[LeetCode] 1026. Maximum Difference Between Node and Ancestor

[grandyang]

Given the root of a binary tree, find the maximum value V for which there exist different nodes A and B where V = |A.val - B.val| and A is an ancestor of B.

A node A is an ancestor of B if either: any child of A is equal to B, or any child of A is an ancestor of B.

Example 1:

Input: root = [8,3,10,1,6,null,14,null,null,4,7,13]
Output: 7
Explanation: We have various ancestor-node differences, some of which are given below :
|8 - 3| = 5
|3 - 7| = 4
|8 - 1| = 7
|10 - 13| = 3
Among all possible differences, the maximum value of 7 is obtained by |8 - 1| = 7.

Example 2:

Input: root = [1,null,2,null,0,3]
Output: 3

Constraints:

• The number of nodes in the tree is in the range [2, 5000].
• 0 <= Node.val <= 105

这道题给了一棵二叉树，让找某个结点和其祖先结点最大的差的绝对值，题目中给了图很好的说明了两个结点之间的关系。注意这里并不是任意两个结点都可以做差取绝对值，必须一个要是另一个的祖先结点，这刚好符合二叉树的先序遍历的顺序，当遍历到某个结点的时候，该结点的祖先结点都已经遍历过了，但是为了找出最大的差绝对值，我们需要记录当前遍历过的祖先结点中的最大值和最小值，用它们和当前结点值做差并取绝对值，并分别更新结果 res，所以整个操作就可以直接在递归函数中进行了，参见代码如下：

解法一：

class Solution {
public:
    int maxAncestorDiff(TreeNode* root) {
        int res = 0;
        helper(root, root->val, root->val, res);
        return res;
    }
    void helper(TreeNode* node, int mn, int mx, int& res) {
        if (!node) return;
        res = max(res, abs(node->val - mn));
        res = max(res, abs(mx - node->val));
        mn = min(mn, node->val);
        mx = max(mx, node->val);
        helper(node->left, mn, mx, res);
        helper(node->right, mn, mx, res);
    }
};

我们也可以写的更简洁一下，用子函数的返回值当作结果 res，这样就少了一个参数了，参见代码如下：

解法二：

class Solution {
public:
    int maxAncestorDiff(TreeNode* root) {
        return helper(root, root->val, root->val);
    }
    int helper(TreeNode* node, int mn, int mx) {
        if (!node) return mx - mn;
        mn = min(mn, node->val);
        mx = max(mx, node->val);
        return max(helper(node->left, mn, mx), helper(node->right, mn, mx));
    }
};

Github 同步地址:

#1026

参考资料：

https://leetcode.com/problems/maximum-difference-between-node-and-ancestor/

https://leetcode.com/problems/maximum-difference-between-node-and-ancestor/discuss/274654/PythonJava-Recursion

https://leetcode.com/problems/maximum-difference-between-node-and-ancestor/discuss/274610/JavaC%2B%2BPython-Top-Down

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