C++怎么解决每个节点的右向指针问题

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每个节点的右向指针

You are given a perfect binary tree where all leaves are on the same level, and every parent has two children. The binary tree has the following definition:

struct Node {
int val;
Node *left;
Node *right;
Node *next;
}

Populate each next pointer to point to its next right node. If there is no next right node, the next pointer should be set to NULL.

Initially, all next pointers are set to NULL.

Example:

Input: {"$id":"1","left":{"$id":"2","left":"$id":"3","left":null,"next":null,"right":null,"val":4},"next":null,"right":{"$id":"4","left":null,"next":null,"right":null,"val":5},"val":2},"next":null,"right":{"$id":"5","left":{"$id":"6","left":null,"next":null,"right":null,"val":6},"next":null,"right":{"$id":"7","left":null,"next":null,"right":null,"val":7},"val":3},"val":1}

Output: {"$id":"1","left":{"$id":"2","left":{"$id":"3","left":null,"next":{"$id":"4","left":null,"next":{"$id":"5","left":null,"next":{"$id":"6","left":null,"next":null,"right":null,"val":7},"right":null,"val":6},"right":null,"val":5},"right":null,"val":4},"next":{"$id":"7","left":{"$ref":"5"},"next":null,"right":{"$ref":"6"},"val":3},"right":{"$ref":"4"},"val":2},"next":null,"right":{"$ref":"7"},"val":1}

Explanation: Given the above perfect binary tree (Figure A), your function should populate each next pointer to point to its next right node, just like in Figure B.

Note:

• You may only use constant extra space.

• Recursive approach is fine, implicit stack space does not count as extra space for this problem.

这道题实际上是树的层序遍历的应用，可以参考之前的博客 Binary Tree Level Order Traversal，既然是遍历，就有递归和非递归两种方法，最好两种方法都要掌握，都要会写。下面先来看递归的解法，由于是完全二叉树，所以若节点的左子结点存在的话，其右子节点必定存在，所以左子结点的 next 指针可以直接指向其右子节点，对于其右子节点的处理方法是，判断其父节点的 next 是否为空，若不为空，则指向其 next 指针指向的节点的左子结点，若为空则指向 NULL，代码如下：

解法一：

class Solution {
public:
    Node* connect(Node* root) {
        if (!root) return NULL;
        if (root->left) root->left->next = root->right;
        if (root->right) root->right->next = root->next? root->next->left : NULL;
        connect(root->left);
        connect(root->right);
        return root;
    }
};

对于非递归的解法要稍微复杂一点，但也不算特别复杂，需要用到 queue 来辅助，由于是层序遍历，每层的节点都按顺序加入 queue 中，而每当从 queue 中取出一个元素时，将其 next 指针指向 queue 中下一个节点即可，对于每层的开头元素开始遍历之前，先统计一下该层的总个数，用个 for 循环，这样当 for 循环结束的时候，该层就已经被遍历完了，参见代码如下：

解法二：

// Non-recursion, more than constant space
class Solution {
public:
    Node* connect(Node* root) {
        if (!root) return NULL;
        queue<Node*> q;
        q.push(root);
        while (!q.empty()) {
            int size = q.size();
            for (int i = 0; i < size; ++i) {
                Node *t = q.front(); q.pop();
                if (i < size - 1) {
                    t->next = q.front();
                }
                if (t->left) q.push(t->left);
                if (t->right) q.push(t->right);
            }
        }
        return root;
    }
};

我们再来看下面这种碉堡了的方法，用两个指针 start 和 cur，其中 start 标记每一层的起始节点，cur 用来遍历该层的节点，设计思路之巧妙，不得不服啊：

解法三：

// Non-recursion, constant space
class Solution {
public:
    Node* connect(Node* root) {
        if (!root) return NULL;
        Node *start = root, *cur = NULL;
        while (start->left) {
            cur = start;
            while (cur) {
                cur->left->next = cur->right;
                if (cur->next) cur->right->next = cur->next->left;
                cur = cur->next;
            }
            start = start->left;
        }
        return root;
    }
};

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