Recover Binary Search Tree

描述

Two elements of a binary search tree (BST) are swapped by mistake.

Recover the tree without changing its structure.

Note: A solution using O(n) space is pretty straight forward. Could you devise a constant space solution?

分析

O(logn)空间的解法是，中序递归遍历，用两个指针存放在遍历过程中碰到的两处逆向的位置。

本题要求O(1)空间，只能用 Morris 中序遍历。

中序遍历，递归方式

Java

// Recover Binary Search Tree
// 中序遍历,递归
// 时间复杂度O(n)，空间复杂度O(logn)
// 本代码仅仅是为了帮助理解题目
public class Solution {
    private TreeNode p1 = null;
    private TreeNode p2 = null;
    private TreeNode prev = null;

    public void recoverTree(TreeNode root) {
        inOrder( root);
        // swap
        int tmp = p1.val;
        p1.val = p2.val;
        p2.val = tmp;
    }

    private void inOrder(TreeNode root) {
        if ( root ==  null ) return;
        if ( root.left != null ) inOrder(root.left);

        if ( prev != null && root.val < prev.val ) {
            if ( p1 == null) {
                p1 = prev;
                p2 = root;
            } else {
                p2 = root;
            }
        }
        prev = root;
        if ( root.right != null ) inOrder(root.right);
    }
}

C++

// Recover Binary Search Tree
// 中序遍历,递归
// 时间复杂度O(n)，空间复杂度O(logn)
// 本代码仅仅是为了帮助理解题目
class Solution {
public:
    void recoverTree(TreeNode *root) {
        inOrder( root);
        swap(p1->val, p2->val);
    }
private:
    void inOrder(TreeNode *root) {
        if ( root ==  nullptr ) return;
        if ( root->left != nullptr ) inOrder(root->left);

        if ( prev != nullptr && root->val < prev->val ) {
            if ( p1 == nullptr) {
                p1 = prev;
                p2 = root;
            } else {
                p2 = root;
            }
        }
        prev = root;
        if ( root->right != nullptr ) inOrder(root->right);
    }
    TreeNode *p1 = nullptr;
    TreeNode *p2 = nullptr;
    TreeNode *prev = nullptr;
};

Morris 中序遍历

Java

// Recover Binary Search Tree
// Morris中序遍历，时间复杂度O(n)，空间复杂度O(1)
public class Solution {
    public void recoverTree(TreeNode root) {
        TreeNode[] broken = new TreeNode[2];
        TreeNode prev = null;
        TreeNode cur = root;

        while (cur != null) {
            if (cur.left == null) {
                detect(broken, prev, cur);
                prev = cur;
                cur = cur.right;
            } else {
                TreeNode node = cur.left;

                while (node.right != null && node.right != cur)
                    node = node.right;

                if (node.right == null) {
                    node.right = cur;
                    //prev = cur; 不能有这句！因为cur还没有被访问
                    cur = cur.left;
                } else {
                    detect(broken, prev, cur);
                    node.right = null;
                    prev = cur;
                    cur = cur.right;
                }
            }
        }
        // swap
        int tmp = broken[0].val;
        broken[0].val = broken[1].val;
        broken[1].val = tmp;
    }

    void detect(TreeNode[] broken, TreeNode prev,
                TreeNode current) {
        if (prev != null && prev.val > current.val) {
            if (broken[0] == null) {
                broken[0] = prev;
            } //不能用else，例如 {0,1}，会导致最后 swap时second为nullptr，
            //会 Runtime Error
            broken[1] = current;
        }
    }
}

C++

// Recover Binary Search Tree
// Morris中序遍历，时间复杂度O(n)，空间复杂度O(1)
class Solution {
public:
    void recoverTree(TreeNode* root) {
        pair<TreeNode*, TreeNode*> broken;
        TreeNode* prev = nullptr;
        TreeNode* cur = root;

        while (cur != nullptr) {
            if (cur->left == nullptr) {
                detect(broken, prev, cur);
                prev = cur;
                cur = cur->right;
            } else {
                auto node = cur->left;

                while (node->right != nullptr && node->right != cur)
                    node = node->right;

                if (node->right == nullptr) {
                    node->right = cur;
                    //prev = cur; 不能有这句！因为cur还没有被访问
                    cur = cur->left;
                } else {
                    detect(broken, prev, cur);
                    node->right = nullptr;
                    prev = cur;
                    cur = cur->right;
                }
            }
        }

        swap(broken.first->val, broken.second->val);
    }

    void detect(pair<TreeNode*, TreeNode*>& broken, TreeNode* prev,
            TreeNode* current) {
        if (prev != nullptr && prev->val > current->val) {
            if (broken.first == nullptr) {
                broken.first = prev;
            } //不能用else，例如 {0,1}，会导致最后 swap时second为nullptr，
              //会 Runtime Error
            broken.second = current;
        }
    }
};

相关题目

• Binary Tree Inorder Traversal