Construct Binary Tree from Preorder and Postorder Traversal

class Solution {
public:
    TreeNode* buildFromPrePost(vector<int>& pre, vector<int>& post) {
        int prePos = 0;
        int postPos = 0;
        return build(prePos, postPos, pre, post);
    }
    
private:
    TreeNode* build(int& prePos, int& postPos, vector<int>& pre, vector<int>& post) {
        TreeNode* node = new TreeNode(pre[prePos]);
        prePos++;
            
        if (node->val != post[postPos]) {
            node->left = build(prePos, postPos, pre, post);
        }
    
        if (node->val != post[postPos]) {
            node->right = build(prePos, postPos, pre, post);
        }
            
        postPos++;
            
        return node;
    }
};

The provided C++ solution describes the process of constructing a binary tree from its preorder and postorder traversal sequences. The buildFromPrePost function serves as the entry point and internally utilizes a helper function build for recursive tree construction.

Here's a breakdown of the approach:

• Use two vectors pre and post representing the preorder and postorder traversal sequences of the binary tree, respectively.

• Start by defining initial positions, prePos and postPos, to keep track of the current node in the construction process and initiate recursive tree building.

• The helper function build performs the following:

  • First, create a new TreeNode with the current value from the preorder sequence.
  • Increment the prePos to move to the next element for subsequent recursive calls.
  • Check if the value at the current prePos does not match the corresponding value in post at postPos to decide if it should recursively create and attach the left child to the current node.
  • Similarly, recheck the condition to decide for the right child. This is essential as the second condition ensures the correct formation of the tree structure respecting both traversals.
  • Upon completion of children assignments, increment postPos to signify that the node and its children have been fully constructed according to the postorder sequence.

This logic efficiently reconstructs the binary tree uniquely determined by the given preorder and postorder lists, assuming no duplicated elements are present. The algorithm utilizes recursion anchored by traversal position tracking to progressively build each node and attach appropriate children until the traversals are fully represented in the tree structure.

class Solution {
    
    private int indexPre = 0;
    private int indexPost = 0;
    
    public TreeNode buildFromPreAndPost(int[] pre, int[] post) {
        return buildTree(pre, post);
    }
    
    private TreeNode buildTree(int[] pre, int[] post) {
        TreeNode node = new TreeNode(pre[indexPre++]);
    
        if (node.val != post[indexPost]) {
            node.left = buildTree(pre, post);
        }
    
        if (node.val != post[indexPost]) {
            node.right = buildTree(pre, post);
        }
    
        indexPost++;
        return node;
    }
}

In the provided Java solution, you construct a binary tree based on given preorder and postorder traversal arrays. The computation leverages a recursive approach for construction. Here's a concise summary of how this code works:

• A TreeNode class needs to be available, which is not shown in the snippet but it generally contains the structure for a binary tree node (int val, TreeNode left, TreeNode right).

• The class Solution contains:

  • Two private instance variables, indexPre and indexPost, initialized at 0. These act as pointers to keep track of the current indices in the preorder and postorder traversal arrays respectively.

  • The buildFromPreAndPost method as a public entry point which directly calls buildTree using the provided preorder and postorder traversal arrays.

  • The buildTree method creates nodes as it recursively parses the traversal arrays:

    • A new TreeNode is instantiated using the current value in preorder indexed by indexPre, which is then incremented.
    • As long as the value of the current node doesn’t match the value at the current postorder index, the left child is recursively populated.
    • The same process checks and assigns the right child (if the values still do not match).
    • After setting potential left and right children, indexPost is incremented.

• The tree construction ends when all elements from the preorder and postorder traversal arrays are used up, ensuring the indices indexPre and indexPost facilitate correct placement of nodes based on both ordering constraints.

With this structure, ensure the implementation of the TreeNode class aligns with this logic, and the approach will correctly build the binary tree from the preorder and postorder traversals. This method balances efficient tree construction while correctly adhering to the constraints intrinsic to the specified tree traversals.

class Solution:
    def __init__(self):
        self.preorder_index = 0
        self.postorder_index = 0
    
    # Helper function to recursively construct the binary tree
    def buildTreeFromPrePost(
        self, preorder: List[int], postorder: List[int]
    ) -> Optional[TreeNode]:
        return self._build_tree(preorder, postorder)
    
    def _build_tree(
        self, preorder: List[int], postorder: List[int]
    ) -> Optional[TreeNode]:
        node = TreeNode(preorder[self.preorder_index])
        self.preorder_index += 1
    
        # Recursively build the left subtree unless the current root is 
        # at the end of its subtree in postorder list
        if node.val != postorder[self.postorder_index]:
            node.left = self._build_tree(preorder, postorder)
    
        # Recursively build the right subtree unless the current root is 
        # at the end of its subtree in postorder list.
        if node.val != postorder[self.postorder_index]:
            node.right = self._build_tree(preorder, postorder)
    
        # Indicate this node and its subtree are fully constructed
        self.postorder_index += 1
        return node

You can construct a binary tree from preorder and postorder traversal using Python3 by implementing a recursive strategy. Begin by initializing class variables to track the indexes during traversal, then use these indexes to build the tree node by node.

• Define a main function buildTreeFromPrePost that begins the recursive construction.

• Implement the recursive helper functionality _build_tree which:

  1. Creates the current tree node from the preorder list using the current index.
  2. Increment the preorder index.
  3. Recursively constructs the left subtree if the current node value does not match the current postorder value.
  4. Recursively constructs the right subtree under the same condition.
  5. After constructing left and right subtrees, increments the postorder index to move to the next subtree root.
  6. Returns the constructed node, which will recursively build up to the complete tree.

This approach effectively leverages the properties of tree traversals: preorder for root identification and postorder for children completion checks, iterating until the entire tree is reconstructed. Each recursive call handles a node construction, and the tree grows as the stack unwinds, piecing together left and right children.