Question

1-Write an efficient algorithm to construct a binary tree from given inorder and postorder traversals.(java only).

2- Apply your proposed algorithm in the previous point to construct the binary tree with the following traversals (java code only):

     In order traversal: 9 8 6 1 2 5 4

     Postorder traversal: 9 6 1 8 5 4 2

Answer 1

`Hey,

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import java.util.HashMap;
import java.util.Map;
import java.util.concurrent.atomic.AtomicInteger;

// Data structure to store a Binary Tree node
class Node
{
   int key;
   Node left, right;

   Node(int key) {
       this.key = key;
   }
}

public class Main
{
   // Recursive function to perform inorder traversal of a binary tree
   public static void inorderTraversal(Node root)
   {
       if (root == null) {
           return;
       }

       inorderTraversal(root.left);
       System.out.print(root.key + " ");
       inorderTraversal(root.right);
   }

   // Recursive function to perform postorder traversal of a binary tree
   public static void postorderTraversal(Node root)
   {
       if (root == null) {
           return;
       }

       postorderTraversal(root.left);
       postorderTraversal(root.right);
       System.out.print(root.key + " ");
   }
       // Recursive function to perform postorder traversal of a binary tree
   public static void preorderTraversal(Node root)
   {
       if (root == null) {
           return;
       }
       System.out.print(root.key + " ");

       postorderTraversal(root.left);
       postorderTraversal(root.right);
   }

   // Recursive function to construct a binary tree from
   // inorder and postorder traversals
   public static Node construct(int start, int end,
               int[] postorder, AtomicInteger pIndex,
               Map<Integer,Integer> map)
   {
       // base case
       if (start > end) {
           return null;
       }

       // Consider the next item from the end of given postorder sequence
       // This value would be the root node of subtree formed by inorder[start, end]
       Node root = new Node(postorder[pIndex.getAndDecrement()]);

       // search the index of current node in inorder sequence to determine
       // the boundary of left and right subtree
       int index = map.get(root.key);

       // recursively construct the right subtree
       root.right = construct(index + 1, end, postorder, pIndex, map);

       // recursively construct the left subtree
       root.left = construct(start, index - 1, postorder, pIndex, map);

       // return root node
       return root;
   }

   // Construct a binary tree from inorder and postorder traversals
   // This function assumes that the input is valid
   // i.e. given inorder and postorder sequence forms a binary tree
   public static Node construct(int[] inorder, int[] postorder)
   {
       // get size
       int n = inorder.length;

       // map is used to efficiently find the index of any element in
       // given inorder sequence
       Map<Integer,Integer> map = new HashMap<>();
       for (int i = 0; i < n; i++) {
           map.put(inorder[i], i);
       }

       // pIndex stores the index of next unprocessed node from the end
       // of postorder sequence
       AtomicInteger pIndex = new AtomicInteger(n - 1);
       return construct(0, n - 1, postorder, pIndex, map);
   }

   public static void main(String[] args)
   {

       int[] inorder = { 9,8,6,1,2,5,4 };
       int[] postorder = { 9,6,1,8,5,4,2 };

       Node root = construct(inorder, postorder);

       // traverse the constructed tree
       System.out.print("Inorder   : "); inorderTraversal(root);
       System.out.print("\nPostorder : "); postorderTraversal(root);
       System.out.print("\nPreorder : "); preorderTraversal(root);
   }
}

Chrome File Edit View History Bookmarks People Tab Window Help 23% O Mon 10:38 PM Q M Inbox - gurkaranpree X C 1-Write An Efficient X </> Online Java Complex WhatsApp + C My Q&A | Chegg.con X tutorialspoint.com/compile_java_online.php ... codingground Compile and Execute Java Online (JDK 1.8.0) 0 Fork & Project - Edit Setting & Login SIMPLY EASY CODING L.lt Result BAL $javac Main.java $java -Xmx128M -Xms16M Main Inorder : 9 8 6 1 2 5 4 Postorder : 9 6 1 8 5 4 2 Preorder: 2 9 6 1 8 5 4 } 4. Execute > Share Source File STDIN 82 83 84 85 public static Node construct(int[] inorder, int[] postorder) 86- 87 88 int n = inorder.length; 89 90 indexOfanlement 91 92 Map<Integer, Integer> map = new HashMap(); 93 for (int i = 0; i<n; i++) { 94 map.put(inorder[i], i); 95 96 97 pIndex rocessed node from the end 98 99 AtomicInteger pIndex = new AtomicInteger(n 1); 100 return construct, n - 1, postorder, pIndex, map); 101 102 103 public static void main(String[] args) 104 105 106 int[] inorder { 9,8,6,1,2,5,4 }; 107 into postorder = { 9,6,1,3,5,4,2 }; 108 109 Node root = construct(inorder, postorder); 110 111 112 System.out.print("Inorder : "); inorderTraversal (root); 113 System.out.print("\nPostorder : "); postorderTraversal (root); System.out.print("\nPreorder : "); preorder Traversal (root); 115 my { 114 JUN tv Р wlx] 9

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