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+# Data Structures Reference
+
+Essential data structures for technical interviews with implementation patterns.
+
+## Arrays
+
+**Use when:** Sequential data, random access needed
+**Time:** Access O(1), Search O(n), Insert/Delete O(n)
+**Space:** O(n)
+
+### Common Patterns
+```python
+# Reverse
+arr[::-1]
+
+# Two pointers
+left, right = 0, len(arr) - 1
+
+# Sliding window
+for end in range(len(arr)):
+    window.add(arr[end])
+    if end >= k:
+        window.remove(arr[end - k])
+```
+
+### Product Example: Instagram Feed
+```python
+class InstagramFeed:
+    def __init__(self):
+        self.posts = []  # Array of posts
+
+    def add_post(self, post):
+        self.posts.insert(0, post)  # New posts at beginning
+
+    def get_feed(self, start, limit):
+        return self.posts[start:start + limit]
+```
+
+## Hash Maps
+
+**Use when:** Fast lookups, counting, caching
+**Time:** O(1) average for all operations
+**Space:** O(n)
+
+### Common Patterns
+```python
+# Frequency counter
+freq = {}
+for item in items:
+    freq[item] = freq.get(item, 0) + 1
+
+# Two sum
+seen = {}
+for i, num in enumerate(nums):
+    complement = target - num
+    if complement in seen:
+        return [seen[complement], i]
+    seen[num] = i
+```
+
+### Product Example: Twitter Hashtags
+```python
+class TrendingHashtags:
+    def __init__(self):
+        self.hashtag_count = {}
+
+    def process_tweet(self, tweet):
+        for hashtag in tweet.hashtags:
+            self.hashtag_count[hashtag] = \
+                self.hashtag_count.get(hashtag, 0) + 1
+
+    def get_trending(self, k):
+        return sorted(self.hashtag_count.items(),
+                     key=lambda x: x[1], reverse=True)[:k]
+```
+
+## Linked Lists
+
+**Use when:** Frequent insertions/deletions, unknown size
+**Time:** Access O(n), Insert/Delete O(1) at known position
+**Space:** O(n)
+
+### Common Patterns
+```python
+# Fast & slow pointers (detect cycle)
+slow = fast = head
+while fast and fast.next:
+    slow = slow.next
+    fast = fast.next.next
+    if slow == fast:
+        return True
+
+# Reverse linked list
+prev = None
+curr = head
+while curr:
+    next_node = curr.next
+    curr.next = prev
+    prev = curr
+    curr = next_node
+```
+
+### Product Example: Browser History
+```python
+class BrowserHistory:
+    def __init__(self):
+        self.current = None
+
+    def visit(self, url):
+        new_page = Page(url)
+        new_page.prev = self.current
+        if self.current:
+            self.current.next = new_page
+        self.current = new_page
+
+    def back(self):
+        if self.current and self.current.prev:
+            self.current = self.current.prev
+        return self.current.url
+
+    def forward(self):
+        if self.current and self.current.next:
+            self.current = self.current.next
+        return self.current.url
+```
+
+## Stacks
+
+**Use when:** LIFO, backtracking, parsing
+**Time:** O(1) for push/pop
+**Space:** O(n)
+
+### Common Patterns
+```python
+# Valid parentheses
+stack = []
+pairs = {'(': ')', '[': ']', '{': '}'}
+
+for char in s:
+    if char in pairs:
+        stack.append(char)
+    elif not stack or pairs[stack.pop()] != char:
+        return False
+
+return len(stack) == 0
+```
+
+### Product Example: Code Editor Undo/Redo
+```python
+class CodeEditor:
+    def __init__(self):
+        self.undo_stack = []
+        self.redo_stack = []
+        self.content = ""
+
+    def type(self, text):
+        self.undo_stack.append(self.content)
+        self.content += text
+        self.redo_stack.clear()
+
+    def undo(self):
+        if self.undo_stack:
+            self.redo_stack.append(self.content)
+            self.content = self.undo_stack.pop()
+
+    def redo(self):
+        if self.redo_stack:
+            self.undo_stack.append(self.content)
+            self.content = self.redo_stack.pop()
