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"""
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Constraints:
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- The number of nodes in the tree is in the range [0, 2000].
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- -1000 <= Node.val <= 1000
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Time Complexity: O(n)
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- ๊ฐ ๋…ธ๋“œ๋ฅผ ํ•œ ๋ฒˆ์”ฉ๋งŒ ๋ฐฉ๋ฌธํ•จ
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Space Complexity: O(n)
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- ๊ฒฐ๊ณผ ๋ฆฌ์ŠคํŠธ๋Š” ๋ชจ๋“  ๋…ธ๋“œ์˜ ๊ฐ’์„ ์ €์žฅํ•จ
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ํ’€์ด๋ฐฉ๋ฒ•:
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1. queue์™€ BFS๋ฅผ ํ™œ์šฉํ•˜์—ฌ ๋ ˆ๋ฒจ ์ˆœ์„œ๋กœ ๋…ธ๋“œ๋ฅผ ์ˆœํšŒ
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2. ๊ฐ ๋ ˆ๋ฒจ์˜ ๋…ธ๋“œ๋“ค์„ ๋ณ„๋„์˜ ๋ฆฌ์ŠคํŠธ๋กœ ๋ชจ์•„์„œ ๊ฒฐ๊ณผ์— ์ถ”๊ฐ€
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3. ๊ฐ ๋…ธ๋“œ๋ฅผ ์ฒ˜๋ฆฌํ•  ๋•Œ ๊ทธ ๋…ธ๋“œ์˜ ์ž์‹๋“ค์„ ํ์— ์ถ”๊ฐ€ํ•˜์—ฌ ๋‹ค์Œ ๋ ˆ๋ฒจ๋กœ ๋„˜์–ด๊ฐ
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"""
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# Definition for a binary tree node.
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# class TreeNode:
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# def __init__(self, val=0, left=None, right=None):
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# self.val = val
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# self.left = left
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# self.right = right
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class Solution:
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def levelOrder(self, root: Optional[TreeNode]) -> List[List[int]]:
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if not root:
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return []
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result = []
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queue = deque([root])
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while queue:
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level_size = len(queue)
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current_level = []
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for _ in range(level_size):
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node = queue.popleft()
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current_level.append(node.val)
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if node.left:
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queue.append(node.left)
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if node.right:
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queue.append(node.right)
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result.append(current_level)
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return result
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/**
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* ์ด์ง„ ํŠธ๋ฆฌ ๋…ธ๋“œ์˜ ์ •์˜์ž…๋‹ˆ๋‹ค.
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* class TreeNode {
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* val: number;
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* left: TreeNode | null;
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* right: TreeNode | null;
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* constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
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* this.val = (val === undefined ? 0 : val);
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* this.left = (left === undefined ? null : left);
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* this.right = (right === undefined ? null : right);
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* }
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* }
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*/
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/**
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* ์ด์ง„ํŠธ๋ฆฌ ๊นŠ์ด๋ณ„ ๋…ธ๋“œ ๊ฐ’๋“ค์„ ๋ฐฐ์—ด๋กœ ์ €์žฅํ•˜๋Š” ํ•จ์ˆ˜.
