[LeetCode] Diameter of Binary Tree 二叉树的直径

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 longestpath 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].

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

这道题让我们求二叉树的直径，并告诉了我们直径就是两点之间的最远距离，根据题目中的例子也不难理解题意。我们再来仔细观察例子中的那两个最长路径[4,2,1,3] 和 [5,2,1,3]，我们转换一种角度来看，是不是其实就是根结点1的左右两个子树的深度之和再加1呢。那么我们只要对每一个结点求出其左右子树深度之和，再加上1就可以更新结果res了。为了减少重复计算，我们用哈希表建立每个结点和其深度之间的映射，这样某个结点的深度之前计算过了，就不用再次计算了，参见代码如下：

解法一：

class Solution {
public:
int diameterOfBinaryTree(TreeNode* root) {
if (!root) return 0;
int res = getHeight(root->left) + getHeight(root->right);
return max(res, max(diameterOfBinaryTree(root->left), diameterOfBinaryTree(root->right)));
}
int getHeight(TreeNode* node) {
if (!node) return 0;
if (m.count(node)) return m[node];
int h = 1 + max(getHeight(node->left), getHeight(node->right));
return m[node] = h;
}

private:
unordered_map<TreeNode*, int> m;
};

上面的方法貌似有两个递归函数，其实我们只需要用一个递归函数就可以了，我们再求深度的递归函数中顺便就把直径算出来了，而且貌似不用进行优化也能通过OJ，参见代码如下：

解法二：

class Solution {
public:
int diameterOfBinaryTree(TreeNode* root) {
int res = 0;
maxDepth(root, res);
return res;
}
int maxDepth(TreeNode* node, int& res) {
if (!node) return 0;
int left = maxDepth(node->left, res);
int right = maxDepth(node->right, res);
res = max(res, left + right);
return max(left, right) + 1;
}
};

虽说不用进行优化也能通过OJ，但是毕竟还是优化一下好一点啊，参见代码如下：

解法三：

class Solution {
public:
int diameterOfBinaryTree(TreeNode* root) {
int res = 0;
maxDepth(root, res);
return res;
}
int maxDepth(TreeNode* node, int& res) {
if (!node) return 0;
if (m.count(node)) return m[node];
int left = maxDepth(node->left, res);
int right = maxDepth(node->right, res);
res = max(res, left + right);
return m[node] = (max(left, right) + 1);
}

private:
unordered_map<TreeNode*, int> m;
};

参考资料：

https://discuss.leetcode.com/topic/83456/java-solution-maxdepth

https://discuss.leetcode.com/topic/83569/543-diameter-of-binary-tree-c-_recursive_with-brief-explanation

LeetCode All in One 题目讲解汇总(持续更新中...)