From de95d89a322f04240827089533d83277e08c877c Mon Sep 17 00:00:00 2001 From: Vansh Date: Mon, 17 Jun 2024 17:12:47 +0530 Subject: [PATCH] added lc 700 --- .../0700-search-in-a-binary-search-tree.md | 260 ++++++++++++++++++ .../lc-solutions/0700-0799/image-1.png | Bin 0 -> 43725 bytes .../lc-solutions/0700-0799/image.png | Bin 0 -> 60825 bytes 3 files changed, 260 insertions(+) create mode 100644 dsa-solutions/lc-solutions/0700-0799/0700-search-in-a-binary-search-tree.md create mode 100644 dsa-solutions/lc-solutions/0700-0799/image-1.png create mode 100644 dsa-solutions/lc-solutions/0700-0799/image.png diff --git a/dsa-solutions/lc-solutions/0700-0799/0700-search-in-a-binary-search-tree.md b/dsa-solutions/lc-solutions/0700-0799/0700-search-in-a-binary-search-tree.md new file mode 100644 index 000000000..9d9d871de --- /dev/null +++ b/dsa-solutions/lc-solutions/0700-0799/0700-search-in-a-binary-search-tree.md @@ -0,0 +1,260 @@ +--- +id: search-in-a-binary-search-tree +title: Search in a Binary Search Tree +sidebar_label: 700. Search in a Binary Search Tree + +tags: +- Binary Tree +- BST +- Search + +description: "This is a solution to the Search in a Binary Search Tree problem on LeetCode." +--- + +## Problem Description +You are given the `root` of a binary search tree (BST) and an integer `val`. +Find the node in the BST that the node's value equals `val` and return the subtree rooted with that node. If such a node does not exist, return `null`. +### Examples + +**Example 1:** + +![Example1](image.png) +``` +Input: root = [4,2,7,1,3], val = 2 +Output: [2,1,3] +``` + +**Example 2:** + +![Example2](image-1.png) +``` +Input: root = [4,2,7,1,3], val = 5 +Output: [] + +``` + + +### Constraints +- The number of nodes in the tree is in the range `[1, 5000]`. +- `1 <= Node.val <= 10^7` +- `root` is a binary search tree. +- `1 <= val <= 10^7` + + + +## Solution for Search in a Binary Search Tree +### Approach +#### Brute Force +- **Traverse the Tree**: Perform a level-order or in-order traversal of the tree. +- **Compare Values**: At each node, compare its value with the given value `val`. +- **Return Subtree**: If the node’s value equals `val`, return the subtree rooted at that node. +- **Return Null**: If the traversal completes without finding the node, return `null`. + +**Implementation:** +```python +class TreeNode: + def __init__(self, val=0, left=None, right=None): + self.val = val + self.left = left + self.right = right + +def findNode(root, val): + if root is None: + return None + + queue = [root] + while queue: + node = queue.pop(0) + if node.val == val: + return node + if node.left: + queue.append(node.left) + if node.right: + queue.append(node.right) + + return None + +# Example usage +root = TreeNode(4, TreeNode(2, TreeNode(1), TreeNode(3)), TreeNode(7)) +val = 2 +subtree = findNode(root, val) +print(subtree.val if subtree else "Node not found") +``` + +**Complexity:** +- Time Complexity: `O(n)` - We might have to visit every node in the tree. +- Space Complexity: `O(n)` - In the worst case, the queue can hold all nodes in the tree (for level-order traversal). + +**Corner Cases:** +- Empty tree: Should return `null`. +- Value not found: Should return `null`. + +#### Optimized Approach +- **Leverage BST Properties**: Use the properties of the BST (left subtree contains nodes with values less than the root, and the right subtree contains nodes with values greater than the root). +- **Binary Search**: Traverse the tree using a binary search-like approach: + - If `val` is less than the current node’s value, move to the left child. + - If `val` is greater than the current node’s value, move to the right child. + - If `val` equals the current node’s value, return the current