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# 543 Diameter of Binary Tree

## 543. Diameter of Binary Tree

## 1. Question

Given a binary tree, you need to compute the length of the diameter of the tree. The diameter of a binary tree is the length of the **longest** path between any two nodes in a tree. This path may or may not pass through the root.

**Example:**\
Given a binary tree

```
          1
         / \
        2   3
       / \     
      4   5
```

Return **3**, which is the length of the path \[4,2,1,3] or \[5,2,1,3].

## 2. Implementation

**(1) DFS**

```java
class Solution {
    public int diameterOfBinaryTree(TreeNode root) {
        int[] max = new int[1];
        getMaxDepth(root, max);
        return max[0];
    }

    public int getMaxDepth(TreeNode node, int[] max) {
        if (node == null) {
            return 0;
        }

        int maxLeftDepth = getMaxDepth(node.left, max);
        int maxRightDepth = getMaxDepth(node.right, max);

        max[0] = Math.max(max[0], maxLeftDepth + maxRightDepth);

        return 1 + Math.max(maxLeftDepth, maxRightDepth);
    }
}
```

## 3. Time & Space Complexity

**DFS:** 时间复杂度: O(n), 空间复杂度: O(h)