feat: add initial frontend and backend dependencies

.gitignore

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+# Python
+__pycache__/
+*.py[cod]
+*$py.class
+.venv/
+venv/
+ENV/
+env/
+.env
+*.egg-info/
+.coverage
+htmlcov/
+.pytest_cache/
+
+# Node.js
+node_modules/
+dist/
+build/
+.npm
+.eslintcache
+
+# OS / IDE
+.DS_Store
+.idea/
+.vscode/
+*.swp
+*.swo
+thumbs.db

Dockerfile

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+# Multi-stage Dockerfile for Algorithm Platform
+
+# Stage 1: Build Frontend
+FROM node:18-alpine AS frontend-build
+WORKDIR /app/frontend
+COPY frontend/package*.json ./
+RUN npm install
+COPY frontend/ ./
+RUN npm run build
+
+# Stage 2: Setup Backend
+FROM python:3.11-slim AS backend
+WORKDIR /app/backend
+COPY backend/requirements.txt ./
+RUN pip install --no-cache-dir -r requirements.txt
+COPY backend/ ./
+
+# Stage 3: Final - Nginx + Backend
+FROM nginx:alpine
+WORKDIR /app
+
+# Install Python and dependencies in final stage
+RUN apk add --no-cache python3 py3-pip
+
+# Copy backend
+COPY --from=backend /app/backend /app/backend
+COPY --from=backend /usr/local/lib/python3.11/site-packages /usr/local/lib/python3.11/site-packages
+
+# Copy frontend build to Nginx
+COPY --from=frontend-build /app/frontend/dist /usr/share/nginx/html
+
+# Copy Nginx configuration
+COPY nginx.conf /etc/nginx/nginx.conf
+
+# Expose ports
+EXPOSE 80
+
+# Start script
+COPY docker-entrypoint.sh /docker-entrypoint.sh
+RUN chmod +x /docker-entrypoint.sh
+
+CMD ["/docker-entrypoint.sh"]

README.md

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+# Algorithm Test Case Generation and Verification Platform
+
+## Project Structure
+- `backend/`: FastAPI Python Backend
+- `frontend/`: React Vite Frontend
+
+## Prerequisites
+- Python 3.8+
+- Node.js 16+
+
+## Setup & Run
+
+### Quick Start with Docker (Recommended)
+```bash
+docker-compose up --build
+```
+Then access:
+- **Frontend**: http://localhost
+- **Backend API**: http://localhost:8000
+- **API Docs**: http://localhost:8000/docs
+
+### Manual Setup
+
+### 1. Backend
+```bash
+cd backend
+# Optional: Create virtual env
+# python -m venv venv
+# source venv/bin/activate
+pip install -r requirements.txt
+uvicorn main:app --reload
+```
+Backend will run at `http://localhost:8000`
+
+### 2. Frontend
+```bash
+cd frontend
+npm install
+npm run dev
+```
+Frontend will run at `http://localhost:5173`
+
+## Features Implemented
+1.  **Maximum Subarray Sum**:
+    -   Brute Force ($O(N^2)$)
+    -   Divide & Conquer ($O(N \log N)$)
+    -   Kadane's Algorithm ($O(N)$)
+    -   Automatic Random Case Generation
+    -   Performance Benchmarking & Visualization

backend/common/base_problem.py

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+from abc import ABC, abstractmethod
+from typing import Any, Dict, List
+
+class BaseProblem(ABC):
+    """
+    Abstract base class for all algorithm problems.
+    """
+
+    @abstractmethod
+    def generate_case(self, **kwargs) -> Dict[str, Any]:
+        """
+        Generate a random test case based on parameters.
+        """
+        pass
+
+    @abstractmethod
+    def solve(self, input_data: Any, algorithm: str) -> Any:
+        """
+        Solve the problem using the specified algorithm.
+        """
+        pass
+
+    @abstractmethod
+    def verify(self, input_data: Any, result: Any) -> bool:
+        """
+        Verify the correctness of the result (optional, or compare with standard answer).
+        """
+        pass

backend/common/timer_utils.py

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+import time
+import functools
+from typing import Tuple, Any
+
+def time_execution(func):
+    """
+    Decorator to measure execution time of a function.
+    Returns a tuple (result, execution_time_in_seconds).
+    """
+    @functools.wraps(func)
+    def wrapper(*args, **kwargs) -> Tuple[Any, float]:
+        start_time = time.perf_counter()
+        result = func(*args, **kwargs)
+        end_time = time.perf_counter()
+        execution_time = end_time - start_time
+        return result, execution_time
+    return wrapper

backend/main.py

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+from fastapi import FastAPI
+from fastapi.middleware.cors import CORSMiddleware
+from routers import max_subarray_router
+
+app = FastAPI(title="Algorithm Platform API")
+
+# Allow CORS for frontend
+app.add_middleware(
+    CORSMiddleware,
+    allow_origins=["*"],  # In production, replace with specific frontend origin
+    allow_credentials=True,
+    allow_methods=["*"],
+    allow_headers=["*"],
+)
+
+@app.get("/")
+def read_root():
+    return {"message": "Welcome to Algorithm Verification Platform API"}
+
+app.include_router(max_subarray_router.router)
+from routers import interval_scheduling_router
+app.include_router(interval_scheduling_router.router)
+from routers import n_queens_router
+app.include_router(n_queens_router.router)
+from routers import knapsack_router
+app.include_router(knapsack_router.router)

backend/problems/interval_scheduling/generator.py

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+import random
+from typing import List, Tuple
+
+def generate_interval_scheduling_case(size: int = 10, min_time: int = 0, max_time: int = 100) -> List[Tuple[int, int]]:
+    """
+    Generates a list of random intervals (start, end).
+    """
+    intervals = []
+    for _ in range(size):
+        start = random.randint(min_time, max_time - 1)
+        # Ensure end > start
+        duration = random.randint(1, (max_time - start) // 2 + 1 if (max_time - start) > 2 else 1) 
+        end = min(start + duration, max_time)
+        if end <= start:
+            end = start + 1
+        intervals.append((start, end))
+    return intervals

backend/problems/interval_scheduling/problem.py

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+from typing import Any, Dict, List
+from common.base_problem import BaseProblem
+from problems.interval_scheduling.generator import generate_interval_scheduling_case
+from problems.interval_scheduling.solvers import solve_greedy, solve_brute_force
+from common.timer_utils import time_execution
+
+class IntervalSchedulingProblem(BaseProblem):
+    def generate_case(self, size: int = 10, min_time: int = 0, max_time: int = 100) -> Dict[str, Any]:
+        intervals = generate_interval_scheduling_case(size, min_time, max_time)
+        return {"intervals": intervals}
+
+    def solve(self, input_data: Dict[str, Any], algorithm: str) -> Dict[str, Any]:
+        intervals = input_data.get("intervals", [])
+        # Ensure intervals are tuples
+        intervals = [tuple(x) for x in intervals]
+        
+        result = None
+        duration = 0.0
+
+        if algorithm == "greedy":
+            result, duration = time_execution(solve_greedy)(intervals)
+        elif algorithm == "brute_force":
+            result, duration = time_execution(solve_brute_force)(intervals)
+        else:
+            raise ValueError(f"Unknown algorithm: {algorithm}")
+        
+        return {
+            "algorithm": algorithm,
+            "result_count": len(result),
+            "result_intervals": result,
+            "time_seconds": duration
+        }
+
+    def verify(self, input_data: Any, result: Any) -> bool:
+        # Use Greedy as the source of truth (it is optimal for this problem)
+        intervals = input_data.get("intervals", [])
+        intervals = [tuple(x) for x in intervals]
+        truth, _ = time_execution(solve_greedy)(intervals)
+        return result.get("result_count") == len(truth)

backend/problems/interval_scheduling/solvers.py

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+from typing import List, Tuple
+
+def solve_greedy(intervals: List[Tuple[int, int]]) -> List[Tuple[int, int]]:
+    """
+    Greedy algorithm: Sort by end time, pick non-overlapping.
+    O(N log N)
+    """
+    if not intervals:
+        return []
+    
+    # Sort by end time
+    sorted_intervals = sorted(intervals, key=lambda x: x[1])
+    
+    selected = []
+    last_end_time = -float('inf')
+    
+    for start, end in sorted_intervals:
+        if start >= last_end_time:
+            selected.append((start, end))
+            last_end_time = end
+            
+    return selected
+
+def solve_brute_force(intervals: List[Tuple[int, int]]) -> List[Tuple[int, int]]:
+    """
+    Brute Force algorithm: Try all combinations.
+    O(2^N) - Only for small inputs!
+    """
+    n = len(intervals)
+    max_count = 0
+    best_subset = []
+    
+    # Helper to check if a subset of intervals is valid (non-overlapping)
+    def is_valid(subset):
+        sorted_subset = sorted(subset, key=lambda x: x[1])
+        last_end = -float('inf')
+        for start, end in sorted_subset:
+            if start < last_end:
+                return False
+            last_end = end
+        return True
+
+    # Iterate through all 2^N subsets (using bitmask)
+    # Limit N to avoid hanging
+    if n > 20: 
+        # Fallback or error for safety, though we handle this in router usually
+        return solve_greedy(intervals) # Cheating slightly for safety if called directly with large N
+
+    for i in range(1 << n):
+        subset = []
+        for j in range(n):
+            if (i >> j) & 1:
+                subset.append(intervals[j])
+        
+        if is_valid(subset):
+            if len(subset) > max_count:
+                max_count = len(subset)
+                best_subset = subset
+                
+    return best_subset

backend/problems/knapsack/generator.py

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+import random
+from typing import List, Dict, Any
+
+def generate_knapsack_case(num_items: int = 10, max_weight: int = 50, max_value: int = 100, capacity_ratio: float = 0.5) -> Dict[str, Any]:
+    """
+    Generates a case for 0/1 Knapsack.
+    """
+    items = []
+    total_weight = 0
+    for i in range(num_items):
+        w = random.randint(1, max_weight)
+        v = random.randint(1, max_value)
+        items.append({"id": i, "weight": w, "value": v})
+        total_weight += w
+    
+    capacity = int(total_weight * capacity_ratio)
+    
+    return {
+        "items": items,
+        "capacity": capacity
+    }

