Longest ZigZag Path in a Binary Tree

class Solution {
public:
    int maxLength = 0;
    void zigzagSearch(TreeNode* current, bool moveLeft, int length) {
        if (current == nullptr) {
            return;
        }
        maxLength = max(maxLength, length);
        if (moveLeft) {
            zigzagSearch(current->left, false, length + 1);
            zigzagSearch(current->right, true, 1);
        } else {
            zigzagSearch(current->left, false, 1);
            zigzagSearch(current->right, true, length + 1);
        }
    }

    int findLongestZigZag(TreeNode* start) {
        zigzagSearch(start, true, 0);
        return maxLength;
    }
};

The provided C++ code defines a solution for finding the longest ZigZag path in a binary tree. The code is encapsulated in a class named Solution which contains the following components:

• An integer member variable maxLength initialized to 0 which serves to store the maximum length of the zigzag path found.
• A recursive function zigzagSearch that performs the main logic to explore the paths in the zigzag manner. This function accepts a TreeNode* indicating the current node, a boolean moveLeft to determine the direction of the movement (left or right), and an integer length which keeps the current length of the zigzag path.
  • The recursive function checks if the current node is nullptr, and if so, it returns immediately as there is no more path to explore.
  • It updates the maxLength with the maximum of its current value and length.
  • Depending on the direction of the movement (stored in moveLeft), it recursively calls itself to continue the exploration either leftward or rightward, appropriately toggling the direction and adjusting the path length.
• Another function findLongestZigZag initializes the zigzag search from a start node. It calls zigzagSearch starting with a movement directed right and a path length of 0. This function ultimately returns the maxLength, representing the length of the longest ZigZag path found in the tree.

To utilize this solution, instantiate the Solution class and call findLongestZigZag function passing the root node of your binary tree as an argument. This approach employs depth-first search techniques combined with specific direction toggling to effectively identify and measure the longest zigzag path available in the given binary tree.

class Solution {
    int maxPath = 0;

    private void zigzagDFS(TreeNode current, boolean leftDirection, int length) {
        if (current == null) {
            return;
        }
        maxPath = Math.max(maxPath, length);
        if (leftDirection) {
            zigzagDFS(current.left, false, length + 1);
            zigzagDFS(current.right, true, 1);
        } else {
            zigzagDFS(current.left, false, 1);
            zigzagDFS(current.right, true, length + 1);
        }
    }

    public int longestZigZag(TreeNode root) {
        zigzagDFS(root, true, 0);
        return maxPath;
    }
}

This Java solution addresses the problem of finding the longest ZigZag path in a binary tree. The solution uses a Depth-First Search (DFS) strategy to traverse the tree and keep track of the path length.

• The Solution class contains an integer maxPath to store the maximum length of a ZigZag path found during the DFS traversal.
• Within the zigzagDFS method:
  • Check for a null node to handle the base case where the traversal reaches a leaf node's child.
  • Update maxPath with the maximum value between the current maxPath and the current length.
  • Continue the DFS traversal by choosing the alternate direction each time. If the current direction is left (leftDirection is true), the next recursive call for the left child will switch to right, and vice versa.
• The longestZigZag method starts the DFS with the root node with an initial direction of true and length 0.
• Returns the maxPath value after completing the DFS, providing the length of the longest ZigZag path found.

By precisely switching directions during the recursive calls and checking all possible paths, this algorithm effectively finds the longest ZigZag path in the binary tree.

class Solution:
    def findMaxZigZag(self, rootNode: Optional[TreeNode]) -> int:
        self.maxLength = 0
        
        def traverseAndCalculate(node, isLeft, length):
            if node:
                self.maxLength = max(self.maxLength, length)
                if isLeft:
                    traverseAndCalculate(node.left, False, length + 1)
                    traverseAndCalculate(node.right, True, 1)
                else:
                    traverseAndCalculate(node.left, False, 1)
                    traverseAndCalculate(node.right, True, length + 1)
        
        traverseAndCalculate(rootNode, True, 0)
        return self.maxLength

The provided Python solution introduces a method to find the longest ZigZag path in a binary tree. The ZigZag path is identified by alternating directions at each node from left to right or right to left. Here's an outline of how the solution works:

• Initiate a Solution class with the method findMaxZigZag, which takes rootNode, the root node of the binary tree, as its input.

• Define a local variable maxLength within the findMaxZigZag method to store the length of the longest ZigZag path found during tree traversal.

• A helper nested function traverseAndCalculate is defined to handle node traversal and ZigZag path length calculation. This function takes three parameters:

  • node: the current node being processed.
  • isLeft: a boolean indicating if the last move was to the left (False indicates a movement to the right).
  • length: the current length of the path.

• Within traverseAndCalculate, if the current node exists:

  • Update the maxLength if the current path length is longer than any previously recorded path.
  • Depending on the direction from the parent node (isLeft), recursively call traverseAndCalculate for both children of the current node, adjusting the path length and direction appropriately.

• Initiate the traversal by calling traverseAndCalculate with the rootNode, setting isLeft to True (assuming an initial move from left), and length to 0, indicating the start of path calculation.

• The method finally returns maxLength, which now holds the length of the longest ZigZag path in the tree.

This Python function is efficient in finding the longest ZigZag path by performing a depth-first search approach, updating the maximum length encountered via the nested helper function. This approach ensures that each node is visited once, maintaining optimal time complexity proportional to the number of nodes in the binary tree.