Construct a binary tree from given Inorder and Level Order Traversal

Objective: Given a inorder and level order traversal, construct a binary tree from that.

Input: Inorder and level order traversal

Approach:

int[] inOrder = { 4, 2, 5, 1, 6, 3, 7 };
int[] levelOrder = { 1, 2, 3, 4, 5, 6, 7 };
  • First element in the levelorder [] will be the root of the tree, here it is 1.
  • Now the search ele­ment 1 in inorder[], say you find it at posi­tion i, once you find it, make note of ele­ments which are left to i (this will con­struct the left­sub­tree) and ele­ments which are right to i ( this will con­struct the rightSubtree).
  • Suppose in previous step, there are X number of elements which are left of ‘i’ (which will construct the leftsubtree), but these X elements will not be in the consecutive in levelorder[] so we will extract these elements from levelorder[] by maintaining their sequence and store it in an array say newLeftLevel[].
  • Similarly if there are Y number of elements which are right of ‘i’ (which will construct the rightsubtree), but these Y elements will not be in the consecutive in levelorder[] so we will extract these elements from levelorder[] by maintaining their sequence and store it in an array say newRightLevel[].
  • From previous two steps construct the left and right subtree and link it to root.left and root.right respectively by making recursive calls using newLeftLevel[] and newRightLevel[].
  • See the picture for better explanation.
Construct-a-binary-tree-from-given-Inorder-and-Level-Order-Traversal

Construct-a-binary-tree-from-given-Inorder-and-Level-Order-Traversal

Complete Code:


Output:

inorder traversal of constructed tree : 
  4  2  5  1  6  3  7

7 Responses

  1. Holden says:

    Great explanation! Thank you 🙂

  2. Jayesh says:

    Nicely explained. What is the time complexity of program?

    • tutorialhorizon says:

      Worst case it would be O(n^3) . extracting the elements in level order[] would be O(n^2) and one traversal for inorder[]. I will update the post. Thanks Jayesh.

      • Jayesh says:

        I have one question. might be silly but would like to understand how Worst case time complexity would
        be O(n^3)? what I am getting is O(n^2). one traversal for inorder[] doesn’t make it O(n^3).

        • tutorialhorizon says:

          Inorder traversal takes O(n) time and for each node traversal we are constructing new levelorder[] which takes O(n^2) time so total it takes O(n^3). Please correct me if I m wrong.

  3. Shiva says:

    Any better algorithm available?

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