Longest ZigZag Path in a Binary Tree in C++

Suppose we have a binary tree root, a ZigZag path for a binary tree is defined as follow −

  • Choose any node in the binary tree and a direction (either right or left).

  • If the current direction is right then moving towards the right child of the current node otherwise move towards the left child.

  • Then change the direction from right to left or vice versa.

  • Repeat the second and third steps until we can't move in the tree.

Here the Zigzag length is defined as the number of nodes visited - 1. (A single node has a length of 0). We have to find the longest ZigZag path contained in that tree. So for example, if the tree is like −

The output will be 3, as (Right, Left, Right)

To solve this, we will follow these steps −

  • Define a method called dfs(), this will take root and leftB

  • if root is null, then return -1

  • if root is only one node in the tree, then return 0

  • leftV := dfs(left of root, true) and rightV := dfs(right of root, false)

  • ret := max of ret and (1 + max of leftV and rightV)

  • if leftB is not 0, then return 1 + rightV, otherwise return 1 + leftV

  • From the main method, set ret := 0

  • call dfs(root, true) and call dfs(root, false)

  • return ret

Example (C++)

Let us see the following implementation to get a better understanding −

 Live Demo

#include <bits/stdc++.h>
using namespace std;
class TreeNode{
   int val;
   TreeNode *left, *right;
   TreeNode(int data){
      val = data;
      left = right = NULL;
void insert(TreeNode **root, int val){
   queue<TreeNode*> q;
      TreeNode *temp = q.front();
         if(val != NULL)
            temp->left = new TreeNode(val);
            temp->left = new TreeNode(0);
         } else {
            if(val != NULL)
               temp->right = new TreeNode(val);
               temp->right = new TreeNode(0);
   TreeNode *make_tree(vector<int> v){
      TreeNode *root = new TreeNode(v[0]);
      for(int i = 1; i<v.size(); i++){
      insert(&root, v[i]);
   return root;
class Solution {
   int ret;
   int dfs(TreeNode* root, bool leftB){
      if(!root) return -1;
      if(!root->left && !root->right) return 0;
      int leftV = dfs(root->left, true);
      int rightV = dfs(root->right, false);
      ret = max(ret, 1 + max(leftV, rightV));
      if(leftB) return 1 + rightV;
         return 1 + leftV;
   int longestZigZag(TreeNode* root) {
      ret = 0;
      dfs(root, true);
      dfs(root, false);
      return ret;
   vector<int> v = {1,NULL,1,1,1,NULL,NULL,1,1,NULL,1,NULL,NULL,NULL,1,NULL,1};
   TreeNode *root = make_tree(v);
   Solution ob;
   cout << (ob.longestZigZag(root));