backend/problems/knapsack/problem.py

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+from typing import Any, Dict, List
+from common.base_problem import BaseProblem
+from problems.knapsack.generator import generate_knapsack_case
+from problems.knapsack.solvers import solve_dp, solve_backtracking
+from common.timer_utils import time_execution
+
+class KnapsackProblem(BaseProblem):
+    def generate_case(self, num_items: int = 10, max_weight: int = 50, max_value: int = 100) -> Dict[str, Any]:
+        return generate_knapsack_case(num_items, max_weight, max_value)
+
+    def solve(self, input_data: Dict[str, Any], algorithm: str) -> Dict[str, Any]:
+        items = input_data.get("items", [])
+        capacity = input_data.get("capacity", 0)
+        
+        result = None
+        duration = 0.0
+
+        if algorithm == "dp":
+            result, duration = time_execution(solve_dp)(items, capacity)
+        elif algorithm == "backtracking":
+            result, duration = time_execution(solve_backtracking)(items, capacity)
+        else:
+            raise ValueError(f"Unknown algorithm: {algorithm}")
+        
+        return {
+            "algorithm": algorithm,
+            "max_value": result["max_value"],
+            "selected_items": result["selected_items"],
+            "time_seconds": duration
+        }
+
+    def verify(self, input_data: Any, result: Any) -> bool:
+        # Use DP as source of truth
+        items = input_data.get("items", [])
+        capacity = input_data.get("capacity", 0)
+        truth, _ = time_execution(solve_dp)(items, capacity)
+        return result["max_value"] == truth["max_value"]

backend/problems/knapsack/solvers.py

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+from typing import List, Dict, Any, Tuple
+
+def solve_dp(items: List[Dict[str, int]], capacity: int) -> Dict[str, Any]:
+    """
+    Dynamic Programming solution for 0/1 Knapsack.
+    O(N * W)
+    """
+    n = len(items)
+    # dp[i][w] = max value using first i items with capacity w
+    dp = [[0] * (capacity + 1) for _ in range(n + 1)]
+    
+    for i in range(1, n + 1):
+        item = items[i-1]
+        w, v = item["weight"], item["value"]
+        for j in range(capacity + 1):
+            if w <= j:
+                dp[i][j] = max(dp[i-1][j], dp[i-1][j-w] + v)
+            else:
+                dp[i][j] = dp[i-1][j]
+    
+    max_value = dp[n][capacity]
+    
+    # Backtrack to find selected items
+    selected_indices = []
+    w = capacity
+    for i in range(n, 0, -1):
+        if dp[i][w] != dp[i-1][w]:
+            item = items[i-1]
+            selected_indices.append(item["id"])
+            w -= item["weight"]
+            
+    return {
+        "max_value": max_value,
+        "selected_items": selected_indices
+    }
+
+def solve_backtracking(items: List[Dict[str, int]], capacity: int) -> Dict[str, Any]:
+    """
+    Backtracking solution for 0/1 Knapsack.
+    O(2^N)
+    """
+    n = len(items)
+    max_val = 0
+    best_selection = []
+    
+    def backtrack(index, current_weight, current_value, selection):
+        nonlocal max_val, best_selection
+        
+        if current_weight > capacity:
+            return
+
+        if current_value > max_val:
+            max_val = current_value
+            best_selection = selection[:]
+            
+        if index == n:
+            return
+
+        # Include current item
+        item = items[index]
+        if current_weight + item["weight"] <= capacity:
+            selection.append(item["id"])
+            backtrack(index + 1, current_weight + item["weight"], current_value + item["value"], selection)
+            selection.pop()
+            
+        # Exclude current item
+        backtrack(index + 1, current_weight, current_value, selection)
+
+    backtrack(0, 0, 0, [])
+    return {
+        "max_value": max_val,
+        "selected_items": best_selection
+    }

backend/problems/max_subarray/generator.py

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+import random
+from typing import List, Dict
+
+def generate_max_subarray_case(size: int = 100, min_val: int = -100, max_val: int = 100) -> List[int]:
+    """
+    Generate a list of random integers.
+    """
+    return [random.randint(min_val, max_val) for _ in range(size)]

backend/problems/max_subarray/problem.py

@@ -0,0 +1,35 @@
+from typing import Any, Dict, List
+from common.base_problem import BaseProblem
+from problems.max_subarray.generator import generate_max_subarray_case
+from problems.max_subarray.solvers import solve_brute_force, solve_divide_conquer, solve_kadane
+from common.timer_utils import time_execution
+
+class MaxSubarrayProblem(BaseProblem):
+    def generate_case(self, size: int = 100, min_val: int = -100, max_val: int = 100) -> Dict[str, Any]:
+        arr = generate_max_subarray_case(size, min_val, max_val)
+        return {"array": arr}
+
+    def solve(self, input_data: Dict[str, Any], algorithm: str) -> Dict[str, Any]:
+        arr = input_data.get("array", [])
+        result = None
+        duration = 0.0
+
+        if algorithm == "brute_force":
+            result, duration = time_execution(solve_brute_force)(arr)
+        elif algorithm == "divide_conquer":
+            result, duration = time_execution(solve_divide_conquer)(arr)
+        elif algorithm == "kadane":
+            result, duration = time_execution(solve_kadane)(arr)
+        else:
+            raise ValueError(f"Unknown algorithm: {algorithm}")
+        
+        return {
+            "algorithm": algorithm,
+            "result": result,
+            "time_seconds": duration
+        }
+
+    def verify(self, input_data: Any, result: Any) -> bool:
+        # Use Kadane as the source of truth
+        truth, _ = time_execution(solve_kadane)(input_data.get("array", []))
+        return result == truth

backend/problems/max_subarray/solvers.py

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+from typing import List, Tuple
+
+# 1. Brute Force O(N^2)
+def solve_brute_force(arr: List[int]) -> int:
+    max_sum = float('-inf')
+    n = len(arr)
+    for i in range(n):
+        current_sum = 0
+        for j in range(i, n):
+            current_sum += arr[j]
+            if current_sum > max_sum:
+                max_sum = current_sum
+    return max_sum
+
+# 2. Divide and Conquer O(N log N)
+def solve_divide_conquer(arr: List[int]) -> int:
+    def max_crossing_sum(arr, low, mid, high):
+        left_sum = float('-inf')
+        curr_sum = 0
+        for i in range(mid, low - 1, -1):
+            curr_sum += arr[i]
+            if curr_sum > left_sum:
+                left_sum = curr_sum
+        
+        right_sum = float('-inf')
+        curr_sum = 0
+        for i in range(mid + 1, high + 1):
+            curr_sum += arr[i]
+            if curr_sum > right_sum:
+                right_sum = curr_sum
+        
+        return left_sum + right_sum
+
+    def solve_recursive(arr, low, high):
+        if low == high:
+            return arr[low]
+        
+        mid = (low + high) // 2
+        
+        return max(
+            solve_recursive(arr, low, mid),
+            solve_recursive(arr, mid + 1, high),
+            max_crossing_sum(arr, low, mid, high)
+        )
+
+    if not arr:
+        return 0
+    return solve_recursive(arr, 0, len(arr) - 1)
+
+# 3. Dynamic Programming (Kadane's Algorithm) O(N)
+def solve_kadane(arr: List[int]) -> int:
+    if not arr:
+        return 0
+    max_so_far = arr[0]
+    curr_max = arr[0]
+    
+    for i in range(1, len(arr)):
+        curr_max = max(arr[i], curr_max + arr[i])
+        max_so_far = max(max_so_far, curr_max)
+        
+    return max_so_far

backend/problems/n_queens/generator.py

@@ -0,0 +1,8 @@
+from typing import Dict, Any
+
+def generate_n_queens_case(n: int = 8) -> Dict[str, int]:
+    """
+    Generates a case for N-Queens.
+    Actually just returns N since the problem is defined by the board size.
+    """
+    return {"n": n}

backend/problems/n_queens/problem.py

@@ -0,0 +1,48 @@
+from typing import Any, Dict, List
+from common.base_problem import BaseProblem
+from problems.n_queens.generator import generate_n_queens_case
+from problems.n_queens.solvers import solve_backtracking
+from common.timer_utils import time_execution
+
+class NQueensProblem(BaseProblem):
+    def generate_case(self, n: int = 8) -> Dict[str, Any]:
+        return generate_n_queens_case(n)
+
+    def solve(self, input_data: Dict[str, Any], algorithm: str) -> Dict[str, Any]:
+        n = input_data.get("n", 8)
+        result = None
+        duration = 0.0
+
+        if algorithm == "backtracking":
+            # For visualization, we usually just want one solution, 
+            # but for benchmarking maybe we want to count all?
+            # Let's default to finding ONE solution for "solve" to be fast enough for UI
+            # If N is small (< 12), we can find all.
+            find_all = n < 10 
+            result, duration = time_execution(solve_backtracking)(n, find_all)
+        else:
+            raise ValueError(f"Unknown algorithm: {algorithm}")
+        
+        return {
+            "algorithm": algorithm,
+            "solution_count": len(result),
+            "first_solution": result[0] if result else None,
+            "time_seconds": duration
+        }
+
+    def verify(self, input_data: Any, result: Any) -> bool:
+        # Verification is tricky without a ground truth. 
+        # We can check if the returned solution is valid.
+        sol = result.get("first_solution")
+        if not sol:
+            return True # No solution found (could be valid for some N, though N>=4 always has sol)
+        
+        n = len(sol)
+        for r in range(n):
+            c = sol[r]
+            # Check conflicts
+            for prev_r in range(r):
+                prev_c = sol[prev_r]
+                if c == prev_c or abs(r - prev_r) == abs(c - prev_c):
+                    return False
+        return True

backend/problems/n_queens/solvers.py

@@ -0,0 +1,38 @@
+from typing import List, Tuple, Optional
+
+def solve_backtracking(n: int, find_all: bool = False) -> List[List[int]]:
+    """
+    Backtracking algorithm for N-Queens.
+    Returns a list of solutions. Each solution is a list of column indices for each row.
+    """
+    solutions = []
+    board = [-1] * n  # board[row] = col
+    cols = [False] * n
+    diag1 = [False] * (2 * n - 1) # row + col
+    diag2 = [False] * (2 * n - 1) # row - col + (n - 1)
+
+    def backtrack(row: int):
+        if row == n:
+            solutions.append(board[:])
+            return True
+
+        for col in range(n):
+            if not cols[col] and not diag1[row + col] and not diag2[row - col + n - 1]:
+                board[row] = col
+                cols[col] = True
+                diag1[row + col] = True
+                diag2[row - col + n - 1] = True
+
+                if backtrack(row + 1):
+                    if not find_all:
+                        return True
+                
+                # Backtrack
+                cols[col] = False
+                diag1[row + col] = False
+                diag2[row - col + n - 1] = False
+        
+        return False
+
+    backtrack(0)
+    return solutions

