Diameter of Binary Tree.

Find diameter of Binary Tree.


What is Diameter of a Binary Tree?

A longest path or route between any two nodes in a tree is called as Diameter/Width of binary tree.
The diameter of tree may or may not pass through the root.
The diagram below shows two trees each with diameter 7, diameter are shaded with blue nodes.

Diameter of node = height of Left sub tree of node + height of Right sub tree of node + 1 (node itself).

Solution


We will discuss 3 ways of finding diameter of Binary tree. Lets start with simple approach,

1. By using Global variable


In this approach, we will check the diameter of each node of a tree and store it in variable "diameter".
For each node, calculate diameter and if it is larger than static variable "diameter", then update "diameter" otherwise not.
At end of the process, static variable
"diameter" will contain maximum distance between any of two nodes in our binary tree.

2. By computing height and diameter of each node.

In this approach, we will not use the global variable,Instead, we will check, which is maximum between,
1. Diameter of a Node, 
2. Diameter of a left sub tree of Node
3. Diameter of a right sub tree of Node,
Whichever is maximum among this 3, that will be diameter of that node and return it to next recursive call.

At each node of binary tree, above comparison is done and maximum diameter count found at that node will be returned.
In this way, by returning the maximum diameter in each iteration, it will help preserving the maximum diameter found at any node in between the tree.




3. By computing height and diameter of each node in optimized way.


In this approach, Every node will return the two infor­ma­tion in the same iter­a­tion,
1. height of that node and 
2. diam­e­ter of tree with respect to that node.
This way it will save 2 extra iteration that need to be done in Approach 2.

Diameter of Binary Tree in Java (Approach 1)


package tree;

public class FindDiameterOfBinaryTree {

 private Node rootNode;
 private static int maxDiameterTillNow;

 public static void main(String[] args) {
  new FindDiameterOfBinaryTree();
 }

 public FindDiameterOfBinaryTree(){
  addNode(rootNode, 100);
  addNode(rootNode, 90);
  addNode(rootNode, 150);
  addNode(rootNode, 80);
  addNode(rootNode, 95);
  addNode(rootNode, 70);
  addNode(rootNode, 92);
  addNode(rootNode, 60);
  addNode(rootNode, 94);

  getDiameterOfBinaryTreeUsingGlobalVariable(rootNode);
  System.out.println(maxDiameterTillNow);
 }
 
 private int getDiameterOfBinaryTreeUsingGlobalVariable(Node startNode){
  if(startNode==null)
   return 0;

  int leftHeight = getDiameterOfBinaryTreeUsingGlobalVariable(startNode.getLeft()); // Height of Left Subtree
  int rightHeight = getDiameterOfBinaryTreeUsingGlobalVariable(startNode.getRight()); // Height of Right Subtree

  if(leftHeight + rightHeight + 1 > maxDiameterTillNow){ // + 1 for node itself
   maxDiameterTillNow = leftHeight + rightHeight + 1;
  }
  if(leftHeight>rightHeight)
   return leftHeight + 1;
  else
   return rightHeight + 1;
 }

 private void addNode(Node rootNode, int data){
  if(rootNode==null){
   Node temp1 = new Node(data);
   this.rootNode=temp1;
  }else{
   addNodeInProperPlace(rootNode, data);
  }
 }

 private void addNodeInProperPlace(Node rootNode, int data){ 
  if(data>rootNode.getData()){
   if(rootNode.getRight()!=null){
    addNode(rootNode.getRight(), data);
   }else{
    Node temp1 = new Node(data);
    rootNode.setRight(temp1);
   }
  }else if(data<rootNode.getData()){
   if(rootNode.getLeft()!=null){
    addNode(rootNode.getLeft(), data);
   }else{
    Node temp1 = new Node(data);
    rootNode.setLeft(temp1);
   }
  }
 }

}


package tree;

public class Node{
 
 private Node left;
 private Node right;
 private int data;
 
 public Node(int data){
  this.data=data;
 }

 public Node getLeft() {
  return left;
 }

 public void setLeft(Node left) {
  this.left = left;
 }

 public Node getRight() {
  return right;
 }

 public void setRight(Node right) {
  this.right = right;
 }

 public int getData() {
  return data;
 }

 public void setData(int data) {
  this.data = data;
 }
}

Diameter of Binary Tree in Java (Approach 2)


package tree;

public class FindDiameterOfBinaryTree {

 private Node rootNode;

 public static void main(String[] args) {
  new FindDiameterOfBinaryTree();
 }

 public FindDiameterOfBinaryTree(){
  addNode(rootNode, 100);
  addNode(rootNode, 90);
  addNode(rootNode, 150);
  addNode(rootNode, 80);
  addNode(rootNode, 95);
  addNode(rootNode, 70);
  addNode(rootNode, 92);
  addNode(rootNode, 60);
  addNode(rootNode, 94);

