Create a binary tree from inorder and preorder traversal given in array form (Fixes: TheAlgorithms#2707) (TheAlgorithms#2710)

Co-authored-by: Amit Kumar <[email protected]>

Author: kumanoit

DataStructures/Trees/BinaryTree.java

@@ -22,7 +22,7 @@ public class BinaryTree {
    *
    * @author Unknown
    */
-  class Node {
+  static class Node {
     /** Data for the node */
     public int data;
     /** The Node to the left of this one */
@@ -53,6 +53,11 @@ public BinaryTree() {
     root = null;
   }
 
+  /** Parameterized Constructor */
+  public BinaryTree(Node root) {
+    this.root = root;
+  }
+
   /**
    * Method to find a Node with a certain value
    *

DataStructures/Trees/CreateBinaryTreeFromInorderPreorder.java

@@ -0,0 +1,95 @@
+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;
+  }
+
+}