backend/requirements.txt

@@ -0,0 +1,5 @@
+fastapi
+uvicorn
+matplotlib
+pandas
+numpy

backend/routers/interval_scheduling_router.py

@@ -0,0 +1,75 @@
+from fastapi import APIRouter, HTTPException
+from pydantic import BaseModel
+from typing import List, Optional, Dict, Any, Tuple
+from problems.interval_scheduling.problem import IntervalSchedulingProblem
+
+router = APIRouter(
+    prefix="/interval_scheduling",
+    tags=["interval_scheduling"],
+    responses={404: {"description": "Not found"}},
+)
+
+problem_solver = IntervalSchedulingProblem()
+
+class GenerateRequest(BaseModel):
+    size: int = 10
+    min_time: int = 0
+    max_time: int = 100
+
+class SolveRequest(BaseModel):
+    intervals: List[Tuple[int, int]]
+    algorithms: List[str] = ["greedy", "brute_force"]
+
+class BenchmarkRequest(BaseModel):
+    sizes: List[int] = [5, 10, 15, 20]
+    algorithms: List[str] = ["greedy", "brute_force"]
+
+@router.post("/generate")
+async def generate_case(req: GenerateRequest):
+    return problem_solver.generate_case(size=req.size, min_time=req.min_time, max_time=req.max_time)
+
+@router.post("/solve")
+async def solve_case(req: SolveRequest):
+    input_data = {"intervals": req.intervals}
+    results = []
+    for algo in req.algorithms:
+        try:
+            # Skip Brute Force for large inputs to avoid timeout
+            if len(req.intervals) > 22 and algo == "brute_force":
+                 results.append({
+                    "algorithm": algo,
+                    "error": "Input too large for Brute Force (limit 22)",
+                    "skipped": True
+                })
+                 continue
+
+            res = problem_solver.solve(input_data, algo)
+            results.append(res)
+        except ValueError as e:
+            results.append({"algorithm": algo, "error": str(e)})
+    return results
+
+@router.post("/benchmark")
+async def benchmark(req: BenchmarkRequest):
+    benchmark_results = []
+    for size in req.sizes:
+        input_data = problem_solver.generate_case(size=size)
+        
+        size_result = {"size": size, "algorithms": []}
+        for algo in req.algorithms:
+            try:
+                if size > 22 and algo == "brute_force":
+                     size_result["algorithms"].append({
+                        "algorithm": algo,
+                        "time_seconds": None,
+                        "skipped": True
+                    })
+                     continue
+
+                res = problem_solver.solve(input_data, algo)
+                size_result["algorithms"].append(res)
+            except Exception as e:
+                size_result["algorithms"].append({"algorithm": algo, "error": str(e)})
+        
+        benchmark_results.append(size_result)
+    return benchmark_results

backend/routers/knapsack_router.py

@@ -0,0 +1,76 @@
+from fastapi import APIRouter, HTTPException
+from pydantic import BaseModel
+from typing import List, Optional, Dict, Any
+from problems.knapsack.problem import KnapsackProblem
+
+router = APIRouter(
+    prefix="/knapsack",
+    tags=["knapsack"],
+    responses={404: {"description": "Not found"}},
+)
+
+problem_solver = KnapsackProblem()
+
+class GenerateRequest(BaseModel):
+    num_items: int = 10
+    max_weight: int = 50
+    max_value: int = 100
+
+class SolveRequest(BaseModel):
+    items: List[Dict[str, int]]
+    capacity: int
+    algorithms: List[str] = ["dp", "backtracking"]
+
+class BenchmarkRequest(BaseModel):
+    sizes: List[int] = [10, 20, 30]
+    algorithms: List[str] = ["dp", "backtracking"]
+
+@router.post("/generate")
+async def generate_case(req: GenerateRequest):
+    return problem_solver.generate_case(num_items=req.num_items, max_weight=req.max_weight, max_value=req.max_value)
+
+@router.post("/solve")
+async def solve_case(req: SolveRequest):
+    input_data = {"items": req.items, "capacity": req.capacity}
+    results = []
+    for algo in req.algorithms:
+        try:
+            # Skip Backtracking for large inputs
+            if len(req.items) > 22 and algo == "backtracking":
+                 results.append({
+                    "algorithm": algo,
+                    "error": "Input too large for Backtracking (limit 22)",
+                    "skipped": True
+                })
+                 continue
+
+            res = problem_solver.solve(input_data, algo)
+            results.append(res)
+        except ValueError as e:
+            results.append({"algorithm": algo, "error": str(e)})
+    return results
+
+@router.post("/benchmark")
+async def benchmark(req: BenchmarkRequest):
+    benchmark_results = []
+    for size in req.sizes:
+        input_data = problem_solver.generate_case(num_items=size)
+        
+        size_result = {"size": size, "algorithms": []}
+        for algo in req.algorithms:
+            try:
+                if size > 22 and algo == "backtracking":
+                     size_result["algorithms"].append({
+                        "algorithm": algo,
+                        "time_seconds": None,
+                        "skipped": True
+                    })
+                     continue
+
+                res = problem_solver.solve(input_data, algo)
+                size_result["algorithms"].append(res)
+            except Exception as e:
+                size_result["algorithms"].append({"algorithm": algo, "error": str(e)})
+        
+        benchmark_results.append(size_result)
+    return benchmark_results

backend/routers/max_subarray_router.py

@@ -0,0 +1,70 @@
+from fastapi import APIRouter, HTTPException
+from pydantic import BaseModel
+from typing import List, Optional, Dict, Any
+from problems.max_subarray.problem import MaxSubarrayProblem
+
+router = APIRouter(
+    prefix="/max_subarray",
+    tags=["max_subarray"],
+    responses={404: {"description": "Not found"}},
+)
+
+problem_solver = MaxSubarrayProblem()
+
+class GenerateRequest(BaseModel):
+    size: int = 100
+    min_val: int = -100
+    max_val: int = 100
+
+class SolveRequest(BaseModel):
+    array: List[int]
+    algorithms: List[str] = ["kadane", "divide_conquer", "brute_force"]
+
+class BenchmarkRequest(BaseModel):
+    sizes: List[int] = [10, 50, 100, 500, 1000]
+    algorithms: List[str] = ["kadane", "divide_conquer", "brute_force"]
+
+@router.post("/generate")
+async def generate_case(req: GenerateRequest):
+    return problem_solver.generate_case(size=req.size, min_val=req.min_val, max_val=req.max_val)
+
+@router.post("/solve")
+async def solve_case(req: SolveRequest):
+    input_data = {"array": req.array}
+    results = []
+    for algo in req.algorithms:
+        try:
+            res = problem_solver.solve(input_data, algo)
+            results.append(res)
+        except ValueError as e:
+            results.append({"algorithm": algo, "error": str(e)})
+    return results
+
+@router.post("/benchmark")
+async def benchmark(req: BenchmarkRequest):
+    benchmark_results = []
+    for size in req.sizes:
+        # Generate a random case for this size
+        # To reduce noise, we might want to run multiple times and average, 
+        # but for now single run per size is fine for demonstration
+        input_data = problem_solver.generate_case(size=size)
+        
+        size_result = {"size": size, "algorithms": []}
+        for algo in req.algorithms:
+            try:
+                # Skip O(N^2) for very large inputs to avoid timeout
+                if size > 5000 and algo == "brute_force":
+                     size_result["algorithms"].append({
+                        "algorithm": algo,
+                        "time_seconds": None,
+                        "skipped": True
+                    })
+                     continue
+
+                res = problem_solver.solve(input_data, algo)
+                size_result["algorithms"].append(res)
+            except Exception as e:
+                size_result["algorithms"].append({"algorithm": algo, "error": str(e)})
+        
+        benchmark_results.append(size_result)
+    return benchmark_results

backend/routers/n_queens_router.py

@@ -0,0 +1,66 @@
+from fastapi import APIRouter, HTTPException
+from pydantic import BaseModel
+from typing import List, Optional, Dict, Any
+from problems.n_queens.problem import NQueensProblem
+
+router = APIRouter(
+    prefix="/n_queens",
+    tags=["n_queens"],
+    responses={404: {"description": "Not found"}},
+)
+
+problem_solver = NQueensProblem()
+
+class GenerateRequest(BaseModel):
+    n: int = 8
+
+class SolveRequest(BaseModel):
+    n: int
+    algorithms: List[str] = ["backtracking"]
+
+class BenchmarkRequest(BaseModel):
+    sizes: List[int] = [4, 8, 10, 12]
+    algorithms: List[str] = ["backtracking"]
+
+@router.post("/generate")
+async def generate_case(req: GenerateRequest):
+    return problem_solver.generate_case(n=req.n)
+
+@router.post("/solve")
+async def solve_case(req: SolveRequest):
+    input_data = {"n": req.n}
+    results = []
+    for algo in req.algorithms:
+        try:
+            res = problem_solver.solve(input_data, algo)
+            results.append(res)
+        except ValueError as e:
+            results.append({"algorithm": algo, "error": str(e)})
+    return results
+
+@router.post("/benchmark")
+async def benchmark(req: BenchmarkRequest):
+    benchmark_results = []
+    for size in req.sizes:
+        input_data = {"n": size}
+        
+        size_result = {"size": size, "algorithms": []}
+        for algo in req.algorithms:
+            try:
+                # Skip large N for backtracking if finding all solutions (though our solve defaults to one for large N)
+                # But for benchmark we might want to be careful.
+                if size > 14 and algo == "backtracking":
+                     size_result["algorithms"].append({
+                        "algorithm": algo,
+                        "time_seconds": None,
+                        "skipped": True
+                    })
+                     continue
+
+                res = problem_solver.solve(input_data, algo)
+                size_result["algorithms"].append(res)
+            except Exception as e:
+                size_result["algorithms"].append({"algorithm": algo, "error": str(e)})
+        
+        benchmark_results.append(size_result)
+    return benchmark_results

