<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>


// Custom hash function for pair<TreeNode*, bool>
struct PairHash {
    template <class T1, class T2>
    size_t operator()(const pair<T1, T2>& p) const {
        auto hash1 = hash<T1>{}(p.first);
        auto hash2 = hash<T2>{}(p.second);
        return hash1 ^ hash2;
    }
};

class Solution {
    unordered_map<pair<TreeNode*, bool>, int, PairHash> mp;
    
public:
    int zigZag(TreeNode* node, bool dirxn) {
        if (node == nullptr) return 0;
        if (mp.find({node, dirxn}) != mp.end()) {
            return mp[{node, dirxn}];
        }
        int path1 = 0, path2 = 0;
        if (dirxn) // dirxn is true, go to the right
            path1 = zigZag(node->right, false);
        else       // dirxn is false, go to the left
            path2 = zigZag(node->left, true);
        return mp[{node, dirxn}] = max(path1, path2) + 1;
    }

    int traverse(TreeNode* root) {
        if (root == nullptr) return 0;
        int leftPart = traverse(root->left);
        int rightPart = traverse(root->right);
        
        int ans = zigZag(root->left, true);
        int ans2 = zigZag(root->right, false);
        return max({leftPart, rightPart, ans, ans2});
    }

    int longestZigZag(TreeNode* root) {
        return traverse(root);
    }
};

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