LeetCode C++ 109. Convert Sorted List to Binary Search Tree【DFS/Linked List】中等

Given the head of a singly linked list where elements are sorted in ascending order, convert it to a height balanced BST.

For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1 .

Example 1:

Input: head = [-10,-3,0,5,9]
Output: [0,-3,9,-10,null,5]
Explanation: One possible answer is [0,-3,9,-10,null,5], which represents the shown height balanced BST.

Example 2:

Input: head = []
Output: []

Example 3:

Input: head = [0]
Output: [0]

Example 4:

Input: head = [1,3]
Output: [3,1]

Constraints:

• The numner of nodes in head is in the range [0, 2 * 10^4] .
• -10^5 <= Node.val <= 10^5

题意：给出一个升序有序的单链表，将其转换成高度平衡的二叉搜索树。

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思路：双指针+递归。两个指针，一快一慢，快的每次走两步，慢的每次走一步，当快指针遍历结束时，慢指针指向的也就是链表的中间位置，将其作为二叉搜索树当前结点的值。然后递归左右链表形成左右子树。注意：需要断开左右链表！

代码：

class Solution {
public:
    TreeNode* sortedListToBST(ListNode* head) { 
        if(!head) return nullptr; 
        if(!head->next) return new TreeNode(head->val); 
		//找到链表的中点slow
        ListNode *slow = head, fast = head, prev = head;
        while(fast && fast->next){
            fast = fast->next->next;
            slow = slow->next;
        }
        //prev指向中间位置的前一个结点
        while(prev->next != slow)
            prev = prev->next; 
        //将中点左边的链表分开
        prev->next = nullptr;
        //递归建立子树     
        root = new TreeNode(slow->val); 
        root->left = sortedListToBST(head);
        root->right = sortedListToBST(slow->next); 
        return root; 
    } 
};

如果将寻找中点和前一个结点的过程结合起来，代码如下：

class Solution {
public:
    TreeNode* sortedListToBST(ListNode* head) {
        if (head == nullptr) return nullptr;
        if (head->next == nullptr) return new TreeNode(head->val);
        //leftEnd指向mid的前一个结点, mid指向第二个结点
        //按照快指针的走法, midNext此时应到第三个结点
        ListNode *leftEnd = head, *mid = head->next, *midNext = mid->next;
        while (midNext && midNext->next) {
            leftEnd = leftEnd->next;
            mid = mid->next; 
            midNext = midNext->next->next;
        }
        leftEnd->next = nullptr;
        TreeNode *root = new TreeNode(mid->val);
        root->left = sortedListToBST(head);
        root->right = sortedListToBST(mid->next);
        return root;
    }
};

效率：

执行用时：28 ms, 在所有 C++ 提交中击败了99.82% 的用户
内存消耗：24.1 MB, 在所有 C++ 提交中击败了100.00% 的用户