backend/verify_all.py

@@ -0,0 +1,58 @@
+import sys
+import os
+import random
+
+# Add backend to path
+sys.path.append(os.path.abspath("/Users/hissin/测试/25-cxsj-final/backend"))
+
+from problems.max_subarray.problem import MaxSubarrayProblem
+from problems.interval_scheduling.problem import IntervalSchedulingProblem
+from problems.n_queens.problem import NQueensProblem
+from problems.knapsack.problem import KnapsackProblem
+
+def test_max_subarray():
+    print("\nTesting Max Subarray...")
+    prob = MaxSubarrayProblem()
+    case = prob.generate_case(size=10)
+    res = prob.solve(case, "kadane")
+    print(f"Max Subarray Result: {res['result']}")
+    assert prob.verify(case, res['result'])
+    print("Max Subarray Passed!")
+
+def test_interval_scheduling():
+    print("\nTesting Interval Scheduling...")
+    prob = IntervalSchedulingProblem()
+    case = prob.generate_case(size=10)
+    res = prob.solve(case, "greedy")
+    print(f"Interval Scheduling Count: {res['result_count']}")
+    assert prob.verify(case, res)
+    print("Interval Scheduling Passed!")
+
+def test_n_queens():
+    print("\nTesting N-Queens...")
+    prob = NQueensProblem()
+    case = prob.generate_case(n=8)
+    res = prob.solve(case, "backtracking")
+    print(f"N-Queens (N=8) Solutions: {res['solution_count']}")
+    assert res['solution_count'] == 92
+    print("N-Queens Passed!")
+
+def test_knapsack():
+    print("\nTesting Knapsack...")
+    prob = KnapsackProblem()
+    case = prob.generate_case(num_items=10, max_weight=20, max_value=100)
+    res_dp = prob.solve(case, "dp")
+    res_back = prob.solve(case, "backtracking")
+    
+    print(f"Knapsack DP Value: {res_dp['max_value']}")
+    print(f"Knapsack Backtracking Value: {res_back['max_value']}")
+    
+    assert res_dp['max_value'] == res_back['max_value']
+    assert prob.verify(case, res_dp)
+    print("Knapsack Passed!")
+
+if __name__ == "__main__":
+    test_max_subarray()
+    test_interval_scheduling()
+    test_n_queens()
+    test_knapsack()

backend/verify_backend.py

@@ -0,0 +1,61 @@
+import sys
+import os
+
+# Add backend to path
+sys.path.append(os.path.abspath("/Users/hissin/测试/25-cxsj-final/backend"))
+
+from problems.interval_scheduling.generator import generate_interval_scheduling_case
+from problems.interval_scheduling.solvers import solve_greedy, solve_brute_force
+from problems.interval_scheduling.problem import IntervalSchedulingProblem
+
+def test_generator():
+    print("Testing Generator...")
+    intervals = generate_interval_scheduling_case(size=10, min_time=0, max_time=100)
+    print(f"Generated {len(intervals)} intervals: {intervals}")
+    assert len(intervals) == 10
+    for start, end in intervals:
+        assert start < end
+        assert start >= 0
+        assert end <= 100
+    print("Generator Passed!")
+
+def test_solvers():
+    print("\nTesting Solvers...")
+    # Known case
+    intervals = [(1, 3), (2, 4), (3, 5)]
+    # Greedy should pick (1,3) and (3,5) -> count 2
+    greedy_res = solve_greedy(intervals)
+    print(f"Greedy result: {greedy_res}")
+    assert len(greedy_res) == 2
+    
+    brute_res = solve_brute_force(intervals)
+    print(f"Brute Force result: {brute_res}")
+    assert len(brute_res) == 2
+    
+    # Complex case
+    intervals = [(1, 4), (3, 5), (0, 6), (5, 7), (3, 9), (5, 9), (6, 10), (8, 11), (8, 12), (2, 14), (12, 16)]
+    greedy_res = solve_greedy(intervals)
+    brute_res = solve_brute_force(intervals)
+    print(f"Complex Greedy: {len(greedy_res)}")
+    print(f"Complex Brute: {len(brute_res)}")
+    assert len(greedy_res) == len(brute_res)
+    print("Solvers Passed!")
+
+def test_problem_class():
+    print("\nTesting Problem Class...")
+    prob = IntervalSchedulingProblem()
+    case = prob.generate_case(size=5)
+    res_greedy = prob.solve(case, "greedy")
+    res_brute = prob.solve(case, "brute_force")
+    
+    print(f"Class Greedy: {res_greedy}")
+    print(f"Class Brute: {res_brute}")
+    
+    assert prob.verify(case, res_greedy)
+    assert res_greedy["result_count"] == res_brute["result_count"]
+    print("Problem Class Passed!")
+
+if __name__ == "__main__":
+    test_generator()
+    test_solvers()
+    test_problem_class()

docs/DESIGN_DOCUMENT.md

@@ -0,0 +1,84 @@
+# 算法测试用例生成与自我验证平台 - 设计文档
+
+## 1. 项目概述
+本项目旨在构建一个集“自动出题”、“多算法求解”、“性能分析”于一体的算法学习与验证平台。通过针对特定算法问题生成随机测试数据，并使用不同复杂度的算法进行求解，验证结果一致性并对比运行效率。项目包含一个现代化 Web 前端界面，用于交互式地配置参数与展示图表。
+
+## 2. 系统架构设计
+系统采用 **前后端分离** 架构：
+
+### 2.1 核心模块
+#### 后端 (Backend)
+1.  **Problem Interface (问题接口)**
+    *   定义问题的通用接口，包括 `generate_case()` (生成用例), `solve()` (求解), `verify()` (验证)。
+2.  **Solver Engine (求解引擎)**
+    *   针对每个问题，实现多种算法策略（暴力、分治、DP、贪心等）。
+3.  **Performance Analyzer (性能分析器)**
+    *   执行基准测试，验证正确性，统计运行时间。
+4.  **API Layer (API 层)**
+    *   基于 **FastAPI** 提供 RESTful 接口，处理前端的配置请求并返回计算结果。
+
+#### 前端 (Frontend)
+1.  **Control Panel (控制面板)**
+    *   选择算法问题（如“最大子数组和”、“0/1背包”）。
+    *   配置生成参数（数据规模、数值范围、稀疏度等）。
+2.  **Visualization (可视化展示)**
+    *   使用图表库展示不同算法的时间复杂度对比曲线。
+    *   展示具体的测试用例数据与解题结果（用于教学演示）。
+
+### 2.2 技术栈
+*   **后端**: Python 3.x, FastAPI (Web框架), Matplotlib/Pandas (数据分析)
+*   **前端**: React, TailwindCSS (样式), Recharts (图表可视化), Axios (网络请求)
+
+## 3. 选定算法问题
+
+### 问题一：最大子数组和 (Maximum Subarray Sum)
+**描述**: 给定一个整数数组，找到一个具有最大和的连续子数组。
+**测试用例生成**:
+*   随机生成长度为 $N$ 的整数数组。
+*   数值范围可配置（包含正负数）。
+**算法实现**:
+1.  **暴力枚举 (Brute Force)**: 双重循环枚举所有子数组，时间复杂度 $O(N^2)$。
+2.  **分治算法 (Divide and Conquer)**: 递归将数组分为左右两半，最大子数组可能在左、右或跨越中点，时间复杂度 $O(N \log N)$。
+3.  **动态规划 (Kadane's Algorithm)**: 线性扫描，时间复杂度 $O(N)$。
+
+### 问题二：0/1 背包问题 (0/1 Knapsack Problem)
+**描述**: 给定一组物品，每种物品都有自己的重量和价值，在限定的总重量内，选择其中若干个（也即每种物品可以选0个或1个），使得物品的总价值最高。
+**测试用例生成**:
+*   随机生成 $N$ 个物品，每个物品具有重量 $w$ 和价值 $v$。
+*   随机生成背包容量 $C$。
+**算法实现**:
+1.  **回溯法 (Backtracking)**: 递归枚举所有可能的选择情况，时间复杂度 $O(2^N)$。
+2.  **动态规划 (Dynamic Programming)**: 使用二维或一维数组记录状态，时间复杂度 $O(N \cdot C)$。
+3.  **贪心算法 (Greedy, 近似解/对比)**: 按价值密度排序选择（注意：0/1背包贪心法通常不能得到最优解，可作为对比项展示“错误”或“近似”的算法，或者用于对比部分背包问题）。*注：本项目中为了验证正确性，主要对比回溯与DP，贪心可作为错误示范分析。*
+
+## 4. 目录结构规划
+```
+algorithm_platform/
+├── README.md
+├── DESIGN_DOCUMENT.md
+├── backend/                # 后端代码
+│   ├── main.py             # FastAPI 入口
+│   ├── common/             # 通用工具
+│   │   ├── __init__.py
+│   │   ├── base_problem.py
+│   │   └── timer_utils.py
+│   ├── problems/           # 算法实现模块
+│   │   ├── __init__.py
+│   │   ├── max_subarray/
+│   │   └── knapsack/
+│   └── routers/            # API 路由
+└── frontend/               # 前端代码
+    ├── src/
+    │   ├── components/     # UI 组件
+    │   ├── pages/          # 页面
+    │   └── services/       # API 调用
+    ├── package.json
+    └── vite.config.js
+```
+
+## 5. 开发计划
+1.  **第一阶段**: 搭建后端核心骨架 (FastAPI + Base Classes)。
+2.  **第二阶段**: 实现“最大子数组和”算法逻辑与 API。
+3.  **第三阶段**: 搭建 React 前端框架，实现基础交互与图表组件。
+4.  **第四阶段**: 实现“0/1背包”算法逻辑，并接入前端。
+5.  **第五阶段**: 优化 UI/UX，完善性能对比的可视化报告。

frontend/index.html

@@ -0,0 +1,14 @@
+<!doctype html>
+<html lang="en">
+  <head>
+    <meta charset="UTF-8" />
+    <link rel="icon" type="image/svg+xml" href="/vite.svg" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>Algorithm Platform</title>
+    <script src="https://cdn.tailwindcss.com"></script>
+  </head>
+  <body>
+    <div id="root"></div>
+    <script type="module" src="/src/main.jsx"></script>
+  </body>
+</html>

frontend/package.json

@@ -0,0 +1,30 @@
+{
+  "name": "algorithm-platform-frontend",
+  "private": true,
+  "version": "0.0.0",
+  "type": "module",
+  "scripts": {
+    "dev": "vite",
+    "build": "vite build",
+    "lint": "eslint .",
+    "preview": "vite preview"
+  },
+  "dependencies": {
+    "axios": "^1.6.0",
+    "lucide-react": "^0.292.0",
+    "react": "^18.2.0",
+    "react-dom": "^18.2.0",
+    "recharts": "^2.9.0",
+    "clsx": "^2.0.0",
+    "tailwind-merge": "^2.0.0"
+  },
+  "devDependencies": {
+    "@types/react": "^18.2.37",
+    "@types/react-dom": "^18.2.15",
+    "@vitejs/plugin-react": "^4.2.0",
+    "autoprefixer": "^10.4.16",
+    "postcss": "^8.4.31",
+    "tailwindcss": "^3.3.5",
+    "vite": "^5.0.0"
+  }
+}

