from typing import Dict, List, Tuple, Optional
import json

class EducationalMode:
    
    def __init__(self, difficulty_level: str = 'beginner'):
        self.difficulty_level = difficulty_level
        self. lessons = self._load_lessons()
        self.progress = {}
    
    def _load_lessons(self) -> Dict[str, List[str]]:
        return {
            'beginner': [
                '4D Basics:  Understanding the Fourth Dimension',
                'Coordinate Systems in 4D',
                'Distance Calculation in 4D Space',
                'Introduction to 4D Projections',
                'Visualizing 4D Objects',
            ],
            'intermediate': [
                'Advanced Rotations in 4D',
                'Tesseract Properties',
                'Minkowski Space',
                'Higher Dimensional Geometry',
                'Physics in 4D Space',
            ],
            'advanced': [
                'Differential Geometry in 4D',
                'Lie Groups and 4D Rotations',
                'Relativity and Spacetime',
                'Quantum Mechanics in 4D',
                'String Theory Basics',
            ]
        }
    
    def get_lesson_content(self, lesson_title: str) -> str:
        lesson_content = {
            '4D Basics:  Understanding the Fourth Dimension': '''
The fourth dimension (W) is perpendicular to all three spatial dimensions (X, Y, Z).
We cannot visualize it directly, but we can: 
1. Use mathematical representations
2. Project 4D objects to 3D
3. Study how 4D objects change when rotated
4. Analyze cross-sections at different W values

Key Concepts:
- A point in 4D is represented as (x, y, z, w)
- Distance formula: d = √((x₁-x₂)² + (y₁-y₂)² + (z₁-z₂)² + (w₁-w₂)²)
- The tesseract is the 4D equivalent of a cube
''',
            'Coordinate Systems in 4D': '''
Cartesian Coordinates:
- Standard (x, y, z, w) representation
- Origin at (0, 0, 0, 0)
- Axes are mutually perpendicular

Hyperspherical Coordinates:
- r: radius
- θ₁, θ₂, θ₃: angles
- Useful for spherical symmetry problems

Minkowski Coordinates:
- Used in relativity
- One time dimension, three spatial dimensions
- Metric: ds² = -c²dt² + dx² + dy² + dz²
''',
            'Distance Calculation in 4D Space': '''
Euclidean Distance: 
d = √((x₁-x₂)² + (y₁-y₂)² + (z₁-z₂)² + (w₁-w₂)²)

Manhattan Distance:
d = |x₁-x₂| + |y₁-y₂| + |z₁-z₂| + |w₁-w₂|

Minkowski Distance:
d = (Σ|xᵢ - yᵢ|ᵖ)^(1/p)

Example:  Distance from (0,0,0,0) to (1,1,1,1)
d = √(1² + 1² + 1² + 1²) = √4 = 2
''',
        }
        
        return lesson_content. get(lesson_title, 'Lesson content not found.')
    
    def get_interactive_quiz(self, lesson_title: str) -> List[Dict[str, str]]:
        quizzes = {
            '4D Basics:  Understanding the Fourth Dimension': [
                {
                    'question': 'What is a point in 4D space represented as?',
                    'options': ['(x, y)', '(x, y, z)', '(x, y, z, w)', '(x, y, z, t)'],
                    'correct':  '(x, y, z, w)'
                },
                {
                    'question': 'How many dimensions does a tesseract have?',
                    'options': ['2', '3', '4', '5'],
                    'correct':  '4'
                },
            ],
            'Distance Calculation in 4D Space':  [
                {
                    'question': 'What is the distance from (0,0,0,0) to (3,4,0,0)?',
                    'options': ['5', '7', '12', '25'],
                    'correct': '5'
                },
            ]
        }
        
        return quizzes.get(lesson_title, [])
    
    def get_interactive_demonstration(self, concept: str) -> Dict[str, any]:
        demonstrations = {
            'rotation_xy': {
                'description': 'Rotating a tesseract in the XY plane',
                'angles': [0.05, 0, 0, 0],
                'duration': 5
            },
            'rotation_xw': {
                'description': 'Rotating a tesseract in the XW plane (4D rotation)',
                'angles': [0, 0, 0, 0.05],
                'duration': 5
            },
            'projection': {
                'description': 'Comparing orthogonal, perspective, and stereographic projections',
                'projection_types': ['orthogonal', 'perspective', 'stereographic'],
            },
            'time_evolution': {
                'description': 'Watching a 4D shape evolve over time',
                'evolution_type': 'spiral',
                'duration': 10
            }
        }
        
        return demonstrations.get(concept, {})
    
    def get_challenges(self) -> List[Dict[str, str]]:
        challenges = [
            {
                'title': 'Rotate the Tesseract',
                'description': 'Rotate the tesseract to show its 4D symmetry',
                'difficulty': 'beginner'
            },
            {
                'title': 'Project a Hypercube',
                'description': 'Create a 3D projection of a 4D hypersphere',
                'difficulty': 'intermediate'
            },
            {
                'title': 'Analyze Symmetry',
                'description': 'Identify all symmetries of a 4D polytope',
                'difficulty': 'advanced'
            },
        ]
        
        return challenges