app.py

import gradio as gr
import plotly.graph_objects as go
import plotly.express as px
from plotly.subplots import make_subplots
import numpy as np
from collections import Counter
import math

# Historical researchers of perfect numbers - Enhanced HTML version
MATHEMATICIANS = """
<div style='background: linear-gradient(135deg, #667eea 0%, #764ba2 100%); padding: 25px; border-radius: 15px; box-shadow: 0 8px 16px rgba(0,0,0,0.2); color: white; font-family: Arial, sans-serif;'>
    <h2 style='text-align: center; margin-top: 0; font-size: 24px; text-shadow: 2px 2px 4px rgba(0,0,0,0.3);'>🎓 Notable Mathematicians & Their Contributions</h2>
    
    <div style='background: rgba(255,255,255,0.15); padding: 15px; border-radius: 10px; margin: 15px 0; border-left: 5px solid #ffd700;'>
        <strong style='font-size: 16px; color: #ffd700;'>⭐ Euclid</strong> <em style='color: #e0e0e0;'>(c. 300 BCE)</em><br/>
        <span style='margin-left: 20px; line-height: 1.6;'>Proved that 2<sup>(p-1)</sup> × (2<sup>p</sup> - 1) generates perfect numbers when 2<sup>p</sup> - 1 is prime</span>
    </div>
    
    <div style='background: rgba(255,255,255,0.15); padding: 15px; border-radius: 10px; margin: 15px 0; border-left: 5px solid #ff6b6b;'>
        <strong style='font-size: 16px; color: #ff6b6b;'>⭐ Leonhard Euler</strong> <em style='color: #e0e0e0;'>(1707-1783)</em><br/>
        <span style='margin-left: 20px; line-height: 1.6;'>Proved all even perfect numbers follow Euclid's formula</span>
    </div>
    
    <div style='background: rgba(255,255,255,0.15); padding: 15px; border-radius: 10px; margin: 15px 0; border-left: 5px solid #4ecdc4;'>
        <strong style='font-size: 16px; color: #4ecdc4;'>⭐ Marin Mersenne</strong> <em style='color: #e0e0e0;'>(1588-1648)</em><br/>
        <span style='margin-left: 20px; line-height: 1.6;'>Studied primes of form 2<sup>p</sup> - 1 (Mersenne primes), linked to perfect numbers</span>
    </div>
    
    <div style='background: rgba(255,255,255,0.15); padding: 15px; border-radius: 10px; margin: 15px 0; border-left: 5px solid #95e1d3;'>
        <strong style='font-size: 16px; color: #95e1d3;'>⭐ Niccolò Paganini</strong><br/>
        <span style='margin-left: 20px; line-height: 1.6;'>Not the violinist! Ancient Greek mathematician who studied perfect numbers</span>
    </div>
    
    <div style='background: rgba(255,255,255,0.15); padding: 15px; border-radius: 10px; margin: 15px 0; border-left: 5px solid #f38181;'>
        <strong style='font-size: 16px; color: #f38181;'>⭐ René Descartes</strong> <em style='color: #e0e0e0;'>(1596-1650)</em><br/>
        <span style='margin-left: 20px; line-height: 1.6;'>Conjectured properties about odd perfect numbers</span>
    </div>
    
    <div style='background: rgba(255,255,255,0.15); padding: 15px; border-radius: 10px; margin: 15px 0; border-left: 5px solid #aa96da;'>
        <strong style='font-size: 16px; color: #aa96da;'>⭐ Pierre de Fermat</strong> <em style='color: #e0e0e0;'>(1607-1665)</em><br/>
        <span style='margin-left: 20px; line-height: 1.6;'>Contributed to number theory including perfect number properties</span>
    </div>
    
    <div style='background: rgba(255,255,255,0.15); padding: 15px; border-radius: 10px; margin: 15px 0; border-left: 5px solid #fcbad3;'>
        <strong style='font-size: 16px; color: #fcbad3;'>⭐ Pythagoras</strong> <em style='color: #e0e0e0;'>(c. 570-495 BCE)</em><br/>
        <span style='margin-left: 20px; line-height: 1.6;'>Ancient Greek philosopher who ascribed mystical properties to perfect numbers</span>
    </div>
    
