<p>Given a binary tree <code>root</code> and a&nbsp;linked list with&nbsp;<code>head</code>&nbsp;as the first node.&nbsp;</p>

<p>Return True if all the elements in the linked list starting from the <code>head</code> correspond to some <em>downward path</em> connected in the binary tree&nbsp;otherwise return False.</p>

<p>In this context downward path means a path that starts at some node and goes downwards.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/02/12/sample_1_1720.png" style="width: 220px; height: 280px;" /></strong></p>

<pre>
<strong>Input:</strong> head = [4,2,8], root = [1,4,4,null,2,2,null,1,null,6,8,null,null,null,null,1,3]
<strong>Output:</strong> true
<strong>Explanation:</strong> Nodes in blue form a subpath in the binary Tree.  
</pre>

<p><strong class="example">Example 2:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/02/12/sample_2_1720.png" style="width: 220px; height: 280px;" /></strong></p>

<pre>
<strong>Input:</strong> head = [1,4,2,6], root = [1,4,4,null,2,2,null,1,null,6,8,null,null,null,null,1,3]
<strong>Output:</strong> true
</pre>

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

<pre>
<strong>Input:</strong> head = [1,4,2,6,8], root = [1,4,4,null,2,2,null,1,null,6,8,null,null,null,null,1,3]
<strong>Output:</strong> false
<strong>Explanation:</strong> There is no path in the binary tree that contains all the elements of the linked list from <code>head</code>.
</pre>

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

<ul>
	<li>The number of nodes in the tree will be in the range <code>[1, 2500]</code>.</li>
	<li>The number of nodes in the list will be in the range <code>[1, 100]</code>.</li>
	<li><code>1 &lt;= Node.val&nbsp;&lt;= 100</code>&nbsp;for each node in the linked list and binary tree.</li>
</ul>

class Solution {
    bool traverseTree(std::vector<int> &kmpPrefix, std::vector<int> &listNums, TreeNode *node, int curIndex = 0) {
        if(curIndex == listNums.size()) return true;
        if(node) {
            // std::cout<<node->val<<", "<<listNums[curIndex]<<", "<<curIndex<<std::endl;
            if(node->val == listNums[curIndex]) {
                return traverseTree(kmpPrefix, listNums, node->right, curIndex + 1) ||
                        traverseTree(kmpPrefix, listNums, node->left, curIndex + 1);
            }
            else {
                curIndex = kmpPrefix[std::max(0, curIndex - 1)];
                if(node->val == listNums[curIndex]) curIndex++;
                return traverseTree(kmpPrefix, listNums, node->right, curIndex) ||
                       traverseTree(kmpPrefix, listNums, node->left, curIndex);
            }
        }
        return false;
    }
public:
    bool isSubPath(ListNode* head, TreeNode* root) {
        /**
         * Use KMP "string" matching to figure out when to restart matching
         */
         std::vector<int> listNums;
         while(head) {
             listNums.push_back(head->val);
             head = head->next;
         }
         std::vector<int> kmpPrefix(listNums.size(), 0);
         for(int i = 1; i < listNums.size(); i++) {
             if(listNums[i] == listNums[kmpPrefix[i - 1]]) kmpPrefix[i] = kmpPrefix[i - 1] + 1;
             else kmpPrefix[i] = 0;
         }
         return traverseTree(kmpPrefix, listNums, root);
    }
};
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