O(1) space solution using Morris single threaded tree traversal to: two elements of a binary search tree (BST) are swapped by mistake, recover the tree without changing its structure.

recover-bst-o1.cc

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
    TreeNode* fst;
    TreeNode* sec;

public:
    void recoverTree(TreeNode* root) {
        fix(root);

        int tmp = fst->val;
        fst->val = sec->val;
        sec->val = tmp;
    }

    void fix(TreeNode *root) {
        TreeNode *cur = root, *pre, *last = NULL;

        if (!root) {
            return;
        }

        while (cur) {
            if (!cur->left) {
                check(last, cur);
                last = cur;
                cur = cur->right;
            } else {
                pre = cur->left;
                while (pre->right != NULL && pre->right != cur) {
                    pre = pre->right;
                }

                if (pre->right == NULL) {
                    pre->right = cur;
                    cur = cur->left;
                } else {
                    check(last, cur);
                    last = cur;
                    pre->right = NULL;
                    cur = cur->right;
                }
            }
        }
    }

    void check(TreeNode *last, TreeNode *cur) {
        if (last != NULL && last->val > cur->val) {
            if (!fst) {
                fst = last;
                sec = cur;
            } else {
                sec = cur;
            }
        }
    }
};