[LeetCode] Find Leaves of Binary Tree 找二叉树的叶节点

Given a binary tree, find all leaves and then remove those leaves. Then repeat the previous steps until the tree is empty.

Example:
Given binary tree

          1
         /         2   3
       / \
      4   5

Returns [4, 5, 3], [2], [1].

Explanation:

1. Remove the leaves [4, 5, 3] from the tree

          1
         /
        2

2. Remove the leaf [2] from the tree

          1

3. Remove the leaf [1] from the tree

          []

Returns [4, 5, 3], [2], [1].

Credits:
Special thanks to @elmirap for adding this problem and creating all test cases.

这道题给了我们一个二叉树，让我们返回其每层的叶节点，就像剥洋葱一样，将这个二叉树一层一层剥掉，最后一个剥掉根节点。那么题目中提示说要用DFS来做，思路是这样的，每一个节点从左子节点和右子节点分开走可以得到两个深度，由于成为叶节点的条件是左右子节点都为空，所以我们取左右子节点中较大值加1为当前节点的深度值，知道了深度值就可以将节点值加入到结果res中的正确位置了，求深度的方法我们可以参见Maximum Depth of Binary Tree中求最大深度的方法，参见代码如下：

解法一：

class Solution {
public:
    vector<vector<int>> findLeaves(TreeNode* root) {
        vector<vector<int>> res;
        helper(root, res);
        return res;
    }
    int helper(TreeNode *root, vector<vector<int>> &res) {
        if (!root) return -1;
        int depth = 1 + max(helper(root->left, res), helper(root->right, res));
        if (depth >= res.size()) res.resize(depth + 1);
        res[depth].push_back(root->val);
        return depth;
    }
};

下面这种DFS方法没有用计算深度的方法，而是使用了一层层剥离的方法，思路是遍历二叉树，找到叶节点，将其赋值为NULL，然后加入leaves数组中，这样一层层剥洋葱般的就可以得到最终结果了：

解法二：

class Solution {
public:
    vector<vector<int>> findLeaves(TreeNode* root) {
        vector<vector<int>> res;
        while (root) {
            vector<int> leaves;
            root = remove(root, leaves);
            res.push_back(leaves);
        }
        return res;
    }
    TreeNode* remove(TreeNode *node, vector<int> &leaves) {
        if (!node) return NULL;
        if (!node->left && !node->right) {
            leaves.push_back(node->val);
            return NULL;
        }
        node->left = remove(node->left, leaves);
        node->right = remove(node->right, leaves);
        return node;
    }
};

类似题目：

Maximum Depth of Binary Tree

Minimum Height Trees

参考资料：

https://leetcode.com/discuss/110406/simple-java-recursive-1ms-solution

https://leetcode.com/discuss/110389/12-lines-simple-java-solution-using-recursion

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