  System.out.println(getDiameterOfBinaryTree(rootNode));
 }

 private int getDiameterOfBinaryTree(Node node){
  if(node == null){
   return 0;
  }
  int leftSubtreeHeight = height(node.getLeft());
  int rightSubtreeHeight = height(node.getRight());
  
  int diameterOfNode = leftSubtreeHeight + rightSubtreeHeight + 1;
  
  int leftDiameter = getDiameterOfBinaryTree(node.getLeft());
  int rightDiameter = getDiameterOfBinaryTree(node.getRight());

  return max(diameterOfNode, max(leftDiameter, rightDiameter));
 }
 
 private int height(Node node){
  if( node == null){
   return 0;
  }
  int lHeight = height(node.getLeft());
  int rHeight = height(node.getRight());
  return (max(lHeight , rHeight)+1);
 }
 
 private int max(int a, int b){
  return a > b ? a : b;
 }
 
 private void addNode(Node rootNode, int data){
  if(rootNode==null){
   Node temp1 = new Node(data);
   this.rootNode=temp1;
  }else{
   addNodeInProperPlace(rootNode, data);
  }
 }

 private void addNodeInProperPlace(Node rootNode, int data){ 
  if(data>rootNode.getData()){
   if(rootNode.getRight()!=null){
    addNode(rootNode.getRight(), data);
   }else{
    Node temp1 = new Node(data);
    rootNode.setRight(temp1);
   }
  }else if(data<rootNode.getData()){
   if(rootNode.getLeft()!=null){
    addNode(rootNode.getLeft(), data);
   }else{
    Node temp1 = new Node(data);
    rootNode.setLeft(temp1);
   }
  }
 }

}

Diameter of Binary Tree in Java (Approach 3)


package tree;

public class FindDiameterOfBinaryTree {

 private Node rootNode;

 public static void main(String[] args) {
  new FindDiameterOfBinaryTree();
 }

 public FindDiameterOfBinaryTree(){

  addNode(rootNode, 100);
  addNode(rootNode, 90);
  addNode(rootNode, 150);
  addNode(rootNode, 80);
  addNode(rootNode, 95);
  addNode(rootNode, 70);
  addNode(rootNode, 92);
  addNode(rootNode, 60);
  addNode(rootNode, 94);

  System.out.println(getDiameterOfBinaryTreeOptimizedSolution(rootNode)[0]);
 }
 
 public static int[] getDiameterOfBinaryTreeOptimizedSolution(Node root) {
  
  //0th element is diameter and 1st element is height
  int[] result = new int[]{0,0};        
  
  if (root == null)  
   return result;
  
  int[] leftResult = getDiameterOfBinaryTreeOptimizedSolution(root.getLeft());
  int[] rightResult = getDiameterOfBinaryTreeOptimizedSolution(root.getRight());
  int height = Math.max(leftResult[1], rightResult[1]) + 1;
  
  int rootDiameter = leftResult[1] + rightResult[1] + 1;
  int leftDiameter = leftResult[0];
  int rightDiameter = rightResult[0];
  
  result[0] = Math.max(rootDiameter, Math.max(leftDiameter, rightDiameter));
  result[1] = height;

  return result;
 }

 private void addNode(Node rootNode, int data){
  if(rootNode==null){
   Node temp1 = new Node(data);
   this.rootNode=temp1;
  }else{
   addNodeInProperPlace(rootNode, data);
  }
 }

 private void addNodeInProperPlace(Node rootNode, int data){ 
  if(data>rootNode.getData()){
   if(rootNode.getRight()!=null){
    addNode(rootNode.getRight(), data);
   }else{
    Node temp1 = new Node(data);
    rootNode.setRight(temp1);
   }
  }else if(data<rootNode.getData()){
   if(rootNode.getLeft()!=null){
    addNode(rootNode.getLeft(), data);
   }else{
    Node temp1 = new Node(data);
    rootNode.setLeft(temp1);
   }
  }
 }

}

Enjoy !!!! 

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