M. The height of a tree is one more than the depth of the deepest node in the tree. All nodes of depth d are at level d in the tree. The root is the only node at level 0, and its depth is 0."
Citation: "A Practical Introduction to Data Structures and Algorithm Analysis"
Edition 3.2 (Java Version)
Clifford A. Shaffer
Department of Computer Science
Virginia Tech
Blacksburg, VA 24061
public int height(){
if(this.root== null) return 0;
int leftDepth = nodeDepth(this.root.left, 1);
int rightDepth = nodeDepth(this.root.right, 1);
int height = leftDepth > rightDepth? leftDepth: rightDepth;
return height;
}
private int nodeDepth(Node node, int startValue){
int nodeDepth = 0;
if(node.left == null && node.right == null) return startValue;
else{
startValue++;
if(node.left!= null){
nodeDepth = nodeDepth(node.left, startValue);
}
if(node.right!= null){
nodeDepth = nodeDepth(node.right, startValue);
}
}
return nodeDepth;
}
//function to find height of BST
int height(Node* root) {
if(root == NULL){
return -1;
}
int sum=0;
int rheight = height(root->right);
int lheight = height(root->left);
if(lheight>rheight){
sum = lheight +1;
}
if(rheight > lheight){
sum = rheight + 1;
}
return sum;
}
int height(Node* root) {
if(root==NULL) return -1;
return max(height(root->left),height(root->right))+1;
}
Take of maximum height from left and right subtree and add 1 to it.This also handles the base case(height of Tree with 1 node is 0).
I know that I’m late to the party. After looking into wonderful answers provided here, I thought mine will add some value to this post. Although the posted answers are amazing and easy to understand however, all are calculating the height to the BST in linear time. I think this can be improved and Height can be retrieved in constant time, hence writing this answer – hope you will like it.
Let’s start with the Node class:
public class Node
{
public Node(string key)
{
Key = key;
Height = 1;
}
public int Height { get; set; }
public string Key { get; set; }
public Node Left { get; set; }
public Node Right { get; set; }
public override string ToString()
{
return $"{Key}";
}
}
BinarySearchTree class
So you might have guessed the trick here… Im keeping node instance variable Height to keep track of each node when added.
Lets move to the BinarySearchTree class that allows us to add nodes into our BST:
public class BinarySearchTree
{
public Node RootNode { get; private set; }
public void Put(string key)
{
if (ContainsKey(key))
{
return;
}
RootNode = Put(RootNode, key);
}
private Node Put(Node node, string key)
{
if (node == null) return new Node(key);
if (node.Key.CompareTo(key) < 0)
{
node.Right = Put(node.Right, key);
}
else
{
node.Left = Put(node.Left, key);
}
// since each node has height property that is maintained through this Put method that creates the binary search tree.
// calculate the height of this node by getting the max height of its left or right subtree and adding 1 to it.
node.Height = Math.Max(GetHeight(node.Left), GetHeight(node.Right)) + 1;
return node;
}
private int GetHeight(Node node)
{
return node?.Height ?? 0;
}
public Node Get(Node node, string key)
{
if (node == null) return null;
if (node.Key == key) return node;
if (node.Key.CompareTo(key) < 0)
{
// node.Key = M, key = P which results in -1
return Get(node.Right, key);
}
return Get(node.Left, key);
}
public bool ContainsKey(string key)
{
Node node = Get(RootNode, key);
return node != null;
}
}
Once we have added the key, values in the BST, we can just call Height property on the RootNode object that will return us the Height of the RootNode tree in constant time.
The trick is to keep the height updated when a new node is added into the tree.
Hope this helps someone out there in the wild world of computer science enthusiast!
Unit test:
[TestCase("SEARCHEXAMPLE", 6)]
[TestCase("SEBAQRCHGEXAMPLE", 6)]
[TestCase("STUVWXYZEBAQRCHGEXAMPLE", 8)]
public void HeightTest(string data, int expectedHeight)
{
// Arrange.
var runner = GetRootNode(data);
// Assert.
Assert.AreEqual(expectedHeight, runner.RootNode.Height);
}
private BinarySearchTree GetRootNode(string data)
{
var runner = new BinarySearchTree();
foreach (char nextKey in data)
{
runner.Put(nextKey.ToString());
}
return runner;
}
Note: This idea of keeping the Height of tree maintained in every Put operation is inspired by the Size of BST method found in the 3rd chapter (page 399) of Algorithm (Fourth Edition) book.
I guess this question could mean two different things...
