binary-tree/traversal/recover-binary-search-tree
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2023-12-01
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
// 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);
}
}
// 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
// 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;
}
}
}
// 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;
}
}
};