    <div style='background: linear-gradient(135deg, #f093fb 0%, #f5576c 100%); padding: 20px; border-radius: 10px; margin-top: 25px; text-align: center; box-shadow: 0 4px 8px rgba(0,0,0,0.2);'>
        <h3 style='margin: 0 0 10px 0; font-size: 20px; color: white; text-shadow: 2px 2px 4px rgba(0,0,0,0.3);'>📊 Known Perfect Numbers</h3>
        <p style='margin: 10px 0; font-size: 16px; line-height: 1.6;'>Only <strong style='font-size: 22px; color: #ffd700;'>51</strong> perfect numbers have been discovered (as of 2024)</p>
        <p style='margin: 10px 0; font-size: 14px;'>The first few:</p>
        <p style='font-size: 18px; font-weight: bold; color: #ffd700; text-shadow: 1px 1px 2px rgba(0,0,0,0.3);'>6, 28, 496, 8128, 33550336...</p>
    </div>
</div>
"""

def prime_factorization(n):
    """Get prime factorization of n"""
    factors = []
    d = 2
    temp = n
    while d * d <= temp:
        while temp % d == 0:
            factors.append(d)
            temp //= d
        d += 1
    if temp > 1:
        factors.append(temp)
    return factors

def divisors(n):
    """Find all divisors of n efficiently"""
    if n == 1:
        return [1]
    
    divs = set()
    sqrt_n = int(math.isqrt(n))
    
    for i in range(1, sqrt_n + 1):
        if n % i == 0:
            divs.add(i)
            divs.add(n // i)
    
    return sorted(divs)

def classify_number(n, proper_sum):
    """Classify number as perfect, abundant, or deficient"""
    if proper_sum == n:
        return "Perfect", "✅"
    elif proper_sum > n:
        return "Abundant", "📈"
    else:
        return "Deficient", "📉"

def check_perfect(n):
    """Check if number is perfect and return detailed info"""
    if n <= 1:
        return False, [], 0, "Invalid", ""
    
    divs = divisors(n)
    proper_divs = [d for d in divs if d != n]
    proper_sum = sum(proper_divs)
    classification, emoji = classify_number(n, proper_sum)
    
    return proper_sum == n, divs, proper_sum, classification, emoji

def create_enhanced_visualization(n):
    """Create comprehensive visualization with Plotly for any positive integer"""
    try:
        n = int(n)
    except (ValueError, TypeError):
        return "Please enter a valid positive integer.", None
    
    if n <= 0:
        return "Please enter a positive integer.", None
    
    is_perfect, divs, proper_sum, classification, emoji = check_perfect(n)
    proper_divs = [d for d in divs if d != n]
    
    # Create subplots with Plotly
    fig = make_subplots(
        rows=2, cols=3,
        subplot_titles=(
            f'Proper Divisors of {n}',
            'Divisor Magnitudes',
            f'{classification} Number Analysis {emoji}',
            'Divisor Pairs',
            f'Prime Factorization of {n}',
            'Perfect Number Definition'
        ),
        specs=[
            [{"type": "pie"}, {"type": "bar"}, {"type": "bar"}],
            [{"type": "table"}, {"type": "table"}, {"type": "table"}]
        ],
        vertical_spacing=0.1,
        horizontal_spacing=0.05
    )
    
    # Define color scheme
    if classification == "Perfect":
        main_color = '#2ecc71'
        colors = px.colors.sequential.Greens[2:8]
    elif classification == "Abundant":
        main_color = '#3498db'
        colors = px.colors.sequential.Blues[2:8]
    else:
        main_color = '#e74c3c'
        colors = px.colors.sequential.Reds[2:8]
    
    # 1. PIE CHART - Divisor Distribution
    if proper_divs:
        # Limit to top 20 divisors for readability
        display_divs = proper_divs[:20] if len(proper_divs) > 20 else proper_divs
        fig.add_trace(
            go.Pie(
                labels=[str(d) for d in display_divs],
                values=display_divs,
                textinfo='label+percent',
                insidetextorientation='radial',
                marker=dict(colors=colors * (len(display_divs) // len(colors) + 1)),
                textfont=dict(size=12),
                hovertemplate="Divisor: %{label}<br>Value: %{value}<extra></extra>"
            ),
            row=1, col=1
        )
    