frontend/src/App.jsx

@@ -0,0 +1,72 @@
+import React, { useState } from 'react';
+import MaxSubarray from './components/MaxSubarray';
+import IntervalScheduling from './components/IntervalScheduling';
+import NQueens from './components/NQueens';
+import Knapsack from './components/Knapsack';
+
+function App() {
+  const [activeTab, setActiveTab] = useState('max_subarray');
+
+  return (
+    <div className="min-h-screen bg-gray-50">
+      <nav className="bg-white shadow-sm">
+        <div className="max-w-7xl mx-auto px-4 sm:px-6 lg:px-8">
+          <div className="flex justify-between h-16">
+            <div className="flex items-center">
+              <span className="text-xl font-bold text-gray-800">算法验证平台</span>
+              <div className="ml-10 flex items-baseline space-x-4">
+                <button
+                  onClick={() => setActiveTab('max_subarray')}
+                  className={`px-3 py-2 rounded-md text-sm font-medium ${activeTab === 'max_subarray'
+                      ? 'bg-blue-100 text-blue-700'
+                      : 'text-gray-600 hover:bg-gray-100'
+                    }`}
+                >
+                  最大子数组和
+                </button>
+                <button
+                  onClick={() => setActiveTab('interval_scheduling')}
+                  className={`px-3 py-2 rounded-md text-sm font-medium ${activeTab === 'interval_scheduling'
+                      ? 'bg-blue-100 text-blue-700'
+                      : 'text-gray-600 hover:bg-gray-100'
+                    }`}
+                >
+                  区间调度
+                </button>
+                <button
+                  onClick={() => setActiveTab('n_queens')}
+                  className={`px-3 py-2 rounded-md text-sm font-medium ${activeTab === 'n_queens'
+                      ? 'bg-blue-100 text-blue-700'
+                      : 'text-gray-600 hover:bg-gray-100'
+                    }`}
+                >
+                  N皇后
+                </button>
+                <button
+                  onClick={() => setActiveTab('knapsack')}
+                  className={`px-3 py-2 rounded-md text-sm font-medium ${activeTab === 'knapsack'
+                      ? 'bg-blue-100 text-blue-700'
+                      : 'text-gray-600 hover:bg-gray-100'
+                    }`}
+                >
+                  0/1 背包
+                </button>
+              </div>
+            </div>
+          </div>
+        </div>
+      </nav>
+
+      <main className="max-w-7xl mx-auto py-6 sm:px-6 lg:px-8">
+        <div className="px-4 py-6 sm:px-0">
+          {activeTab === 'max_subarray' && <MaxSubarray />}
+          {activeTab === 'interval_scheduling' && <IntervalScheduling />}
+          {activeTab === 'n_queens' && <NQueens />}
+          {activeTab === 'knapsack' && <Knapsack />}
+        </div>
+      </main>
+    </div>
+  );
+}
+
+export default App;

frontend/src/api.js

@@ -0,0 +1,103 @@
+import axios from 'axios';
+
+const API_URL = 'http://localhost:8000';
+
+export const generateCase = async (size, minVal, maxVal) => {
+    const response = await axios.post(`${API_URL}/max_subarray/generate`, {
+        size,
+        min_val: minVal,
+        max_val: maxVal
+    });
+    return response.data;
+};
+
+export const solveCase = async (array, algorithms) => {
+    const response = await axios.post(`${API_URL}/max_subarray/solve`, {
+        array,
+        algorithms
+    });
+    return response.data;
+};
+
+export const runBenchmark = async (sizes, algorithms) => {
+    const response = await axios.post(`${API_URL}/max_subarray/benchmark`, {
+        sizes,
+        algorithms
+    });
+    return response.data;
+};
+
+// Interval Scheduling API
+export const generateIntervalCase = async (size, minTime, maxTime) => {
+    const response = await axios.post(`${API_URL}/interval_scheduling/generate`, {
+        size,
+        min_time: minTime,
+        max_time: maxTime
+    });
+    return response.data;
+};
+
+export const solveIntervalCase = async (intervals, algorithms) => {
+    const response = await axios.post(`${API_URL}/interval_scheduling/solve`, {
+        intervals,
+        algorithms
+    });
+    return response.data;
+};
+
+export const runIntervalBenchmark = async (sizes, algorithms) => {
+    const response = await axios.post(`${API_URL}/interval_scheduling/benchmark`, {
+        sizes,
+        algorithms
+    });
+    return response.data;
+};
+
+// N-Queens API
+export const generateNQueensCase = async (n) => {
+    const response = await axios.post(`${API_URL}/n_queens/generate`, { n });
+    return response.data;
+};
+
+export const solveNQueensCase = async (n, algorithms) => {
+    const response = await axios.post(`${API_URL}/n_queens/solve`, {
+        n,
+        algorithms
+    });
+    return response.data;
+};
+
+export const runNQueensBenchmark = async (sizes, algorithms) => {
+    const response = await axios.post(`${API_URL}/n_queens/benchmark`, {
+        sizes,
+        algorithms
+    });
+    return response.data;
+};
+
+// Knapsack API
+export const generateKnapsackCase = async (numItems, maxWeight, maxValue) => {
+    const response = await axios.post(`${API_URL}/knapsack/generate`, {
+        num_items: numItems,
+        max_weight: maxWeight,
+        max_value: maxValue
+    });
+    return response.data;
+};
+
+export const solveKnapsackCase = async (items, capacity, algorithms) => {
+    const response = await axios.post(`${API_URL}/knapsack/solve`, {
+        items,
+        capacity,
+        algorithms
+    });
+    return response.data;
+};
+
+export const runKnapsackBenchmark = async (sizes, algorithms) => {
+    const response = await axios.post(`${API_URL}/knapsack/benchmark`, {
+        sizes,
+        algorithms
+    });
+    return response.data;
+};

frontend/src/components/IntervalScheduling.jsx

@@ -0,0 +1,250 @@
+import React, { useState } from 'react';
+import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+import { generateIntervalCase, solveIntervalCase, runIntervalBenchmark } from '../api';
+
+const IntervalScheduling = () => {
+    const [params, setParams] = useState({ size: 10, min: 0, max: 100 });
+    const [currentCase, setCurrentCase] = useState(null);
+    const [solveResults, setSolveResults] = useState(null);
+    const [benchmarkResults, setBenchmarkResults] = useState(null);
+    const [loading, setLoading] = useState(false);
+
+    // Algorithm selection state
+    const [selectedAlgorithms, setSelectedAlgorithms] = useState({
+        greedy: true,
+        brute_force: true
+    });
+
+    const algorithmsList = [
+        { id: 'greedy', name: '贪心算法 (Greedy) O(N log N)' },
+        { id: 'brute_force', name: '暴力求解 (Brute Force) O(2^N)' }
+    ];
+
+    const getSelectedAlgoKeys = () => {
+        return Object.keys(selectedAlgorithms).filter(k => selectedAlgorithms[k]);
+    };
+
+    const handleGenerate = async () => {
+        setLoading(true);
+        try {
+            const data = await generateIntervalCase(params.size, params.min, params.max);
+            setCurrentCase(data.intervals);
+            setSolveResults(null);
+        } catch (error) {
+            console.error("Error generating case:", error);
+            alert("生成测试用例失败");
+        }
+        setLoading(false);
+    };
+
+    const handleSolve = async () => {
+        if (!currentCase) return;
+        const algos = getSelectedAlgoKeys();
+        if (algos.length === 0) {
+            alert("请至少选择一种算法");
+            return;
+        }
+
+        setLoading(true);
+        try {
+            const results = await solveIntervalCase(currentCase, algos);
+            setSolveResults(results);
+        } catch (error) {
+            console.error("Error solving case:", error);
+            alert("求解失败");
+        }
+        setLoading(false);
+    };
+
+    const handleBenchmark = async () => {
+        const algos = getSelectedAlgoKeys();
+        if (algos.length === 0) {
+            alert("请至少选择一种算法");
+            return;
+        }
+
+        setLoading(true);
+        try {
+            // Smaller sizes for Brute Force safety
+            const sizes = [5, 10, 15, 20, 22];
+            const results = await runIntervalBenchmark(sizes, algos);
+
+            // Transform data for Recharts
+            const chartData = results.map(item => {
+                const point = { size: item.size };
+                item.algorithms.forEach(algo => {
+                    if (algo.time_seconds !== undefined && algo.time_seconds !== null) {
+                        point[algo.algorithm] = algo.time_seconds;
+                    }
+                });
+                return point;
+            });
+
+            setBenchmarkResults(chartData);
+        } catch (error) {
+            console.error("Error running benchmark:", error);
+            alert("性能测试失败");
+        }
+        setLoading(false);
+    };
+
+    const toggleAlgorithm = (algoId) => {
+        setSelectedAlgorithms(prev => ({
+            ...prev,
+            [algoId]: !prev[algoId]
+        }));
+    };
+
+    return (
+        <div className="p-6 space-y-8">
+            <h1 className="text-3xl font-bold text-gray-800">区间调度问题 (Interval Scheduling)</h1>
+            <p className="text-gray-600">目标：在给定的一组区间中，选择尽可能多的互不重叠的区间。</p>
+
+            {/* Algorithm Selection */}
+            <div className="bg-white p-6 rounded-lg shadow">
+                <h2 className="text-xl font-semibold mb-4">算法选择</h2>
+                <div className="flex flex-wrap gap-4">
+                    {algorithmsList.map(algo => (
+                        <label key={algo.id} className="flex items-center space-x-2 cursor-pointer">
+                            <input
+                                type="checkbox"
+                                checked={selectedAlgorithms[algo.id]}
+                                onChange={() => toggleAlgorithm(algo.id)}
+                                className="form-checkbox h-5 w-5 text-blue-600"
+                            />
+                            <span className="text-gray-700">{algo.name}</span>
+                        </label>
+                    ))}
+                </div>
+            </div>
+
+            {/* Section 1: Generate & Solve */}
+            <div className="grid grid-cols-1 md:grid-cols-2 gap-6">
+                <div className="bg-white p-6 rounded-lg shadow">
+                    <h2 className="text-xl font-semibold mb-4">1. 生成测试用例</h2>
+                    <div className="space-y-4">
+                        <div className="grid grid-cols-3 gap-4">
+                            <div>
+                                <label className="block text-sm font-medium text-gray-700">区间数量 (N)</label>
+                                <input
+                                    type="number"
+                                    value={params.size}
+                                    onChange={(e) => setParams({ ...params, size: parseInt(e.target.value) })}
+                                    className="mt-1 block w-full border rounded-md p-2"
+                                />
+                            </div>
+                            <div>
+                                <label className="block text-sm font-medium text-gray-700">最小时间</label>
+                                <input
+                                    type="number"
+                                    value={params.min}
+                                    onChange={(e) => setParams({ ...params, min: parseInt(e.target.value) })}
+                                    className="mt-1 block w-full border rounded-md p-2"
+                                />
+                            </div>
+                            <div>
+                                <label className="block text-sm font-medium text-gray-700">最大时间</label>
+                                <input
+                                    type="number"
+                                    value={params.max}
+                                    onChange={(e) => setParams({ ...params, max: parseInt(e.target.value) })}
+                                    className="mt-1 block w-full border rounded-md p-2"
+                                />
+                            </div>
+                        </div>
+                        <button
+                            onClick={handleGenerate}
+                            disabled={loading}
+                            className="w-full bg-blue-600 text-white py-2 px-4 rounded-md hover:bg-blue-700 disabled:bg-gray-400"
+                        >
+                            {loading ? '处理中...' : '生成测试用例'}
+                        </button>
+                    </div>
+
+                    {currentCase && (
+                        <div className="mt-4">
+                            <h3 className="font-medium">已生成区间 (预览):</h3>
+                            <div className="font-mono text-sm bg-gray-100 p-2 rounded break-all max-h-64 overflow-y-auto">
+                                {currentCase.map((interval, idx) => (
+                                    <div key={idx} className="mb-1">
+                                        [{interval[0]}, {interval[1]}]
+                                    </div>
+                                ))}
+                            </div>
+                            <p className="text-xs text-gray-500 mt-1">总区间数量: {currentCase.length}</p>
+                        </div>
+                    )}
+                </div>
+
+                <div className="bg-white p-6 rounded-lg shadow">
+                    <h2 className="text-xl font-semibold mb-4">2. 求解与验证</h2>
+                    <button
+                        onClick={handleSolve}
+                        disabled={!currentCase || loading}
+                        className="w-full bg-green-600 text-white py-2 px-4 rounded-md hover:bg-green-700 disabled:bg-gray-400 mb-4"
+                    >
+                        运行选中算法
+                    </button>
+
+                    {solveResults && (
+                        <div className="overflow-x-auto">
+                            <table className="min-w-full divide-y divide-gray-200">
+                                <thead>
+                                    <tr>
+                                        <th className="px-4 py-2 text-left text-xs font-medium text-gray-500 uppercase">算法</th>
+                                        <th className="px-4 py-2 text-left text-xs font-medium text-gray-500 uppercase">选中数量</th>
+                                        <th className="px-4 py-2 text-left text-xs font-medium text-gray-500 uppercase">耗时 (秒)</th>
+                                    </tr>
+                                </thead>
+                                <tbody className="divide-y divide-gray-200">
+                                    {solveResults.map((res, idx) => (
+                                        <tr key={idx}>
+                                            <td className="px-4 py-2 text-sm font-medium text-gray-900">{res.algorithm}</td>
+                                            <td className="px-4 py-2 text-sm text-gray-500">{res.result_count}</td>
+                                            <td className="px-4 py-2 text-sm text-gray-500">{res.time_seconds?.toFixed(6)}</td>
+                                        </tr>
+                                    ))}
+                                </tbody>
+                            </table>
+                        </div>
+                    )}
+                </div>
+            </div>
+
+            {/* Section 2: Benchmark */}
+            <div className="bg-white p-6 rounded-lg shadow">
+                <div className="flex justify-between items-center mb-6">
+                    <h2 className="text-xl font-semibold">3. 性能对比测试</h2>
+                    <button
+                        onClick={handleBenchmark}
+                        disabled={loading}
+                        className="bg-purple-600 text-white py-2 px-4 rounded-md hover:bg-purple-700 disabled:bg-gray-400"
+                    >
+                        运行性能测试
+                    </button>
+                </div>
+
+                {benchmarkResults && (
+                    <div className="h-96 w-full">
+                        <ResponsiveContainer width="100%" height="100%">
+                            <LineChart
+                                data={benchmarkResults}
+                                margin={{ top: 5, right: 30, left: 20, bottom: 5 }}
+                            >
+                                <CartesianGrid strokeDasharray="3 3" />
+                                <XAxis dataKey="size" label={{ value: '区间数量 (N)', position: 'insideBottomRight', offset: -10 }} />
+                                <YAxis label={{ value: '耗时 (秒)', angle: -90, position: 'insideLeft' }} />
+                                <Tooltip />
+                                <Legend />
+                                <Line type="monotone" dataKey="greedy" stroke="#00ff00" name="贪心算法" />
+                                <Line type="monotone" dataKey="brute_force" stroke="#ff0000" name="暴力求解" />
+                            </LineChart>
+                        </ResponsiveContainer>
+                    </div>
+                )}
+            </div>
+        </div>
+    );
+};
+
+export default IntervalScheduling;

