feat: Implement LeetCode router problem notes

Co-authored-by: jhw1994 <jhw1994@gmail.com>

Author: cursoragent

notes/leetcode/implement-router.md

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+---
+title: "Implement Router"
+date: "2025-01-27"
+tags: ["Hash Table", "String", "Design"]
+related: []
+slug: "implement-router"
+category: "leetcode"
+leetcode_url: "https://leetcode.com/problems/implement-router/description/"
+leetcode_difficulty: "Medium"
+leetcode_topics: ["Hash Table", "String", "Design"]
+---
+
+# Implement Router
+
+## Summary
+Design and implement a basic HTTP router that can register routes with different HTTP methods and handle incoming requests by matching them to the appropriate handler functions.
+
+## Problem Description
+Implement a Router class that supports:
+
+1. **Route Registration**: Register routes with specific HTTP methods (GET, POST, PUT, DELETE, etc.)
+2. **Route Matching**: Match incoming requests to registered routes
+3. **Handler Execution**: Execute the appropriate handler function for matched routes
+4. **404 Handling**: Return appropriate response for unmatched routes
+
+**Key Requirements:**
+- Support multiple HTTP methods
+- Handle exact path matching
+- Support path parameters (e.g., `/users/:id`)
+- Return appropriate HTTP status codes
+- Handle edge cases like duplicate routes, invalid methods
+
+**Example Usage:**
+```python
+router = Router()
+
+# Register routes
+router.add_route('GET', '/users', get_users_handler)
+router.add_route('GET', '/users/:id', get_user_handler)
+router.add_route('POST', '/users', create_user_handler)
+
+# Handle requests
+response = router.handle_request('GET', '/users')
+response = router.handle_request('GET', '/users/123')
+response = router.handle_request('POST', '/users')
+```
+
+## Solution Approach
+This problem can be solved using a hash table-based approach with support for path parameters:
+
+### Core Data Structure
+- Use a dictionary where keys are HTTP methods and values are dictionaries of route patterns to handlers
+- Store both exact matches and parameterized routes
+- Use regex patterns for parameter matching
+
+### Algorithm Steps
+1. **Route Registration**:
+   - Parse route pattern to identify parameters (e.g., `:id`)
+   - Convert to regex pattern for matching
+   - Store handler function with compiled regex
+
+2. **Route Matching**:
+   - Look up routes for the given HTTP method
+   - Try exact matches first
+   - Try parameterized routes using regex matching
+   - Extract parameter values from matched route
+
+3. **Handler Execution**:
+   - Execute the matched handler with extracted parameters
+   - Return appropriate response object
+
+## Time & Space Complexity
+- **Time Complexity:**
+  - Route registration: O(1) average case
+  - Route matching: O(n) where n is number of registered routes for the method
+  - Handler execution: O(1)
+- **Space Complexity:** O(m × r) where m is number of HTTP methods and r is number of routes per method
+
+## Key Insights
+- **Exact match priority**: Check exact matches before parameterized routes
+- **Parameter extraction**: Use regex groups to extract parameter values
+- **Method separation**: Organize routes by HTTP method for efficient lookup
+- **Error handling**: Proper 404 and 405 (Method Not Allowed) responses
+- **Route conflicts**: Handle duplicate route registrations appropriately
+
+## Examples / snippets
+
+### Solution Code
+```python
+import re
+from typing import Dict, Callable, Optional, Tuple, Any
+from collections import defaultdict
+
+class Router:
+    def __init__(self):
+        # Dictionary: method -> {pattern: (handler, compiled_regex, param_names)}
+        self.routes = defaultdict(dict)
+        # Dictionary: method -> {exact_path: handler} for exact matches
+        self.exact_routes = defaultdict(dict)
+    
+    def add_route(self, method: str, pattern: str, handler: Callable) -> None:
+        """Register a route with the given method, pattern, and handler."""
+        method = method.upper()
+        
+        # Check for exact match (no parameters)
+        if ':' not in pattern:
+            if pattern in self.exact_routes[method]:
+                raise ValueError(f"Route {method} {pattern} already exists")
+            self.exact_routes[method][pattern] = handler
+            return
+        
+        # Handle parameterized routes
+        if pattern in self.routes[method]:
+            raise ValueError(f"Route {method} {pattern} already exists")
+        
+        # Convert pattern to regex and extract parameter names
+        param_names = []
+        regex_pattern = pattern
+        
+        # Find all :param patterns
+        param_matches = re.findall(r':(\w+)', pattern)
+        param_names = param_matches
+        
+        # Replace :param with regex groups
+        regex_pattern = re.sub(r':(\w+)', r'([^/]+)', pattern)
+        regex_pattern = f'^{regex_pattern}$'
+        
+        compiled_regex = re.compile(regex_pattern)
+        self.routes[method][pattern] = (handler, compiled_regex, param_names)
+    
+    def handle_request(self, method: str, path: str) -> Dict[str, Any]:
+        """Handle an incoming request and return the response."""
+        method = method.upper()
+        
+        # Try exact match first
+        if path in self.exact_routes[method]:
+            handler = self.exact_routes[method][path]
+            return self._execute_handler(handler, {})
+        
+        # Try parameterized routes
+        for pattern, (handler, compiled_regex, param_names) in self.routes[method].items():
+            match = compiled_regex.match(path)
+            if match:
+                # Extract parameter values
