[LeetCode] 450. Delete Node in a BST 删除二叉搜索树中的节点

2021年09月15日 阅读数:1
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Given a root node reference of a BST and a key, delete the node with the given key in the BST. Return the root node reference (possibly updated) of the BST.html

Basically, the deletion can be divided into two stages:java

  1. Search for a node to remove.
  2. If the node is found, delete the node.

 

Note: Time complexity should be O(height of tree).node

Example:python

root = [5,3,6,2,4,null,7]
key = 3

    5
   / \
  3   6
 / \   \
2   4   7

Given key to delete is 3. So we find the node with value 3 and delete it.

One valid answer is [5,4,6,2,null,null,7], shown in the following BST.

    5
   / \
  4   6
 /     \
2       7

Another valid answer is [5,2,6,null,4,null,7].

    5
   / \
  2   6
   \   \
    4   7

给一个二叉搜索树BST的root节点和一个key值,删除节点值是key的节点,并把它子节点中的一个放在删除节点的位置。less

解法1:递归ide

解法2:迭代post

Java:url

public TreeNode deleteNode(TreeNode root, int key) {
    if(root == null){
        return null;
    }
    if(key < root.val){
        root.left = deleteNode(root.left, key);
    }else if(key > root.val){
        root.right = deleteNode(root.right, key);
    }else{
        if(root.left == null){
            return root.right;
        }else if(root.right == null){
            return root.left;
        }
        
        TreeNode minNode = findMin(root.right);
        root.val = minNode.val;
        root.right = deleteNode(root.right, root.val);
    }
    return root;
}

private TreeNode findMin(TreeNode node){
    while(node.left != null){
        node = node.left;
    }
    return node;
}

Java: Iterativehtm

    private TreeNode deleteRootNode(TreeNode root) {
        if (root == null) {
            return null;
        }
        if (root.left == null) {
            return root.right;
        }
        if (root.right == null) {
            return root.left;
        }
        TreeNode next = root.right;
        TreeNode pre = null;
        for(; next.left != null; pre = next, next = next.left);
        next.left = root.left;
        if(root.right != next) {
            pre.left = next.right;
            next.right = root.right;
        }
        return next;
    }
    
    public TreeNode deleteNode(TreeNode root, int key) {
        TreeNode cur = root;
        TreeNode pre = null;
        while(cur != null && cur.val != key) {
            pre = cur;
            if (key < cur.val) {
                cur = cur.left;
            } else if (key > cur.val) {
                cur = cur.right;
            }
        }
        if (pre == null) {
            return deleteRootNode(cur);
        }
        if (pre.left == cur) {
            pre.left = deleteRootNode(cur);
        } else {
            pre.right = deleteRootNode(cur);
        }
        return root;
    }  

Python:blog

# Time:  O(h)
# Space: O(h)

class Solution(object):
    def deleteNode(self, root, key):
        """
        :type root: TreeNode
        :type key: int
        :rtype: TreeNode
        """
        if not root:
            return root

        if root.val > key:
            root.left = self.deleteNode(root.left, key)
        elif root.val < key:
            root.right = self.deleteNode(root.right, key)
        else:
            if not root.left:
                right = root.right
                del root
                return right
            elif not root.right:
                left = root.left
                del root
                return left
            else:
                successor = root.right
                while successor.left:
                    successor = successor.left

                root.val = successor.val
                root.right = self.deleteNode(root.right, successor.val)

        return root

Python:

def deleteNode(root, key):
	if not root: # if root doesn't exist, just return it
		return root
	if root.val > key: # if key value is less than root value, find the node in the left subtree
		root.left = deleteNode(root.left, key)
	elif root.val < key: # if key value is greater than root value, find the node in right subtree
		root.right= deleteNode(root.right, key)
	else: #if we found the node (root.value == key), start to delete it
		if not root.right: # if it doesn't have right children, we delete the node then new root would be root.left
			return root.left
		if not root.left: # if it has no left children, we delete the node then new root would be root.right
			return root.right
               # if the node have both left and right children,  we replace its value with the minmimum value in the right subtree and then delete that minimum node in the right subtree
		temp = root.right
		mini = temp.val
		while temp.left:
			temp = temp.left
			mini = temp.val
		root.val = mini # replace value
		root.right = deleteNode(root.right,root.val) # delete the minimum node in right subtree
	return root 

C++: 

class Solution {
public:
    TreeNode* deleteNode(TreeNode* root, int key) {
        if (!root) return NULL;
        if (root->val > key) {
            root->left = deleteNode(root->left, key);
        } else if (root->val < key) {
            root->right = deleteNode(root->right, key);
        } else {
            if (!root->left || !root->right) {
                root = (root->left) ? root->left : root->right;
            } else {
                TreeNode *cur = root->right;
                while (cur->left) cur = cur->left;
                root->val = cur->val;
                root->right = deleteNode(root->right, cur->val);
            }
        }
        return root;
    }
};

C++:

class Solution {
public:
    TreeNode* deleteNode(TreeNode* root, int key) {
        TreeNode *cur = root, *pre = NULL;
        while (cur) {
            if (cur->val == key) break;
            pre = cur;
            if (cur->val > key) cur = cur->left;
            else cur = cur->right;
        }
        if (!cur) return root;
        if (!pre) return del(cur);
        if (pre->left && pre->left->val == key) pre->left = del(cur);
        else pre->right = del(cur);
        return root;
    }
    TreeNode* del(TreeNode* node) {
        if (!node->left && !node->right) return NULL;
        if (!node->left || !node->right) {
            return (node->left) ? node->left : node->right;
        }
        TreeNode *pre = node, *cur = node->right;
        while (cur->left) {
            pre = cur;
            cur = cur->left;
        }
        node->val = cur->val;
        (pre == node ? node->right : pre->left) = cur->right;
        return node;
    }
}; 

C++: 

// Time:  O(h)
// Space: O(h)

/**
 * 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 {
public:
    TreeNode* deleteNode(TreeNode* root, int key) {
        if (!root) {
            return nullptr;
        } 
        if (root->val > key) {
            root->left = deleteNode(root->left, key);
        } else if (root->val < key) {
            root->right = deleteNode(root->right, key);
        } else {
            if (!root->left) {
                auto right = root->right;
                delete root;
                return right;
            } else if (!root->right) {
                auto left = root->left;
                delete root;
                return left;
            } else {
                auto successor = root->right;
                while (successor->left) {
                    successor = successor->left;
                }
                root->val = successor->val;
                root->right = deleteNode(root->right, successor->val);
            }
        }
        return root;
    }
};

  

  

 

 

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