CreateBinaryTreeFromInorderPreorder.java

package DataStructures.Trees;

import java.util.HashMap;
import java.util.Map;
import DataStructures.Trees.BinaryTree.Node;

/**
 * Approach: Naive Solution: Create root node from first value present in
 * preorder traversal. Look for the index of root node's value in inorder
 * traversal. That will tell total nodes present in left subtree and right
 * subtree. Based on that index create left and right subtree.
 * Complexity:
 * Time: O(n^2) for each node there is iteration to find index in inorder array
 * Space: Stack size = O(height) = O(lg(n))
 *
 * Optimized Solution: Instead of iterating over inorder array to find index of
 * root value, create a hashmap and find out the index of root value.
 * Complexity:
 * Time: O(n) hashmap reduced iteration to find index in inorder array
 * Space: O(n) space taken by hashmap
 *
 */
public class CreateBinaryTreeFromInorderPreorder {
  public static void main(String[] args) {
    test(new Integer[] {}, new Integer[] {}); // empty tree
    test(new Integer[] { 1 }, new Integer[] { 1 }); // single node tree
    test(new Integer[] { 1, 2, 3, 4 }, new Integer[] { 1, 2, 3, 4 }); // right skewed tree
    test(new Integer[] { 1, 2, 3, 4 }, new Integer[] { 4, 3, 2, 1 }); // left skewed tree
    test(new Integer[] { 3, 9, 20, 15, 7 }, new Integer[] { 9, 3, 15, 20, 7 }); // normal tree
  }

  private static void test(final Integer[] preorder, final Integer[] inorder) {
    System.out.println("\n====================================================");
    System.out.println("Naive Solution...");
    BinaryTree root = new BinaryTree(createTree(preorder, inorder, 0, 0, inorder.length));
    System.out.println("Preorder Traversal: ");
    root.preOrder(root.getRoot());
    System.out.println("\nInorder Traversal: ");
    root.inOrder(root.getRoot());
    System.out.println("\nPostOrder Traversal: ");
    root.postOrder(root.getRoot());

    Map<Integer, Integer> map = new HashMap<>();
    for (int i = 0; i < inorder.length; i++) {
      map.put(inorder[i], i);
    }
    BinaryTree optimizedRoot = new BinaryTree(createTreeOptimized(preorder, inorder, 0, 0, inorder.length, map));
    System.out.println("\n\nOptimized solution...");
    System.out.println("Preorder Traversal: ");
    optimizedRoot.preOrder(root.getRoot());
    System.out.println("\nInorder Traversal: ");
    optimizedRoot.inOrder(root.getRoot());
    System.out.println("\nPostOrder Traversal: ");
    optimizedRoot.postOrder(root.getRoot());
  }

  private static Node createTree(final Integer[] preorder, final Integer[] inorder,
                     final int preStart, final int inStart, final int size) {
    if (size == 0) {
      return null;
    }

    Node root = new Node(preorder[preStart]);
    int i = inStart;
    while (preorder[preStart] != inorder[i]) {
      i++;
    }
    int leftNodesCount = i - inStart;
    int rightNodesCount = size - leftNodesCount - 1;
    root.left = createTree(preorder, inorder, preStart + 1, inStart, leftNodesCount);
    root.right = createTree(preorder, inorder, preStart + leftNodesCount + 1, i + 1,
        rightNodesCount);
    return root;

  }

  private static Node createTreeOptimized(final Integer[] preorder, final Integer[] inorder,
                        final int preStart, final int inStart, final int size,
                        final Map<Integer, Integer> inorderMap) {
    if (size == 0) {
      return null;
    }

    Node root = new Node(preorder[preStart]);
    int i = inorderMap.get(preorder[preStart]);
    int leftNodesCount = i - inStart;
    int rightNodesCount = size - leftNodesCount - 1;
    root.left = createTreeOptimized(preorder, inorder, preStart + 1, inStart,
        leftNodesCount, inorderMap);
    root.right = createTreeOptimized(preorder, inorder, preStart + leftNodesCount + 1,
        i + 1, rightNodesCount, inorderMap);
    return root;
  }

}