+```
+
+## Queues
+
+**Use when:** FIFO, BFS, scheduling
+**Time:** O(1) for enqueue/dequeue
+**Space:** O(n)
+
+### Common Patterns
+```python
+from collections import deque
+
+# BFS
+queue = deque([start])
+visited = {start}
+
+while queue:
+    node = queue.popleft()
+    for neighbor in node.neighbors:
+        if neighbor not in visited:
+            visited.add(neighbor)
+            queue.append(neighbor)
+```
+
+### Product Example: Uber Request Queue
+```python
+from collections import deque
+
+class UberQueue:
+    def __init__(self):
+        self.requests = deque()
+
+    def add_request(self, rider, location):
+        self.requests.append({
+            'rider': rider,
+            'location': location,
+            'timestamp': time.time()
+        })
+
+    def match_driver(self, driver):
+        if self.requests:
+            request = self.requests.popleft()
+            return request
+        return None
+```
+
+## Heaps (Priority Queues)
+
+**Use when:** Top K, median, scheduling by priority
+**Time:** O(log n) insert/delete, O(1) peek
+**Space:** O(n)
+
+### Common Patterns
+```python
+import heapq
+
+# Top K elements (min heap)
+min_heap = []
+for num in nums:
+    heapq.heappush(min_heap, num)
+    if len(min_heap) > k:
+        heapq.heappop(min_heap)
+
+# K closest points (max heap with negation)
+max_heap = []
+for point in points:
+    dist = -distance(point)  # Negative for max heap
+    heapq.heappush(max_heap, (dist, point))
+    if len(max_heap) > k:
+        heapq.heappop(max_heap)
+```
+
+### Product Example: Uber Driver Matching
+```python
+import heapq
+
+class UberMatching:
+    def __init__(self):
+        self.available_drivers = []  # Min heap by distance
+
+    def add_driver(self, driver, distance):
+        heapq.heappush(self.available_drivers, (distance, driver))
+
+    def match_closest_driver(self):
+        if self.available_drivers:
+            distance, driver = heapq.heappop(self.available_drivers)
+            return driver
+        return None
+```
+
+## Trees (Binary Trees)
+
+**Use when:** Hierarchical data, BST operations
+**Time:** O(log n) balanced, O(n) worst case
+**Space:** O(h) for recursion
+
+### Common Patterns
+```python
+# Inorder traversal (DFS)
+def inorder(root):
+    if not root:
+        return []
+    return inorder(root.left) + [root.val] + inorder(root.right)
+
+# Level order (BFS)
+def levelOrder(root):
+    if not root:
+        return []
+    result, queue = [], deque([root])
+    while queue:
+        level = []
+        for _ in range(len(queue)):
+            node = queue.popleft()
+            level.append(node.val)
+            if node.left: queue.append(node.left)
+            if node.right: queue.append(node.right)
+        result.append(level)
+    return result
+```
+
+### Product Example: File System
+```python
+class FileSystem:
+    def __init__(self):
+        self.root = Directory("/")
+
+    def create_path(self, path):
+        parts = path.split("/")[1:]  # Skip empty first element
+        current = self.root
+
+        for part in parts:
+            if part not in current.children:
+                current.children[part] = Directory(part)
+            current = current.children[part]
+
+        return current
+
+    def find(self, path):
+        parts = path.split("/")[1:]
+        current = self.root
+
+        for part in parts:
+            if part not in current.children:
+                return None
+            current = current.children[part]
+
+        return current
+```
+
+## Graphs
+
+**Use when:** Networks, relationships, dependencies
+**Time:** BFS/DFS O(V + E)
+**Space:** O(V + E) for adjacency list
+
+### Common Patterns
+```python
+# Adjacency list representation
+graph = {
+    'A': ['B', 'C'],
+    'B': ['D'],
+    'C': ['D'],
+    'D': []
+}
+
+# DFS
+def dfs(node, visited=set()):
+    if node in visited:
+        return
+    visited.add(node)