frontend/src/components/Knapsack.jsx

@@ -0,0 +1,261 @@
+import React, { useState } from 'react';
+import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+import { generateKnapsackCase, solveKnapsackCase, runKnapsackBenchmark } from '../api';
+
+const Knapsack = () => {
+    const [params, setParams] = useState({ num_items: 10, max_weight: 50, max_value: 100 });
+    const [currentCase, setCurrentCase] = useState(null);
+    const [solveResults, setSolveResults] = useState(null);
+    const [benchmarkResults, setBenchmarkResults] = useState(null);
+    const [loading, setLoading] = useState(false);
+
+    // Algorithm selection state
+    const [selectedAlgorithms, setSelectedAlgorithms] = useState({
+        dp: true,
+        backtracking: true
+    });
+
+    const algorithmsList = [
+        { id: 'dp', name: '动态规划 (DP) O(NW)' },
+        { id: 'backtracking', name: '回溯算法 (Backtracking) O(2^N)' }
+    ];
+
+    const getSelectedAlgoKeys = () => {
+        return Object.keys(selectedAlgorithms).filter(k => selectedAlgorithms[k]);
+    };
+
+    const handleGenerate = async () => {
+        setLoading(true);
+        try {
+            const data = await generateKnapsackCase(params.num_items, params.max_weight, params.max_value);
+            setCurrentCase(data);
+            setSolveResults(null);
+        } catch (error) {
+            console.error("Error generating case:", error);
+            alert("生成测试用例失败");
+        }
+        setLoading(false);
+    };
+
+    const handleSolve = async () => {
+        if (!currentCase) return;
+        const algos = getSelectedAlgoKeys();
+        if (algos.length === 0) {
+            alert("请至少选择一种算法");
+            return;
+        }
+
+        setLoading(true);
+        try {
+            const results = await solveKnapsackCase(currentCase.items, currentCase.capacity, algos);
+            setSolveResults(results);
+        } catch (error) {
+            console.error("Error solving case:", error);
+            alert("求解失败");
+        }
+        setLoading(false);
+    };
+
+    const handleBenchmark = async () => {
+        const algos = getSelectedAlgoKeys();
+        if (algos.length === 0) {
+            alert("请至少选择一种算法");
+            return;
+        }
+
+        setLoading(true);
+        try {
+            const sizes = [10, 15, 20, 22, 25];
+            const results = await runKnapsackBenchmark(sizes, algos);
+
+            const chartData = results.map(item => {
+                const point = { size: item.size };
+                item.algorithms.forEach(algo => {
+                    if (algo.time_seconds !== undefined && algo.time_seconds !== null) {
+                        point[algo.algorithm] = algo.time_seconds;
+                    }
+                });
+                return point;
+            });
+
+            setBenchmarkResults(chartData);
+        } catch (error) {
+            console.error("Error running benchmark:", error);
+            alert("性能测试失败");
+        }
+        setLoading(false);
+    };
+
+    const toggleAlgorithm = (algoId) => {
+        setSelectedAlgorithms(prev => ({
+            ...prev,
+            [algoId]: !prev[algoId]
+        }));
+    };
+
+    return (
+        <div className="p-6 space-y-8">
+            <h1 className="text-3xl font-bold text-gray-800">0/1 背包问题 (0/1 Knapsack)</h1>
+            <p className="text-gray-600">目标：在不超过背包容量的情况下，选择物品使得总价值最大。</p>
+
+            {/* Algorithm Selection */}
+            <div className="bg-white p-6 rounded-lg shadow">
+                <h2 className="text-xl font-semibold mb-4">算法选择</h2>
+                <div className="flex flex-wrap gap-4">
+                    {algorithmsList.map(algo => (
+                        <label key={algo.id} className="flex items-center space-x-2 cursor-pointer">
+                            <input
+                                type="checkbox"
+                                checked={selectedAlgorithms[algo.id]}
+                                onChange={() => toggleAlgorithm(algo.id)}
+                                className="form-checkbox h-5 w-5 text-blue-600"
+                            />
+                            <span className="text-gray-700">{algo.name}</span>
+                        </label>
+                    ))}
+                </div>
+            </div>
+
+            {/* Section 1: Generate & Solve */}
+            <div className="grid grid-cols-1 md:grid-cols-2 gap-6">
+                <div className="bg-white p-6 rounded-lg shadow">
+                    <h2 className="text-xl font-semibold mb-4">1. 生成测试用例</h2>
+                    <div className="space-y-4">
+                        <div className="grid grid-cols-3 gap-4">
+                            <div>
+                                <label className="block text-sm font-medium text-gray-700">物品数量</label>
+                                <input
+                                    type="number"
+                                    value={params.num_items}
+                                    onChange={(e) => setParams({ ...params, num_items: parseInt(e.target.value) })}
+                                    className="mt-1 block w-full border rounded-md p-2"
+                                />
+                            </div>
+                            <div>
+                                <label className="block text-sm font-medium text-gray-700">最大重量</label>
+                                <input
+                                    type="number"
+                                    value={params.max_weight}
+                                    onChange={(e) => setParams({ ...params, max_weight: parseInt(e.target.value) })}
+                                    className="mt-1 block w-full border rounded-md p-2"
+                                />
+                            </div>
+                            <div>
+                                <label className="block text-sm font-medium text-gray-700">最大价值</label>
+                                <input
+                                    type="number"
+                                    value={params.max_value}
+                                    onChange={(e) => setParams({ ...params, max_value: parseInt(e.target.value) })}
+                                    className="mt-1 block w-full border rounded-md p-2"
+                                />
+                            </div>
+                        </div>
+                        <button
+                            onClick={handleGenerate}
+                            disabled={loading}
+                            className="w-full bg-blue-600 text-white py-2 px-4 rounded-md hover:bg-blue-700 disabled:bg-gray-400"
+                        >
+                            {loading ? '处理中...' : '生成测试用例'}
+                        </button>
+                    </div>
+
+                    {currentCase && (
+                        <div className="mt-4">
+                            <h3 className="font-medium">背包容量: {currentCase.capacity}</h3>
+                            <h3 className="font-medium mt-2">物品列表 (预览):</h3>
+                            <div className="font-mono text-sm bg-gray-100 p-2 rounded break-all max-h-64 overflow-y-auto">
+                                <table className="min-w-full text-xs">
+                                    <thead>
+                                        <tr>
+                                            <th className="text-left">ID</th>
+                                            <th className="text-left">重量</th>
+                                            <th className="text-left">价值</th>
+                                        </tr>
+                                    </thead>
+                                    <tbody>
+                                        {currentCase.items.map((item) => (
+                                            <tr key={item.id}>
+                                                <td>{item.id}</td>
+                                                <td>{item.weight}</td>
+                                                <td>{item.value}</td>
+                                            </tr>
+                                        ))}
+                                    </tbody>
+                                </table>
+                            </div>
+                        </div>
+                    )}
+                </div>
+
+                <div className="bg-white p-6 rounded-lg shadow">
+                    <h2 className="text-xl font-semibold mb-4">2. 求解与验证</h2>
+                    <button
+                        onClick={handleSolve}
+                        disabled={!currentCase || loading}
+                        className="w-full bg-green-600 text-white py-2 px-4 rounded-md hover:bg-green-700 disabled:bg-gray-400 mb-4"
+                    >
+                        运行选中算法
+                    </button>
+
+                    {solveResults && (
+                        <div className="overflow-x-auto">
+                            <table className="min-w-full divide-y divide-gray-200">
+                                <thead>
+                                    <tr>
+                                        <th className="px-4 py-2 text-left text-xs font-medium text-gray-500 uppercase">算法</th>
+                                        <th className="px-4 py-2 text-left text-xs font-medium text-gray-500 uppercase">最大价值</th>
+                                        <th className="px-4 py-2 text-left text-xs font-medium text-gray-500 uppercase">耗时 (秒)</th>
+                                    </tr>
+                                </thead>
+                                <tbody className="divide-y divide-gray-200">
+                                    {solveResults.map((res, idx) => (
+                                        <tr key={idx}>
+                                            <td className="px-4 py-2 text-sm font-medium text-gray-900">{res.algorithm}</td>
+                                            <td className="px-4 py-2 text-sm text-gray-500">{res.max_value}</td>
+                                            <td className="px-4 py-2 text-sm text-gray-500">{res.time_seconds?.toFixed(6)}</td>
+                                        </tr>
+                                    ))}
+                                </tbody>
+                            </table>
+                        </div>
+                    )}
+                </div>
+            </div>
+
+            {/* Section 2: Benchmark */}
+            <div className="bg-white p-6 rounded-lg shadow">
+                <div className="flex justify-between items-center mb-6">
+                    <h2 className="text-xl font-semibold">3. 性能对比测试</h2>
+                    <button
+                        onClick={handleBenchmark}
+                        disabled={loading}
+                        className="bg-purple-600 text-white py-2 px-4 rounded-md hover:bg-purple-700 disabled:bg-gray-400"
+                    >
+                        运行性能测试
+                    </button>
+                </div>
+
+                {benchmarkResults && (
+                    <div className="h-96 w-full">
+                        <ResponsiveContainer width="100%" height="100%">
+                            <LineChart
+                                data={benchmarkResults}
+                                margin={{ top: 5, right: 30, left: 20, bottom: 5 }}
+                            >
+                                <CartesianGrid strokeDasharray="3 3" />
+                                <XAxis dataKey="size" label={{ value: '物品数量 (N)', position: 'insideBottomRight', offset: -10 }} />
+                                <YAxis label={{ value: '耗时 (秒)', angle: -90, position: 'insideLeft' }} />
+                                <Tooltip />
+                                <Legend />
+                                <Line type="monotone" dataKey="dp" stroke="#00ff00" name="动态规划" />
+                                <Line type="monotone" dataKey="backtracking" stroke="#ff0000" name="回溯算法" />
+                            </LineChart>
+                        </ResponsiveContainer>
+                    </div>
+                )}
+            </div>
+        </div>
+    );
+};
+
+export default Knapsack;

