Construct Binary Tree from Preorder and Inorder
Given preorder and inorder traversal arrays, construct the binary tree.
Output the level-order traversal of the constructed tree, space-separated.
Example:
3,9,20,15,7 9,3,15,20,7
3 9 20 null null 15 7
- The preorder traversal array
[3, 9, 20, 15, 7]represents the order in which nodes are visited: root, left subtree, right subtree. The first element3is the root node. - The inorder traversal array
[9, 3, 15, 20, 7]represents the order in which nodes are visited: left subtree, root, right subtree. This helps to identify the left and right child nodes of the root3, which are9and20respectively. - The left subtree of
3only contains9, and the right subtree of3is constructed from the remaining elements[15, 20, 7]in the inorder array, with20as the root,15as its left child, and7as its right child. - The constructed binary tree is then traversed level-by-level to produce the output:
3(root),9(left child of3),20(right child of3),null(no left child of9),null(no right child of9),15(left child of20),7(right child of20).
Constraints:
- 1 <= len(preorder) == len(inorder) <= 3000
- All values are unique
Background Knowledge
The problem involves constructing a binary tree from given preorder and inorder traversal arrays. To tackle this, it's essential to understand the concepts of tree traversals. In a preorder traversal, we visit the root node first, then recursively traverse the left subtree, and finally the right subtree. On the other hand, in an inorder traversal, we visit the left subtree, then the root node, and finally the right subtree. These traversal techniques are fundamental in tree data structures.
Understanding the properties of binary trees is also crucial. A binary tree is a tree data structure in which each node has at most two children, referred to as the left child and the right child. The root node is the topmost node in the tree. The height of a tree is the number of edges on the longest path from the root to a leaf node. Familiarity with tree-related terminology, such as node, edge, leaf node, and internal node, will help in visualizing and solving the problem.
To construct a binary tree from the given traversals, we need to identify the root node and then recursively construct the left and right subtrees. This process involves finding the correct positions of nodes in the inorder traversal based on the preorder traversal. The relationship between the preorder and inorder traversals will be key in solving this problem. We will use this relationship to identify the root node and the boundaries of the left and right subtrees in the inorder traversal.
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