+    for neighbor in graph[node]:
+        dfs(neighbor, visited)
+
+# BFS
+def bfs(start):
+    visited = {start}
+    queue = deque([start])
+    while queue:
+        node = queue.popleft()
+        for neighbor in graph[node]:
+            if neighbor not in visited:
+                visited.add(neighbor)
+                queue.append(neighbor)
+```
+
+### Product Example: Social Network
+```python
+class SocialNetwork:
+    def __init__(self):
+        self.friends = {}  # user_id -> [friend_ids]
+
+    def add_friendship(self, user1, user2):
+        if user1 not in self.friends:
+            self.friends[user1] = []
+        if user2 not in self.friends:
+            self.friends[user2] = []
+
+        self.friends[user1].append(user2)
+        self.friends[user2].append(user1)
+
+    def degrees_of_separation(self, user1, user2):
+        """BFS to find shortest path"""
+        if user1 == user2:
+            return 0
+
+        visited = {user1}
+        queue = deque([(user1, 0)])
+
+        while queue:
+            current, degree = queue.popleft()
+
+            for friend in self.friends.get(current, []):
+                if friend == user2:
+                    return degree + 1
+
+                if friend not in visited:
+                    visited.add(friend)
+                    queue.append((friend, degree + 1))
+
+        return -1  # Not connected
+```
+
+## Tries (Prefix Trees)
+
+**Use when:** Autocomplete, prefix matching, dictionary
+**Time:** O(m) for word length m
+**Space:** O(ALPHABET_SIZE * m * n)
+
+### Common Patterns
+```python
+class TrieNode:
+    def __init__(self):
+        self.children = {}
+        self.is_end = False
+
+class Trie:
+    def __init__(self):
+        self.root = TrieNode()
+
+    def insert(self, word):
+        node = self.root
+        for char in word:
+            if char not in node.children:
+                node.children[char] = TrieNode()
+            node = node.children[char]
+        node.is_end = True
+
+    def search(self, word):
+        node = self.root
+        for char in word:
+            if char not in node.children:
+                return False
+            node = node.children[char]
+        return node.is_end
+
+    def starts_with(self, prefix):
+        node = self.root
+        for char in prefix:
+            if char not in node.children:
+                return False
+            node = node.children[char]
+        return True
+```
+
+### Product Example: Google Search Autocomplete
+```python
+class Autocomplete:
+    def __init__(self):
+        self.trie = Trie()
+        self.word_frequency = {}
+
+    def add_search(self, query):
+        self.trie.insert(query)
+        self.word_frequency[query] = \
+            self.word_frequency.get(query, 0) + 1
+
+    def get_suggestions(self, prefix):
+        suggestions = []
+
+        def dfs(node, current_word):
+            if node.is_end:
+                suggestions.append(current_word)
+
+            for char, child_node in node.children.items():
+                dfs(child_node, current_word + char)
+
+        # Find prefix node
+        node = self.trie.root
+        for char in prefix:
+            if char not in node.children:
+                return []
+            node = node.children[char]
+
+        # DFS from prefix node
+        dfs(node, prefix)
+
+        # Sort by frequency
+        return sorted(suggestions,
+                     key=lambda x: self.word_frequency.get(x, 0),
+                     reverse=True)[:5]
+```
+
+## Summary
+
+Master these data structures with their common patterns:
+- Arrays: Two pointers, sliding window
+- Hash Maps: Frequency, caching
+- Linked Lists: Fast/slow pointers
+- Stacks: LIFO, parsing
+- Queues: FIFO, BFS
+- Heaps: Top K, priority
+- Trees: DFS, BFS
+- Graphs: Traversal, shortest path
+- Tries: Prefix operations
+
+Each data structure has specific use cases - choose the right tool for the problem!