node. +- **Return Null**: If a leaf node is reached without finding the value, return `null`. + +**Implementation:** + +```python +class TreeNode: + def __init__(self, val=0, left=None, right=None): + self.val = val + self.left = left + self.right = right + +def findNode(root, val): + current = root + while current: + if current.val == val: + return current + elif val < current.val: + current = current.left + else: + current = current.right + return None + +# Example usage +root = TreeNode(4, TreeNode(2, TreeNode(1), TreeNode(3)), TreeNode(7)) +val = 2 +subtree = findNode(root, val) +print(subtree.val if subtree else "Node not found") +``` + +**Complexity:** +- Time Complexity: `O(h)`- `h` is the height of the tree. In the worst case, it can be O(n) for a skewed tree, but in a balanced tree, it is O(log n). +- Space Complexity: `O(1)`- We are not using any extra space except for the input and output. + +**Corner Cases:** +- Empty tree: Should return `null`. +- Value not found: Should return `null`. +- Single node tree: If the single node does not match `val`, should return `null`. + + + ## Code in Different Languages + + + + + + + ```javascript + var searchBST = function(root, val) { + if (root === null) { + return null; + } else { + if (root.val === val) { + return root; + } else if (root.val < val) { + return searchBST(root.right, val); + } else { + return searchBST(root.left, val); + } + } + }; + ``` + + + + + + + ```typescript + function searchBST(root: TreeNode | null, val: number): TreeNode | null { + if (root === null) { + return null; + } else { + if (root.val === val) { + return root; + } else if (root.val < val) { + return searchBST(root.right, val); + } else { + return searchBST(root.left, val); + } + } + } + ``` + + + + + + + ```python + + class Solution(object): + def searchBST(self, root, val): + if root is None: + return None + else: + if root.val == val: + return root + elif root.val < val: + return self.searchBST(root.right, val) + else: + return self.searchBST(root.left, val) + ``` + + + + + + + ```java + import java.util.Arrays; + + class Solution { + public TreeNode searchBST(TreeNode root, int val) { + if (root == null) { + return null; + } else { + if (root.val == val) { + return root; + } else if (root.val < val) { + return searchBST(root.right, val); + } else { + return searchBST(root.left, val); + } + } + } + } + ``` + + + + + + + ```cpp + class Solution { + public: + TreeNode* searchBST(TreeNode* root, int val) { + if(root==NULL){ + return NULL; + } + else{ + if(root->val == val){ + return root; + }else if(root->val < val){ + return searchBST(root->right,val); + }else{ + return searchBST(root->left,val); + } + return NULL; + } + return NULL; + } + }; + ``` + + + + +## References + +- **LeetCode Problem**: [Search in a Binary Search Tree](https://leetcode.com/problems/search-in-a-binary-search-tree/description) + +- **Solution Link**: [LeetCode Solution](https://leetcode.com/problems/search-in-a-binary-search-tree/solutions) \ No newline at end of file diff --git a/dsa-solutions/lc-solutions/0700-0799/image-1.png b/dsa-solutions/lc-solutions/0700-0799/image-1.png new file mode 100644 index 0000000000000000000000000000000000000000..97173a57aa91b2356d7ed1d87c78691a7885c076 GIT binary patch literal 43725 zcmYIwby!sU_q74iATXo|(lc~PNJ)3M2uO=agGdY`4Fe(_(k)j)LYhH9T1f?w7#frq zx`tuiGu-?Ay?^lVz$0hQIiJ1PUVH7ejn&sxBO_)czH#FQnTEQu;f))&$Zy=Z8Ax~s z_>I@%m=EynrjMbT;*IJNra!I6~{tmA{YGz}Ar2{2DWxh^EG&v)oBb6@Kl`f>;c!31 zf?A_=%$jPPYfx9XQ2}gGm#}t<#-L%S=#BnAYloNHEjGU@!BRYOohIvjGXx9sx*GkdFd{T*ZJ- zs?Ux;tq$JdEWS_Y80x)OytnT2cu_^?!-OsV3#XP5}oJY_s~de$k{w9WSYnC zR41}}BE$G-8gcSDy7N4{lc73jeoMS}X{rfv{Ass!i~QcpPhFnbvvXw-Q2mnJ0xL?` 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