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*
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* @param {TreeNode | null} root - ์ด์ง„ ํŠธ๋ฆฌ์˜ ๋ฃจํŠธ ๋…ธ๋“œ
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* @returns {number[][]} - ๊ฐ ๋ ˆ๋ฒจ๋ณ„ ๋…ธ๋“œ ๊ฐ’๋“ค์ด ๋‹ด๊ธด 2์ฐจ์› ๋ฐฐ์—ด ๋ฐ˜ํ™˜
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*
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* ์‹œ๊ฐ„ ๋ณต์žก๋„: O(n)
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* - ๋ชจ๋“  ๋…ธ๋“œ๋ฅผ ํ•œ ๋ฒˆ์”ฉ ๋ฐฉ๋ฌธ
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* ๊ณต๊ฐ„ ๋ณต์žก๋„: O(n)
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* - ์žฌ๊ท€ ํ˜ธ์ถœ ์Šคํƒ ๋ฐ ๊ฒฐ๊ณผ ๋ฐฐ์—ด ์‚ฌ์šฉ
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*/
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function levelOrder(root: TreeNode | null): number[][] {
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// idx -> ๊ฐ ๊นŠ์ด๋ณ„ ๋…ธ๋“œ ๊ฐ’๋“ค์„ ์ €์žฅ
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const result: number[][] = [];
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const dfs = (node: TreeNode | null, depth: number): void => {
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// ๋…ธ๋“œ๊ฐ€ null์ด๋ฉด ์žฌ๊ท€ ์ข…๋ฃŒ
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if (node === null) return;
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// ํ˜„์žฌ depth๋ฅผ ์ฒ˜์Œ ๋ฐฉ๋ฌธ๋˜๋Š” ๊ฒฝ์šฐ, ๊ฒฐ๊ณผ ๋ฐฐ์—ด์— ์ƒˆ๋กœ์šด depth ๋ฐฐ์—ด์„ ์ถ”๊ฐ€
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if (result.length === depth) {
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result.push([]);
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}
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// ํ˜„์žฌ ๋…ธ๋“œ์˜ ๊ฐ’์„ ํ•ด๋‹น ๋ ˆ๋ฒจ ๋ฐฐ์—ด์— ์ถ”๊ฐ€
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result[depth].push(node.val);
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// ์™ผ์ชฝ ์ž์‹ ๋…ธ๋“œ๋ฅผ ๋ฐฉ๋ฌธ (depth 1 ์ฆ๊ฐ€์‹œํ‚ด)
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dfs(node.left, depth + 1);
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// ์˜ค๋ฅธ์ชฝ ์ž์‹ ๋…ธ๋“œ๋ฅผ ๋ฐฉ๋ฌธ (depth 1 ์ฆ๊ฐ€์‹œํ‚ด)
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dfs(node.right, depth + 1);
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}
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// depth 0๋ถ€ํ„ฐ ํƒ์ƒ‰ ์‹œ์ž‘
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dfs(root, 0);
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return result;
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};
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'''
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# Leetcode 102. Binary Tree Level Order Traversal
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do level order traversal
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```
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๐Ÿ’ก why use BFS?:
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BFS is the recommended approach, because it aligns with the problem's concept of processing the binary tree level by level and avoids issues related to recursion depth, making the solution both cleaner and more reliable.
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- DFS doesn't naturally support level-by-level traversal, so we need an extra variable like "dep" (depth).
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- BFS is naturally designed for level traversal, making it a better fit for the problem.
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- additionally, BFS can avoid potential stack overflow.
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```
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## A. BFS
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### re-structuring the tree into a queue:
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- use the queue for traverse the binary tree by level.
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### level traversal:
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- pop the leftmost node
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- append the node's value to current level's array
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- enqueue the left and right children to queue
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- can only process nodes at the current level, because of level_size.
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## B. DFS
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- travase with a dep parameter => dp(node, dep)
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- store the traversal result
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'''
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class Solution:
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'''
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A. BFS
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TC: O(n)
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SC: O(n)
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'''
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def levelOrder(self, root: Optional[TreeNode]) -> List[List[int]]:
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if not root:
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return []
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result = [] # SC: O(n)
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queue = deque([root]) # SC: O(n)
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while queue: # TC: O(n)
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level_size = len(queue)
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level = []
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for _ in range(level_size):
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node = queue.popleft()
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level.append(node.val)
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if node.left:
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queue.append(node.left)
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if node.right:
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queue.append(node.right)
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result.append(level)
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return result
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'''
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B. DFS
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TC: O(n)
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SC: O(n)
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'''
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def levelOrderDP(self, root: Optional[TreeNode]) -> List[List[int]]:
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result = [] # SC: O(n)
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def dp(node, dep):
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if node is None:
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return
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if len(result) <= dep:
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result.append([])
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result[dep].append(node.val)
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dp(node.left, dep + 1)
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dp(node.right, dep + 1)
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dp(root, 0) # TC: O(n) call stack
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return result
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/*
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# Time Complexity: O(n)
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# Space Complexity: O(n)
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- ์žฌ๊ท€ ํ˜ธ์ถœ ํ•จ์ˆ˜์˜ ํŒŒ๋ผ๋ฏธํ„ฐ root, depth, ans
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*/
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/**
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* Definition for a binary tree node.