--- a/skills/leetcode-teacher/references/patterns.md
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+# LeetCode Patterns Reference
+
+The 20 essential coding patterns for technical interviews with templates and real product examples.
+
+## Pattern 1: Two Pointers
+
+**When to Use:** Find pairs, triplets, or process sorted arrays
+**Time:** O(n), **Space:** O(1)
+
+### Template (Python)
+```python
+def two_pointers(arr):
+    left, right = 0, len(arr) - 1
+
+    while left < right:
+        # Process current pair
+        if condition:
+            # Found solution
+            return [left, right]
+        elif arr[left] + arr[right] < target:
+            left += 1
+        else:
+            right -= 1
+
+    return []
+```
+
+### Real Example: Instagram Mutual Likes
+```python
+def find_mutual_likes(user_ids, target_sum):
+    """Find two users whose IDs sum to target"""
+    left, right = 0, len(user_ids) - 1
+
+    while left < right:
+        current_sum = user_ids[left] + user_ids[right]
+
+        if current_sum == target_sum:
+            return [left, right]
+        elif current_sum < target_sum:
+            left += 1
+        else:
+            right -= 1
+
+    return []
+```
+
+## Pattern 2: Sliding Window
+
+**When to Use:** Find subarray/substring with property
+**Time:** O(n), **Space:** O(k)
+
+### Template (Python)
+```python
+def sliding_window(arr, k):
+    window_start = 0
+    max_sum = 0
+    window_sum = 0
+
+    for window_end in range(len(arr)):
+        window_sum += arr[window_end]
+
+        if window_end >= k - 1:
+            max_sum = max(max_sum, window_sum)
+            window_sum -= arr[window_start]
+            window_start += 1
+
+    return max_sum
+```
+
+### Real Example: Twitter Trending Topics
+```python
+def trending_in_window(tweets, time_window):
+    """Find most mentioned hashtag in time window"""
+    hashtag_count = {}
+    max_count = 0
+    trending = ""
+
+    for i, tweet in enumerate(tweets):
+        # Add new tweet
+        if tweet.hashtag in hashtag_count:
+            hashtag_count[tweet.hashtag] += 1
+        else:
+            hashtag_count[tweet.hashtag] = 1
+
+        # Remove old tweets outside window
+        if i >= time_window:
+            old_tag = tweets[i - time_window].hashtag
+            hashtag_count[old_tag] -= 1
+            if hashtag_count[old_tag] == 0:
+                del hashtag_count[old_tag]
+
+        # Track max
+        for tag, count in hashtag_count.items():
+            if count > max_count:
+                max_count = count
+                trending = tag
+
+    return trending
+```
+
+## Pattern 3: Fast & Slow Pointers
+
+**When to Use:** Detect cycles, find middle element
+**Time:** O(n), **Space:** O(1)
+
+### Template (Python)
+```python
+def has_cycle(head):
+    slow = fast = head
+
+    while fast and fast.next:
+        slow = slow.next
+        fast = fast.next.next
+
+        if slow == fast:
+            return True
+
+    return False
+```
+
+### Real Example: Package Manager Circular Dependency
+```python
+def detect_circular_dependency(package):
+    """Detect if package has circular dependencies"""
+    slow = fast = package
+
+    while fast and fast.next_dependency:
+        slow = slow.next_dependency
+        fast = fast.next_dependency.next_dependency
+
+        if slow == fast:
+            return True  # Circular dependency found!