Height is the number of nodes in the longest branch:-
int calcHeight(node* root){
if(root==NULL)
return 0;
int l=calcHeight(root->left);
int r=calcHeight(root->right);
if(l>r)
return l+1;
else
return r+1;
}
Height is the total number of nodes in the tree itself:
int calcSize(node* root){
if(root==NULL)
return 0;
return(calcSize(root->left)+1+calcSize(root->right));
}
public int getHeight(Node node)
{
if(node == null)
return 0;
int left_val = getHeight(node.left);
int right_val = getHeight(node.right);
if(left_val > right_val)
return left_val+1;
else
return right_val+1;
}
Set a tempHeight as a static variable(initially 0).
static void findHeight(Node node, int count) {
if (node == null) {
return;
}
if ((node.right == null) && (node.left == null)) {
if (tempHeight < count) {
tempHeight = count;
}
}
findHeight(node.left, ++count);
count--; //reduce the height while traversing to a different branch
findHeight(node.right, ++count);
}
Here is a solution in Java a bit lengthy but works..
public static int getHeight (Node root){
int lheight = 0, rheight = 0;
if(root==null) {
return 0;
}
else {
if(root.left != null) {
lheight = 1 + getHeight(root.left);
System.out.println("lheight" + " " + lheight);
}
if (root.right != null) {
rheight = 1+ getHeight(root.right);
System.out.println("rheight" + " " + rheight);
}
if(root != null && root.left == null && root.right == null) {
lheight += 1;
rheight += 1;
}
}
return Math.max(lheight, rheight);
}
int getHeight(Node* root)
{
if(root == NULL) return -1;
else return max(getHeight(root->left), getHeight(root->right)) + 1;
}
Here is a solution in C#
private static int heightOfTree(Node root)
{
if (root == null)
{
return 0;
}
int left = 1 + heightOfTree(root.left);
int right = 1 + heightOfTree(root.right);
return Math.Max(left, right);
}
For anyone else that reads this!!!!
HEIGHT is defined as the number of nodes in the longest path from the root node to a leaf node. Therefore: a tree with only a root node has a height of 1 and not 0.
The LEVEL of a given node is the distance from the root plus 1. Therefore: The root is on level 1, its child nodes are on level 2 and so on.
(Information courtesy of Data Structures: Abstraction and Design Using Java, 2nd Edition, by Elliot B. Koffman & Paul A. T. Wolfgang) - Book used in Data Structures Course I am currently taking at Columbus State University.
enter image description here
According to "Introduction to Algorithms" by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein, following is the definition of tree height:
The height of a node in a
tree is the number of edges on the longest simple downward path from the node to
a leaf, and the height of a tree is the height of its root. The height of a tree is also
equal to the largest depth of any node in the tree.
Following is my ruby solution. Most of the people forgot about height of empty tree or tree of single node in their implementation.
def height(node, current_height)
return current_height if node.nil? || (node.left.nil? && node.right.nil?)
return [height(node.left, current_height + 1), height(node.right, current_height + 1)].max if node.left && node.right
return height(node.left, current_height + 1) if node.left
return height(node.right, current_height + 1)
end
int maxDepth(BinaryTreeNode root) {
if(root == null || (root.left == null && root.right == null)) {
return 0;
}
return 1 + Math.max(maxDepth(root.left), maxDepth(root.right));
}
Height of Binary Tree
public static int height(Node root)
{
// Base case: empty tree has height 0
if (root == null) {
return 0;
}
// recursively for left and right subtree and consider maximum depth
return 1 + Math.max(height(root.left), height(root.right));
}
I struggled with this myself trying to find something elegant that still resulted in the correct value. Here's what I came up with using Swift. Note that height is a computed variable and technically not a function.
class Node<T: Comparable>: NSObject
{
var left: Node<T>? = nil
var right: Node<T>? = nil
var isLeaf: Bool { left == nil && right == nil }
var height: Int {
if isLeaf { return 0 }
return 1 + max(left?.height ?? 0, right?.height ?? 0)
}
}
There's more to this Node definition but you can see the left and right variables (possibly nil) and an isLeaf var that is true when both left and right are nil. Might not be the most efficient but I believe it yields the correct result.
The BST definition also has a computed height variable and returns -1 when the tree is empty.
class BST<T: Comparable>: NSObject
{
var root: Node<T>?
var height: Int { root != nil ? root!.height : -1 }
}
HackerRank Day 22: Finding height in Binary Search Tree, in C#.
static int getHeight(Node root)
{
//Write your code here
int countr = 0,countl=0;
Node Leftsubtree=root.left;
Node rightsubtree = root.right;
int data=root.data;
if(root==null ||(root.left == null && root.right == null))
{
return 0;
}
else
{
while (Leftsubtree != null)
{
if(Leftsubtree.data<data)
{
Leftsubtree = Leftsubtree.left==null?Leftsubtree.right:Leftsubtree.left;
countl++;
}
}
while (rightsubtree != null)
{
if (rightsubtree.data > data)
{
rightsubtree = rightsubtree.right == null ? rightsubtree.left : rightsubtree.right;
countr++;
}
}
}
return countr >= countl ? countr : countl;
}