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* public class TreeNode {
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* int val;
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* TreeNode left;
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* TreeNode right;
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* TreeNode() {}
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* TreeNode(int val) { this.val = val; }
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* TreeNode(int val, TreeNode left, TreeNode right) {
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* this.val = val;
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* this.left = left;
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* this.right = right;
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* }
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* }
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*/
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class Solution {
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public List<List<Integer>> levelOrder(TreeNode root) {
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List<List<Integer>> ans = new ArrayList<>();
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dfs(root, 0, ans);
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return ans;
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}
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private void dfs(TreeNode root, int depth, List<List<Integer>> ans) {
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if (root == null) return;
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if (ans.size() == depth) {
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ans.add(new ArrayList<>());
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}
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ans.get(depth).add(root.val);
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dfs(root.left, depth + 1, ans);
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dfs(root.right, depth + 1, ans);
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}
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}
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// n: number of nodes
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// Time complexity: O(n)
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// Space complexity: O(n)
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class _Queue {
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constructor() {
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this.q = [];
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this.front = 0;
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this.rear = 0;
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}
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push(value) {
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this.q.push(value);
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this.rear++;
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}
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shift() {
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const rv = this.q[this.front];
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delete this.q[this.front++];
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return rv;
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}
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isEmpty() {
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return this.front === this.rear;
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}
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}
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/**
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* Definition for a binary tree node.
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* function TreeNode(val, left, right) {
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* this.val = (val===undefined ? 0 : val)
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* this.left = (left===undefined ? null : left)
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* this.right = (right===undefined ? null : right)
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* }
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*/
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/**
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* @param {TreeNode} root
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* @return {number[][]}
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*/
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var levelOrder = function (root) {
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const answer = [];
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const q = new _Queue();
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if (root) {
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q.push([root, 0]);
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}
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while (!q.isEmpty()) {
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const [current, lv] = q.shift();
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if (answer.at(lv) === undefined) {
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answer[lv] = [];
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}
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answer[lv].push(current.val);
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if (current.left) {
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q.push([current.left, lv + 1]);
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}
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if (current.right) {
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q.push([current.right, lv + 1]);
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}
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}
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return answer;