+
+    return False
+```
+
+## Pattern 4: Merge Intervals
+
+**When to Use:** Overlapping intervals, scheduling
+**Time:** O(n log n), **Space:** O(n)
+
+### Template (Python)
+```python
+def merge_intervals(intervals):
+    if not intervals:
+        return []
+
+    intervals.sort(key=lambda x: x[0])
+    merged = [intervals[0]]
+
+    for current in intervals[1:]:
+        last = merged[-1]
+
+        if current[0] <= last[1]:
+            # Overlapping, merge
+            merged[-1] = [last[0], max(last[1], current[1])]
+        else:
+            # Non-overlapping
+            merged.append(current)
+
+    return merged
+```
+
+### Real Example: Google Calendar Free Slots
+```python
+def find_free_slots(calendars, duration):
+    """Find free meeting slots for all attendees"""
+    # Merge all busy times
+    busy = []
+    for calendar in calendars:
+        busy.extend(calendar.busy_times)
+
+    busy.sort()
+    merged_busy = merge_intervals(busy)
+
+    # Find gaps >= duration
+    free_slots = []
+    for i in range(len(merged_busy) - 1):
+        gap_start = merged_busy[i][1]
+        gap_end = merged_busy[i + 1][0]
+
+        if gap_end - gap_start >= duration:
+            free_slots.append([gap_start, gap_end])
+
+    return free_slots
+```
+
+## Pattern 5: Binary Search (Modified)
+
+**When to Use:** Search in O(log n), find boundary
+**Time:** O(log n), **Space:** O(1)
+
+### Template (Python)
+```python
+def binary_search_modified(arr, target):
+    left, right = 0, len(arr) - 1
+
+    while left <= right:
+        mid = (left + right) // 2
+
+        if arr[mid] == target:
+            return mid
+        elif arr[mid] < target:
+            left = mid + 1
+        else:
+            right = mid - 1
+
+    return -1
+```
+
+### Real Example: GitHub Find Bug Introduction Version
+```python
+def find_first_bad_version(versions):
+    """Binary search to find when bug was introduced"""
+    left, right = 0, len(versions) - 1
+    first_bad = -1
+
+    while left <= right:
+        mid = (left + right) // 2
+
+        if is_bad_version(versions[mid]):
+            first_bad = mid
+            right = mid - 1  # Look for earlier bad version
+        else:
+            left = mid + 1
+
+    return first_bad
+```
+
+## Pattern 6: Top K Elements
+
+**When to Use:** Find top/bottom K items
+**Time:** O(n log k), **Space:** O(k)
+
+### Template (Python)
+```python
+import heapq
+
+def top_k_elements(nums, k):
+    # Min heap of size k
+    min_heap = []
+
+    for num in nums:
+        heapq.heappush(min_heap, num)
+
+        if len(min_heap) > k:
+            heapq.heappop(min_heap)
+
+    return min_heap
+```
+
+### Real Example: Reddit Top Posts
+```python
+def get_top_k_posts(posts, k):
+    """Get top K posts by upvotes"""
+    min_heap = []
+
+    for post in posts:
+        heapq.heappush(min_heap, (post.upvotes, post))
+
+        if len(min_heap) > k:
+            heapq.heappop(min_heap)
+
+    return [post for (upvotes, post) in sorted(min_heap, reverse=True)]
+```
+
+## Pattern 7: BFS (Breadth-First Search)
+
+**When to Use:** Shortest path, level-order traversal
+**Time:** O(V + E), **Space:** O(V)
+
+### Template (Python)
+```python
+from collections import deque
+
+def bfs(root):
+    if not root:
+        return []
+
+    result = []
+    queue = deque([root])
+
+    while queue:
+        level_size = len(queue)
+
+        for _ in range(level_size):
+            node = queue.popleft()
+            result.append(node.val)
+
+            if node.left:
+                queue.append(node.left)
+            if node.right:
+                queue.append(node.right)
+
+    return result
+```
+
+### Real Example: LinkedIn Degrees of Connection
+```python
+def degrees_of_connection(user1, user2):
+    """Find shortest connection path between users"""
+    if user1 == user2:
+        return 0
+
+    visited = {user1}
+    queue = deque([(user1, 0)])
+
+    while queue:
+        current_user, degree = queue.popleft()
+
+        for connection in current_user.connections:
+            if connection == user2:
+                return degree + 1
+
+            if connection not in visited:
+                visited.add(connection)
+                queue.append((connection, degree + 1))
+
+    return -1  # Not connected
+```
+
+## Pattern 8: DFS (Depth-First Search)
+
+**When to Use:** Path finding, backtracking
+**Time:** O(V + E), **Space:** O(V)
+
+### Template (Python)
+```python
+def dfs(node, visited=None):
+    if visited is None:
+        visited = set()
+
+    if node in visited:
+        return
+
+    visited.add(node)
+    process(node)
+
+    for neighbor in node.neighbors:
+        dfs(neighbor, visited)
+
+    return visited
+```
+
+### Real Example: File System Path Finding
+```python
+def find_all_paths(start_dir, target_file):
+    """Find all paths to target file"""
+    paths = []
+
+    def dfs(current_dir, path):
+        if current_dir.name == target_file:
+            paths.append(path + [current_dir.name])
+            return
+
+        for subdir in current_dir.subdirectories:
+            dfs(subdir, path + [current_dir.name])
+
+    dfs(start_dir, [])
+    return paths
+```
+
+## Pattern 9: Dynamic Programming
+
+**When to Use:** Optimization, counting problems
+**Time:** Varies (often O(n²)), **Space:** O(n) or O(n²)
+
+### Template (Python)
+```python
+def dp_solution(n):
+    # Initialize DP array
+    dp = [0] * (n + 1)
+    dp[0] = base_case
+
+    # Fill DP array
+    for i in range(1, n + 1):
+        dp[i] = transition(dp[i-1], dp[i-2], ...)
+
+    return dp[n]
+```
+
+### Real Example: Minimum Venmo Transactions
+```python
+def min_transactions(debts):
+    """Minimum transactions to settle all debts"""
+    # Calculate net balance for each person
+    balance = {}
+    for payer, payee, amount in debts:
+        balance[payer] = balance.get(payer, 0) - amount
+        balance[payee] = balance.get(payee, 0) + amount
+
+    # Remove zero balances
+    amounts = [v for v in balance.values() if v != 0]
+
+    def dfs(idx):
+        # Skip settled accounts
+        while idx < len(amounts) and amounts[idx] == 0:
+            idx += 1
+
+        if idx == len(amounts):
+            return 0
+
+        min_trans = float('inf')
+
+        for i in range(idx + 1, len(amounts)):
+            # Try settling idx with i
+            if amounts[idx] * amounts[i] < 0:  # Different signs
+                amounts[i] += amounts[idx]
+                min_trans = min(min_trans, 1 + dfs(idx + 1))
+                amounts[i] -= amounts[idx]  # Backtrack
+
+        return min_trans
+
+    return dfs(0)
+```
+
+## Pattern 10: Backtracking
+
+**When to Use:** Generate all combinations, permutations
+**Time:** Exponential, **Space:** O(n)
+
+### Template (Python)
+```python
+def backtrack(path, choices):
+    if is_solution(path):
+        result.append(path[:])
+        return
+
+    for choice in choices:
+        # Make choice
+        path.append(choice)
+
+        # Recurse
+        backtrack(path, remaining_choices)
+
+        # Undo choice (backtrack)
+        path.pop()
+```
+
+### Real Example: Slack Channel Combinations
+```python
+def generate_team_combinations(members, team_size):
+    """Generate all possible teams of given size"""
+    teams = []
+
+    def backtrack(start, current_team):
+        if len(current_team) == team_size:
+            teams.append(current_team[:])
+            return
+
+        for i in range(start, len(members)):
+            current_team.append(members[i])
+            backtrack(i + 1, current_team)
+            current_team.pop()
+
+    backtrack(0, [])
+    return teams
+```
+
+## Summary
+
+Master these 10 core patterns (plus 10 more in advanced practice) and you'll be able to solve 90%+ of LeetCode problems. Focus on:
+
+1. **Recognition**: "I've seen this pattern before"
+2. **Template**: "I know the code structure"
+3. **Adaptation**: "I can modify for this specific problem"
+4. **Optimization**: "I can improve time/space complexity"
+
+Practice each pattern 5-10 times until it becomes second nature!