> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/trees/linked-list-in-binary-tree.md).

# Linked List in Binary Tree

Given a binary tree `root` and a linked list with `head` as the first node. 

Return True if all the elements in the linked list starting from the `head` correspond to some *downward path* connected in the binary tree otherwise return False.

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

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/02/12/sample_1_1720.png)

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

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/02/12/sample_2_1720.png)

```
Input: head = [1,4,2,6], root = [1,4,4,null,2,2,null,1,null,6,8,null,null,null,null,1,3]
Output: true
```

**Example 3:**

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

**Constraints:**

* `1 <= node.val <= 100` for each node in the linked list and binary tree.
* The given linked list will contain between `1` and `100` nodes.
* The given binary tree will contain between `1` and `2500` nodes.

```java
class Solution {
    // Brute Force O(M*N)
    public boolean isSubPath(ListNode head, TreeNode root) {
        if (head == null)
            return true;
        if (root == null)
            return false;
        return dfs(head, root) || isSubPath(head, root.left) || isSubPath(head, root.right);
    }

    private boolean dfs(ListNode head, TreeNode root) {
        if (head == null)
            return true;
        if (root == null)
            return false;
        return head.val == root.val && (dfs(head.next, root.left) || dfs(head.next, root.right));
    }

    // KMP Solution
    int[] needle, lps;

    public boolean isSubPath(ListNode head, TreeNode root) {
        needle = convertLinkedListToArray(head);
        lps = computeKMPTable(needle);
        return kmpSearch(root, 0);
    }

    boolean kmpSearch(TreeNode i, int j) {
        if (j == needle.length)
            return true;
        if (i == null)
            return false;
        while (j > 0 && i.val != needle[j])
            j = lps[j - 1];
        if (i.val == needle[j])
            j++;
        return kmpSearch(i.left, j) || kmpSearch(i.right, j);
    }

    int[] computeKMPTable(int[] pattern) {
        int n = pattern.length;
        int[] lps = new int[n];
        for (int i = 1, j = 0; i < n; i++) {
            while (j > 0 && pattern[i] != pattern[j])
                j = lps[j - 1];
            if (pattern[i] == pattern[j])
                lps[i] = ++j;
        }
        return lps;
    }

    int[] convertLinkedListToArray(ListNode head) {
        List<Integer> list = new ArrayList<>();
        while (head != null) {
            list.add(head.val);
            head = head.next;
        }
        int[] arr = new int[list.size()];
        for (int i = 0; i < list.size(); i++)
            arr[i] = list.get(i);
        return arr;
    }
}
```


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