<p>You are given the <code>root</code> of a binary tree.</p>

<p>A ZigZag path for a binary tree is defined as follow:</p>

<ul>
	<li>Choose <strong>any </strong>node in the binary tree and a direction (right or left).</li>
	<li>If the current direction is right, move to the right child of the current node; otherwise, move to the left child.</li>
	<li>Change the direction from right to left or from left to right.</li>
	<li>Repeat the second and third steps until you can&#39;t move in the tree.</li>
</ul>

<p>Zigzag length is defined as the number of nodes visited - 1. (A single node has a length of 0).</p>

<p>Return <em>the longest <strong>ZigZag</strong> path contained in that tree</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/01/22/sample_1_1702.png" style="width: 221px; height: 383px;" />
<pre>
<strong>Input:</strong> root = [1,null,1,1,1,null,null,1,1,null,1,null,null,null,1]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Longest ZigZag path in blue nodes (right -&gt; left -&gt; right).
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/01/22/sample_2_1702.png" style="width: 157px; height: 329px;" />
<pre>
<strong>Input:</strong> root = [1,1,1,null,1,null,null,1,1,null,1]
<strong>Output:</strong> 4
<strong>Explanation:</strong> Longest ZigZag path in blue nodes (left -&gt; right -&gt; left -&gt; right).
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> root = [1]
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 5 * 10<sup>4</sup>]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 100</code></li>
</ul>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */


int solve(TreeNode*node, int dir, vector<vector<int>>&dp){
    if(node == NULL)return 0;
    int key = node->val;

    if(dp[key][dir] != -1)return dp[key][dir];
    int x1 = 0,y1 = 0;

    x1 = solve(node->left, 0,dp);
    y1 = solve(node->left,1,dp);

    int x2 = 0,y2 = 0;
    x2 = solve(node->right,0,dp);
    y2 = solve(node->right,1,dp);
    int ans = 0;

    if(dir == 0){
        if(node->left){
            ans = y1+1;
        }
    }
    else{
        if(node->right){
            ans = x2+1;
        }
    }

    return dp[key][dir] = ans;
}

class Solution {
public:
    int longestZigZag(TreeNode* root) {
        
        queue<TreeNode*>q;
        q.push(root);
        int curr = 0;

        while(!q.empty()){
            TreeNode*temp = q.front();
            temp->val = curr++;
            q.pop();

            if(temp->left != NULL){
                q.push(temp->left);
            }
            if(temp->right != NULL){
                q.push(temp->right);
            }
        }

        vector<vector<int>>dp(curr,vector<int>(2,-1));

        int a = solve(root,0,dp);
        int b = solve(root,1,dp);

        int ans = 0;

        for(int i = 0; i<curr; i++){
            ans = max(ans,max(dp[i][0],dp[i][1]));
        }

        return ans;
    }
};
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