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};
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class TreeNode {
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val: number;
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left: TreeNode | null;
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right: TreeNode | null;
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constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
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this.val = val === undefined ? 0 : val;
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this.left = left === undefined ? null : left;
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this.right = right === undefined ? null : right;
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}
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}
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/**
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*@link https://leetcode.com/problems/binary-tree-level-order-traversal/
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*
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* ์ ‘๊ทผ ๋ฐฉ๋ฒ• : DFS ์‚ฌ์šฉ
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* - ๊ฐ™์€ ๋†’์ด์˜ ๋…ธ๋“œ๋“ค์„ result ๋ฐฐ์—ด์— ๋„ฃ๊ธฐ ์œ„ํ•ด์„œ dfs๋กœ ์žฌ๊ท€ ํ˜ธ์ถœ
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* - result ๋ฐฐ์—ด์— ํ˜„์žฌ level์— ๋Œ€ํ•œ ๋ฐฐ์—ด์ด ์—†์œผ๋ฉด ์ถ”๊ฐ€ํ•˜๊ณ , ํ˜„์žฌ ๋…ธ๋“œ์˜ ๊ฐ’์„ push
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* - ํ•˜์œ„ ์ž์‹ ๋…ธ๋“œ๊ฐ€ ์กด์žฌํ•˜๋ฉด dfs ์žฌ๊ท€ ํ˜ธ์ถœ (level์€ 1 ์ฆ๊ฐ€)
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*
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* ์‹œ๊ฐ„๋ณต์žก๋„ : O(n)
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* - n = ๋…ธ๋“œ์˜ ๊ฐœ์ˆ˜, ๋ชจ๋“  ๋…ธ๋“œ ์ˆœํšŒ
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*
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* ๊ณต๊ฐ„๋ณต์žก๋„ : O(n)
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* - ํŠธ๋ฆฌ ๊ธฐ์šธ์–ด์ง„ ๊ฒฝ์šฐ, ์žฌ๊ท€ ํ˜ธ์ถœ n๋ฒˆ ๋งŒํผ ์Šคํƒ ์‚ฌ์šฉ
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*/
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function levelOrder(root: TreeNode | null): number[][] {
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const result: number[][] = [];
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const dfs = (node: TreeNode | null, level: number) => {
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if (!node) return;
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if (!result[level]) result[level] = [];
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result[level].push(node.val);
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if (node.left) dfs(node.left, level + 1);
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if (node.right) dfs(node.right, level + 1);
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};
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dfs(root, 0);
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return result;
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}
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/**
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*
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* ์ ‘๊ทผ ๋ฐฉ๋ฒ• : BFS ์‚ฌ์šฉ
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* - ๋™์ผ ๋ ˆ๋ฒจ์˜ ๋…ธ๋“œ ๊ฐ’ ๋‹ด๊ธฐ ์œ„ํ•ด์„œ ํ๋ฅผ ์‚ฌ์šฉ
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* - ํƒ์ƒ‰ํ•  ๋…ธ๋“œ๋ฅผ ํ์— ๋จผ์ € ๋‹ด๊ณ , ํ์—์„œ ํ•˜๋‚˜์”ฉ ๊บผ๋‚ด๋ฉด์„œ ๋™์ผ ๋ ˆ๋ฒจ์˜ ๋…ธ๋“œ ๊ฐ’ ๋‹ด๊ธฐ
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* - ๋…ธ๋“œ์˜ ์ž์‹๋…ธ๋“œ๊ฐ€ ์กด์žฌํ•˜๋ฉด ๋‹ค์‹œ ํ์— ์ถ”๊ฐ€ํ•ด์„œ ํƒ์ƒ‰ํ•  ์ˆ˜ ์žˆ๋„๋ก ํ•จ
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* - ์ด ๊ณผ์ • ๋ฐ˜๋ณตํ•˜๊ธฐ
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*
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* ์‹œ๊ฐ„๋ณต์žก๋„ : O(n)
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* - n = ๋…ธ๋“œ์˜ ๊ฐœ์ˆ˜, ๋ชจ๋“  ๋…ธ๋“œ ์ˆœํšŒ
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*
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* ๊ณต๊ฐ„๋ณต์žก๋„ : O(n)
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* - ํ์— ๋ชจ๋“  ๋…ธ๋“œ ์ €์žฅํ•จ
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*/
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function levelOrder(root: TreeNode | null): number[][] {
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if (!root) return [];
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// ํƒ์ƒ‰ํ•  ๋…ธ๋“œ ๋‹ด์•„๋†“๋Š” ๋Œ€๊ธฐ์ค„
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const queue: TreeNode[] = [root];
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const result: number[][] = [];
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while (queue.length > 0) {
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// ๋™์ผ ๋ ˆ๋ฒจ์— ์žˆ๋Š” ๋…ธ๋“œ ๊ฐ’ ๋‹ด๋Š” ์šฉ๋„
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const currentLevel: number[] = [];
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// queue ์‚ฌ์ด์ฆˆ๊ฐ€ ๋™์ ์œผ๋กœ ๋ณ€ํ•˜๊ธฐ ๋•Œ๋ฌธ์— ๋ฏธ๋ฆฌ ๊ณ„์‚ฐํ•œ ๊ฐ’ ๋ณ€์ˆ˜์— ์ €์žฅ
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const size = queue.length;
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for (let i = 0; i < size; i++) {
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const node = queue.shift()!;
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currentLevel.push(node.val);
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if (node.left) queue.push(node.left);
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if (node.right) queue.push(node.right);
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}
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result.push(currentLevel);
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}
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return result;
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}

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