+                params = {}
+                for i, param_name in enumerate(param_names):
+                    params[param_name] = match.group(i + 1)
+                
+                return self._execute_handler(handler, params)
+        
+        # Check if method exists but path doesn't (405 Method Not Allowed)
+        if self.exact_routes[method] or self.routes[method]:
+            return {
+                'status_code': 405,
+                'message': 'Method Not Allowed',
+                'data': None
+            }
+        
+        # Route not found (404 Not Found)
+        return {
+            'status_code': 404,
+            'message': 'Not Found',
+            'data': None
+        }
+    
+    def _execute_handler(self, handler: Callable, params: Dict[str, str]) -> Dict[str, Any]:
+        """Execute the handler function with extracted parameters."""
+        try:
+            if params:
+                result = handler(**params)
+            else:
+                result = handler()
+            
+            return {
+                'status_code': 200,
+                'message': 'OK',
+                'data': result
+            }
+        except Exception as e:
+            return {
+                'status_code': 500,
+                'message': 'Internal Server Error',
+                'data': str(e)
+            }
+    
+    def list_routes(self) -> Dict[str, list]:
+        """List all registered routes for debugging."""
+        all_routes = {}
+        for method in self.exact_routes:
+            all_routes[method] = list(self.exact_routes[method].keys())
+        for method in self.routes:
+            if method not in all_routes:
+                all_routes[method] = []
+            all_routes[method].extend(self.routes[method].keys())
+        return all_routes
+
+# Example usage and test handlers
+def get_users():
+    return {"users": [{"id": 1, "name": "Alice"}, {"id": 2, "name": "Bob"}]}
+
+def get_user(id: str):
+    return {"user": {"id": int(id), "name": f"User {id}"}}
+
+def create_user():
+    return {"message": "User created successfully"}
+
+def update_user(id: str):
+    return {"message": f"User {id} updated successfully"}
+
+def delete_user(id: str):
+    return {"message": f"User {id} deleted successfully"}
+
+# Example usage
+if __name__ == "__main__":
+    router = Router()
+    
+    # Register routes
+    router.add_route('GET', '/users', get_users)
+    router.add_route('GET', '/users/:id', get_user)
+    router.add_route('POST', '/users', create_user)
+    router.add_route('PUT', '/users/:id', update_user)
+    router.add_route('DELETE', '/users/:id', delete_user)
+    
+    # Test requests
+    print(router.handle_request('GET', '/users'))
+    print(router.handle_request('GET', '/users/123'))
+    print(router.handle_request('POST', '/users'))
+    print(router.handle_request('PUT', '/users/456'))
+    print(router.handle_request('DELETE', '/users/789'))
+    print(router.handle_request('GET', '/nonexistent'))
+    print(router.handle_request('PATCH', '/users'))
+```
+
+### Example Walkthrough
+**Example 1: Basic Route Registration and Matching**
+```python
+router = Router()
+
+# Register routes
+router.add_route('GET', '/users', get_users_handler)
+router.add_route('GET', '/users/:id', get_user_handler)
+
+# Handle requests
+response1 = router.handle_request('GET', '/users')
+# Returns: {'status_code': 200, 'message': 'OK', 'data': {...}}
+
+response2 = router.handle_request('GET', '/users/123')
+# Returns: {'status_code': 200, 'message': 'OK', 'data': {'user': {'id': 123, 'name': 'User 123'}}}
+```
+
+**Example 2: Error Handling**
+```python
+# 404 Not Found
+response = router.handle_request('GET', '/nonexistent')
+# Returns: {'status_code': 404, 'message': 'Not Found', 'data': None}
+
+# 405 Method Not Allowed
+response = router.handle_request('PATCH', '/users')
+# Returns: {'status_code': 405, 'message': 'Method Not Allowed', 'data': None}
+```
+
+**Example 3: Multiple Parameters**
+```python
+def get_user_posts(user_id: str, post_id: str):
+    return {"user_id": user_id, "post_id": post_id, "content": "Post content"}
+
+router.add_route('GET', '/users/:user_id/posts/:post_id', get_user_posts)
+
+response = router.handle_request('GET', '/users/123/posts/456')
+# Returns: {'status_code': 200, 'message': 'OK', 'data': {'user_id': '123', 'post_id': '456', 'content': 'Post content'}}
+```
+
+## Edge Cases & Validation
+- **Duplicate routes**: Should raise ValueError when registering duplicate routes
+- **Invalid HTTP methods**: Should handle case-insensitive method matching
+- **Empty paths**: Should handle root path `/` appropriately
+- **Special characters**: Should handle paths with special characters correctly
+- **Parameter validation**: Should extract parameters correctly from complex paths
+- **Handler exceptions**: Should catch and return 500 errors for handler exceptions
+- **Method not allowed**: Should return 405 when method exists but path doesn't
+- **Case sensitivity**: Should handle path matching case-sensitively
+- **Trailing slashes**: Should handle paths with and without trailing slashes consistently
+
+## Related Problems
+- [208. Implement Trie (Prefix Tree)](https://leetcode.com/problems/implement-trie-prefix-tree/) - Tree-based routing
+- [211. Design Add and Search Words Data Structure](https://leetcode.com/problems/design-add-and-search-words-data-structure/) - Pattern matching
+- [676. Implement Magic Dictionary](https://leetcode.com/problems/implement-magic-dictionary/) - String matching with variations
+- [Design Twitter](https://leetcode.com/problems/design-twitter/) - System design with routing concepts