frontend/src/components/MaxSubarray.jsx

@@ -0,0 +1,248 @@
+import React, { useState } from 'react';
+import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+import { generateCase, solveCase, runBenchmark } from '../api';
+
+const MaxSubarray = () => {
+  const [params, setParams] = useState({ size: 100, min: -100, max: 100 });
+  const [currentCase, setCurrentCase] = useState(null);
+  const [solveResults, setSolveResults] = useState(null);
+  const [benchmarkResults, setBenchmarkResults] = useState(null);
+  const [loading, setLoading] = useState(false);
+
+  // Algorithm selection state
+  const [selectedAlgorithms, setSelectedAlgorithms] = useState({
+    brute_force: true,
+    divide_conquer: true,
+    kadane: true
+  });
+
+  const algorithmsList = [
+    { id: 'brute_force', name: '暴力求解 (Brute Force) O(N^2)' },
+    { id: 'divide_conquer', name: '分治算法 (Divide & Conquer) O(N log N)' },
+    { id: 'kadane', name: 'Kadane算法 (Kadane) O(N)' }
+  ];
+
+  const getSelectedAlgoKeys = () => {
+    return Object.keys(selectedAlgorithms).filter(k => selectedAlgorithms[k]);
+  };
+
+  const handleGenerate = async () => {
+    setLoading(true);
+    try {
+      const data = await generateCase(params.size, params.min, params.max);
+      setCurrentCase(data.array);
+      setSolveResults(null);
+    } catch (error) {
+      console.error("Error generating case:", error);
+      alert("生成测试用例失败");
+    }
+    setLoading(false);
+  };
+
+  const handleSolve = async () => {
+    if (!currentCase) return;
+    const algos = getSelectedAlgoKeys();
+    if (algos.length === 0) {
+      alert("请至少选择一种算法");
+      return;
+    }
+
+    setLoading(true);
+    try {
+      const results = await solveCase(currentCase, algos);
+      setSolveResults(results);
+    } catch (error) {
+      console.error("Error solving case:", error);
+      alert("求解失败");
+    }
+    setLoading(false);
+  };
+
+  const handleBenchmark = async () => {
+    const algos = getSelectedAlgoKeys();
+    if (algos.length === 0) {
+      alert("请至少选择一种算法");
+      return;
+    }
+
+    setLoading(true);
+    try {
+      // Smaller sizes for quick demo
+      const sizes = [10, 50, 100, 200, 500, 1000, 2000];
+      const results = await runBenchmark(sizes, algos);
+
+      // Transform data for Recharts
+      const chartData = results.map(item => {
+        const point = { size: item.size };
+        item.algorithms.forEach(algo => {
+          if (algo.time_seconds !== undefined && algo.time_seconds !== null) {
+            point[algo.algorithm] = algo.time_seconds;
+          }
+        });
+        return point;
+      });
+
+      setBenchmarkResults(chartData);
+    } catch (error) {
+      console.error("Error running benchmark:", error);
+      alert("性能测试失败");
+    }
+    setLoading(false);
+  };
+
+  const toggleAlgorithm = (algoId) => {
+    setSelectedAlgorithms(prev => ({
+      ...prev,
+      [algoId]: !prev[algoId]
+    }));
+  };
+
+  return (
+    <div className="p-6 space-y-8">
+      <h1 className="text-3xl font-bold text-gray-800">最大子数组和问题 (Maximum Subarray Sum)</h1>
+
+      {/* Algorithm Selection */}
+      <div className="bg-white p-6 rounded-lg shadow">
+        <h2 className="text-xl font-semibold mb-4">算法选择</h2>
+        <div className="flex flex-wrap gap-4">
+          {algorithmsList.map(algo => (
+            <label key={algo.id} className="flex items-center space-x-2 cursor-pointer">
+              <input
+                type="checkbox"
+                checked={selectedAlgorithms[algo.id]}
+                onChange={() => toggleAlgorithm(algo.id)}
+                className="form-checkbox h-5 w-5 text-blue-600"
+              />
+              <span className="text-gray-700">{algo.name}</span>
+            </label>
+          ))}
+        </div>
+      </div>
+
+      {/* Section 1: Generate & Solve */}
+      <div className="grid grid-cols-1 md:grid-cols-2 gap-6">
+        <div className="bg-white p-6 rounded-lg shadow">
+          <h2 className="text-xl font-semibold mb-4">1. 生成测试用例</h2>
+          <div className="space-y-4">
+            <div className="grid grid-cols-3 gap-4">
+              <div>
+                <label className="block text-sm font-medium text-gray-700">数据规模 (N)</label>
+                <input
+                  type="number"
+                  value={params.size}
+                  onChange={(e) => setParams({ ...params, size: parseInt(e.target.value) })}
+                  className="mt-1 block w-full border rounded-md p-2"
+                />
+              </div>
+              <div>
+                <label className="block text-sm font-medium text-gray-700">最小值</label>
+                <input
+                  type="number"
+                  value={params.min}
+                  onChange={(e) => setParams({ ...params, min: parseInt(e.target.value) })}
+                  className="mt-1 block w-full border rounded-md p-2"
+                />
+              </div>
+              <div>
+                <label className="block text-sm font-medium text-gray-700">最大值</label>
+                <input
+                  type="number"
+                  value={params.max}
+                  onChange={(e) => setParams({ ...params, max: parseInt(e.target.value) })}
+                  className="mt-1 block w-full border rounded-md p-2"
+                />
+              </div>
+            </div>
+            <button
+              onClick={handleGenerate}
+              disabled={loading}
+              className="w-full bg-blue-600 text-white py-2 px-4 rounded-md hover:bg-blue-700 disabled:bg-gray-400"
+            >
+              {loading ? '处理中...' : '生成测试用例'}
+            </button>
+          </div>
+
+          {currentCase && (
+            <div className="mt-4">
+              <h3 className="font-medium">已生成数组 (预览):</h3>
+              <p className="font-mono text-sm bg-gray-100 p-2 rounded break-all max-h-32 overflow-y-auto">
+                [{currentCase.slice(0, 50).join(', ')}{currentCase.length > 50 ? '...' : ''}]
+              </p>
+              <p className="text-xs text-gray-500 mt-1">总元素数量: {currentCase.length}</p>
+            </div>
+          )}
+        </div>
+
+        <div className="bg-white p-6 rounded-lg shadow">
+          <h2 className="text-xl font-semibold mb-4">2. 求解与验证</h2>
+          <button
+            onClick={handleSolve}
+            disabled={!currentCase || loading}
+            className="w-full bg-green-600 text-white py-2 px-4 rounded-md hover:bg-green-700 disabled:bg-gray-400 mb-4"
+          >
+            运行选中算法
+          </button>
+
+          {solveResults && (
+            <div className="overflow-x-auto">
+              <table className="min-w-full divide-y divide-gray-200">
+                <thead>
+                  <tr>
+                    <th className="px-4 py-2 text-left text-xs font-medium text-gray-500 uppercase">算法</th>
+                    <th className="px-4 py-2 text-left text-xs font-medium text-gray-500 uppercase">结果</th>
+                    <th className="px-4 py-2 text-left text-xs font-medium text-gray-500 uppercase">耗时 (秒)</th>
+                  </tr>
+                </thead>
+                <tbody className="divide-y divide-gray-200">
+                  {solveResults.map((res, idx) => (
+                    <tr key={idx}>
+                      <td className="px-4 py-2 text-sm font-medium text-gray-900">{res.algorithm}</td>
+                      <td className="px-4 py-2 text-sm text-gray-500">{res.result}</td>
+                      <td className="px-4 py-2 text-sm text-gray-500">{res.time_seconds?.toFixed(6)}</td>
+                    </tr>
+                  ))}
+                </tbody>
+              </table>
+            </div>
+          )}
+        </div>
+      </div>
+
+      {/* Section 2: Benchmark */}
+      <div className="bg-white p-6 rounded-lg shadow">
+        <div className="flex justify-between items-center mb-6">
+          <h2 className="text-xl font-semibold">3. 性能对比测试</h2>
+          <button
+            onClick={handleBenchmark}
+            disabled={loading}
+            className="bg-purple-600 text-white py-2 px-4 rounded-md hover:bg-purple-700 disabled:bg-gray-400"
+          >
+            运行性能测试
+          </button>
+        </div>
+
+        {benchmarkResults && (
+          <div className="h-96 w-full">
+            <ResponsiveContainer width="100%" height="100%">
+              <LineChart
+                data={benchmarkResults}
+                margin={{ top: 5, right: 30, left: 20, bottom: 5 }}
+              >
+                <CartesianGrid strokeDasharray="3 3" />
+                <XAxis dataKey="size" label={{ value: '数据规模 (N)', position: 'insideBottomRight', offset: -10 }} />
+                <YAxis label={{ value: '耗时 (秒)', angle: -90, position: 'insideLeft' }} />
+                <Tooltip />
+                <Legend />
+                <Line type="monotone" dataKey="brute_force" stroke="#ff0000" name="暴力求解" />
+                <Line type="monotone" dataKey="divide_conquer" stroke="#00ff00" name="分治算法" />
+                <Line type="monotone" dataKey="kadane" stroke="#0000ff" name="Kadane算法" />
+              </LineChart>
+            </ResponsiveContainer>
+          </div>
+        )}
+      </div>
+    </div>
+  );
+};
+
+export default MaxSubarray;

