687. Longest Univalue Path
Description
Given the root
of a binary tree, return the length of the longest path, where each node in the path has the same value. This path may or may not pass through the root.
The length of the path between two nodes is represented by the number of edges between them.
Example 1:
Input: root = [5,4,5,1,1,null,5] Output: 2 Explanation: The shown image shows that the longest path of the same value (i.e. 5).
Example 2:
Input: root = [1,4,5,4,4,null,5] Output: 2 Explanation: The shown image shows that the longest path of the same value (i.e. 4).
Constraints:
- The number of nodes in the tree is in the range
[0, 104]
. -1000 <= Node.val <= 1000
- The depth of the tree will not exceed
1000
.
Solutions
Solution 1: DFS
We design a function $\textit{dfs}(root)$, which represents the longest univalue path length extending downward with the $\textit{root}$ node as one endpoint of the path.
In $\textit{dfs}(root)$, we first recursively call $\textit{dfs}(root.\textit{left})$ and $\textit{dfs}(root.\textit{right})$ to get two return values $\textit{l}$ and $\textit{r}$. These two return values represent the longest univalue path lengths extending downward with the left and right children of the $\textit{root}$ node as one endpoint of the path, respectively.
If the $\textit{root}$ has a left child and $\textit{root}.\textit{val} = \textit{root}.\textit{left}.\textit{val}$, then the longest univalue path length extending downward with the left child of the $\textit{root}$ as one endpoint of the path should be $\textit{l} + 1$; otherwise, this length is $0$. If the $\textit{root}$ has a right child and $\textit{root}.\textit{val} = \textit{root}.\textit{right}.\textit{val}$, then the longest univalue path length extending downward with the right child of the $\textit{root}$ as one endpoint of the path should be $\textit{r} + 1$; otherwise, this length is $0$.
After recursively calling the left and right children, we update the answer to $\max(\textit{ans}, \textit{l} + \textit{r})$, which is the longest univalue path length passing through the $\textit{root}$ with the $\textit{root}$ as one endpoint of the path.
Finally, the $\textit{dfs}(root)$ function returns the longest univalue path length extending downward with the $\textit{root}$ as one endpoint of the path, which is $\max(\textit{l}, \textit{r})$.
In the main function, we call $\textit{dfs}(root)$ to get the answer.
The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ is the number of nodes in the binary tree.
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