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：

      1
     / \
    2   3
   / \     
  4   5    

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

Note：

The length of path between two nodes is represented by the number of edges between them.

解釋下題目：

找到一棵樹里的最長路徑，該路徑可能不經過根節點

1. 遞歸

實際耗時：0ms

int globalMax = 0;

public int diameterOfBinaryTree(TreeNode root) {
    helper(root);
    return globalMax;
}

private int helper(TreeNode root) {
    if (root == null) {
        return 0;
    } else {
        int left = helper(root.left);
        int right = helper(root.right);
        globalMax = Math.max(globalMax, left + right);
        return Math.max(left, right) + 1;
    }
}

??思路其實跟尋找最深子樹是一樣的，只不過多了一個全局變量用來記錄一下最長的距離而已。

時間復雜度O(n) n為節點數，因為每個節點我們只訪問了一次。

空間復雜度O(n) n為節點數，因為每個節點我們只訪問了一次。