frontend/src/components/NQueens.jsx

@@ -0,0 +1,174 @@
+import React, { useState } from 'react';
+import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, ResponsiveContainer } from 'recharts';
+import { generateNQueensCase, solveNQueensCase, runNQueensBenchmark } from '../api';
+
+const NQueens = () => {
+    const [n, setN] = useState(8);
+    const [currentSolution, setCurrentSolution] = useState(null);
+    const [solutionCount, setSolutionCount] = useState(null);
+    const [solveTime, setSolveTime] = useState(null);
+    const [benchmarkResults, setBenchmarkResults] = useState(null);
+    const [loading, setLoading] = useState(false);
+
+    const handleSolve = async () => {
+        setLoading(true);
+        try {
+            // Generate is trivial (just N), so we skip explicit generate step for UI simplicity
+            // and just call solve directly
+            const results = await solveNQueensCase(n, ["backtracking"]);
+            if (results && results.length > 0) {
+                const res = results[0];
+                setCurrentSolution(res.first_solution);
+                setSolutionCount(res.solution_count);
+                setSolveTime(res.time_seconds);
+            }
+        } catch (error) {
+            console.error("Error solving N-Queens:", error);
+            alert("求解失败");
+        }
+        setLoading(false);
+    };
+
+    const handleBenchmark = async () => {
+        setLoading(true);
+        try {
+            const sizes = [4, 8, 10, 12, 13];
+            const results = await runNQueensBenchmark(sizes, ["backtracking"]);
+
+            const chartData = results.map(item => {
+                const point = { size: item.size };
+                item.algorithms.forEach(algo => {
+                    if (algo.time_seconds !== undefined && algo.time_seconds !== null) {
+                        point[algo.algorithm] = algo.time_seconds;
+                    }
+                });
+                return point;
+            });
+
+            setBenchmarkResults(chartData);
+        } catch (error) {
+            console.error("Error running benchmark:", error);
+            alert("性能测试失败");
+        }
+        setLoading(false);
+    };
+
+    // Render the chess board
+    const renderBoard = () => {
+        if (!currentSolution) return null;
+
+        const boardSize = 400;
+        const cellSize = boardSize / n;
+
+        return (
+            <div
+                className="relative border-2 border-gray-800"
+                style={{ width: boardSize, height: boardSize }}
+            >
+                {Array.from({ length: n }).map((_, row) => (
+                    Array.from({ length: n }).map((_, col) => {
+                        const isBlack = (row + col) % 2 === 1;
+                        const hasQueen = currentSolution[row] === col;
+                        return (
+                            <div
+                                key={`${row}-${col}`}
+                                className={`absolute flex items-center justify-center ${isBlack ? 'bg-gray-600' : 'bg-white'}`}
+                                style={{
+                                    width: cellSize,
+                                    height: cellSize,
+                                    top: row * cellSize,
+                                    left: col * cellSize
+                                }}
+                            >
+                                {hasQueen && <span className="text-red-500 font-bold" style={{ fontSize: cellSize * 0.7 }}>♛</span>}
+                            </div>
+                        );
+                    })
+                ))}
+            </div>
+        );
+    };
+
+    return (
+        <div className="p-6 space-y-8">
+            <h1 className="text-3xl font-bold text-gray-800">N皇后问题 (N-Queens)</h1>
+            <p className="text-gray-600">目标：在 N×N 的棋盘上放置 N 个皇后，使得它们互不攻击。</p>
+
+            <div className="grid grid-cols-1 md:grid-cols-2 gap-6">
+                {/* Controls */}
+                <div className="bg-white p-6 rounded-lg shadow space-y-6">
+                    <div>
+                        <label className="block text-sm font-medium text-gray-700">棋盘大小 (N)</label>
+                        <input
+                            type="number"
+                            min="4"
+                            max="14"
+                            value={n}
+                            onChange={(e) => setN(parseInt(e.target.value))}
+                            className="mt-1 block w-full border rounded-md p-2"
+                        />
+                        <p className="text-xs text-gray-500 mt-1">建议 N &le; 14，否则计算时间过长</p>
+                    </div>
+
+                    <button
+                        onClick={handleSolve}
+                        disabled={loading}
+                        className="w-full bg-blue-600 text-white py-2 px-4 rounded-md hover:bg-blue-700 disabled:bg-gray-400"
+                    >
+                        {loading ? '计算中...' : '求解 (Backtracking)'}
+                    </button>
+
+                    {solutionCount !== null && (
+                        <div className="mt-4 p-4 bg-green-50 rounded-md">
+                            <p className="font-medium text-green-800">找到解的数量: {solutionCount}</p>
+                            <p className="text-sm text-green-600">耗时: {solveTime?.toFixed(6)} 秒</p>
+                        </div>
+                    )}
+                </div>
+
+                {/* Visualization */}
+                <div className="bg-white p-6 rounded-lg shadow flex justify-center items-center min-h-[450px]">
+                    {currentSolution ? renderBoard() : (
+                        <div className="text-gray-400 text-center">
+                            <p>点击求解以查看结果</p>
+                        </div>
+                    )}
+                </div>
+            </div>
+
+            {/* Benchmark */}
+            <div className="bg-white p-6 rounded-lg shadow">
+                <div className="flex justify-between items-center mb-6">
+                    <h2 className="text-xl font-semibold">性能测试 (N=4 to 13)</h2>
+                    <button
+                        onClick={handleBenchmark}
+                        disabled={loading}
+                        className="bg-purple-600 text-white py-2 px-4 rounded-md hover:bg-purple-700 disabled:bg-gray-400"
+                    >
+                        运行性能测试
+                    </button>
+                </div>
+
+                {benchmarkResults && (
+                    <div className="h-96 w-full">
+                        <ResponsiveContainer width="100%" height="100%">
+                            <LineChart
+                                data={benchmarkResults}
+                                margin={{ top: 5, right: 30, left: 20, bottom: 5 }}
+                            >
+                                <CartesianGrid strokeDasharray="3 3" />
+                                <XAxis dataKey="size" label={{ value: 'N', position: 'insideBottomRight', offset: -10 }} />
+                                <YAxis label={{ value: '耗时 (秒)', angle: -90, position: 'insideLeft' }} />
+                                <Tooltip />
+                                <Legend />
+                                <Line type="monotone" dataKey="backtracking" stroke="#ff0000" name="回溯算法" />
+                            </LineChart>
+                        </ResponsiveContainer>
+                    </div>
+                )}
+            </div>
+        </div>
+    );
+};
+
+export default NQueens;

frontend/src/index.css

@@ -0,0 +1,3 @@
+@tailwind base;
+@tailwind components;
+@tailwind utilities;

frontend/src/main.jsx

@@ -0,0 +1,10 @@
+import React from 'react'
+import ReactDOM from 'react-dom/client'
+import App from './App.jsx'
+import './index.css'
+
+ReactDOM.createRoot(document.getElementById('root')).render(
+  <React.StrictMode>
+    <App />
+  </React.StrictMode>,
+)

frontend/vite.config.js

@@ -0,0 +1,7 @@
+import { defineConfig } from 'vite'
+import react from '@vitejs/plugin-react'
+
+// https://vitejs.dev/config/
+export default defineConfig({
+  plugins: [react()],
+})

nginx.conf

@@ -0,0 +1,44 @@
+events {
+    worker_connections 1024;
+}
+
+http {
+    include /etc/nginx/mime.types;
+    default_type application/octet-stream;
+
+    upstream backend {
+        server backend:8000;
+    }
+
+    server {
+        listen 80;
+        server_name localhost;
+
+        # Frontend static files
+        location / {
+            root /usr/share/nginx/html;
+            try_files $uri $uri/ /index.html;
+        }
+
+        # Proxy API requests to backend
+        location /api/ {
+            proxy_pass http://backend/;
+            proxy_set_header Host $host;
+            proxy_set_header X-Real-IP $remote_addr;
+            proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
+            proxy_set_header X-Forwarded-Proto $scheme;
+        }
+
+        # Proxy docs to backend
+        location /docs {
+            proxy_pass http://backend/docs;
+            proxy_set_header Host $host;
+            proxy_set_header X-Real-IP $remote_addr;
+        }
+
+        location /openapi.json {
+            proxy_pass http://backend/openapi.json;
+            proxy_set_header Host $host;
+        }
+    }
+}