    # 2. BAR CHART - Divisor Values
    if proper_divs:
        # Limit to top 20 divisors for readability
        display_divs = proper_divs[:20] if len(proper_divs) > 20 else proper_divs
        fig.add_trace(
            go.Bar(
                x=[str(d) for d in display_divs],
                y=display_divs,
                marker_color=main_color,
                text=display_divs,
                textposition='outside',
                hovertemplate="Divisor: %{x}<br>Value: %{y}<extra></extra>"
            ),
            row=1, col=2
        )
        fig.update_xaxes(tickangle=45, row=1, col=2)
    
    # 3. COMPARISON BAR - Sum vs Number
    comparison = [proper_sum, n]
    labels = [f'Sum of Divisors<br>({proper_sum})', f'Number<br>({n})']
    fig.add_trace(
        go.Bar(
            x=labels,
            y=comparison,
            marker_color=[main_color, '#95a5a6'],
            text=comparison,
            textposition='outside',
            hovertemplate="%{x}<br>Value: %{y}<extra></extra>"
        ),
        row=1, col=3
    )
    
    # Add difference annotation
    diff = abs(proper_sum - n)
    diff_pct = (diff / n) * 100 if n != 0 else 0
    fig.add_annotation(
        x=0.5, y=max(comparison) * 0.5,
        text=f"Difference: {diff}<br>({diff_pct:.1f}%)",
        showarrow=False,
        bgcolor="wheat",
        bordercolor="black",
        font=dict(size=12, color="black"),
        row=1, col=3
    )
    
    # 4. DIVISOR PAIRS VISUALIZATION
    sqrt_n = int(math.isqrt(n))
    pairs = []
    for d in proper_divs:
        if d <= sqrt_n and d != n // d:
            pairs.append((d, n // d))
    
    if pairs:
        pair_labels = [f"{d1} × {d2}" for d1, d2 in pairs]
        pair_values = [n] * len(pairs)
        fig.add_trace(
            go.Table(
                header=dict(values=["Divisor Pairs", "Product"]),
                cells=dict(values=[pair_labels, pair_values]),
                columnwidth=[100, 50]
            ),
            row=2, col=1
        )
    else:
        fig.add_trace(
            go.Table(
                header=dict(values=["Divisor Pairs"]),
                cells=dict(values=[["No pairs found"]])
            ),
            row=2, col=1
        )
    
    # 5. PRIME FACTORIZATION
    prime_factors = prime_factorization(n)
    if prime_factors:
        factor_counts = Counter(prime_factors)
        factor_parts = []
        for prime in sorted(factor_counts.keys()):
            count = factor_counts[prime]
            if count == 1:
                factor_parts.append(f"{prime}")
            else:
                factor_parts.append(f"{prime}^{count}")
        factorization = " × ".join(factor_parts)
    else:
        factorization = "1 (unity)"
    
    properties = [
        f"Total divisors: {len(divs)}",
        f"Proper divisors: {len(proper_divs)}",
        f"Sum of all divisors: {sum(divs)}",
        f"Classification: {classification} {emoji}"
    ]
    
    fig.add_trace(
        go.Table(
            header=dict(values=["Prime Factorization", "Number Properties"]),
            cells=dict(values=[[factorization], ["<br>".join(properties)]])
        ),
        row=2, col=2
    )
    
    # 6. MATHEMATICAL FORMULA
    if proper_divs:
        sum_parts = " + ".join([str(d) for d in proper_divs[:10]])  # Limit to first 10
        if len(proper_divs) > 10:
            sum_parts += " + ..."
        formula = f"{sum_parts} = {proper_sum}"
    else:
        formula = "No proper divisors"
    
    result = f"{'✅' if is_perfect else '❌'} {proper_sum} {'=' if is_perfect else '≠'} {n}"
    
    if is_perfect:
        conclusion = "PERFECT NUMBER! 🎉"
    elif classification == "Abundant":
        conclusion = f"Abundant (Excess: {proper_sum - n})"
    else:
        conclusion = f"Deficient (Deficiency: {n - proper_sum})"
    
    fig.add_trace(
        go.Table(
            header=dict(values=["Perfect Number Definition"]),
            cells=dict(values=[[formula, result, conclusion]])
        ),
        row=2, col=3
    )
    
    # Update layout
    fig.update_layout(
        height=800,
        showlegend=False,
        title_text=f"Comprehensive Analysis of {n}",
        title_x=0.5,
        title_font_size=24,
        plot_bgcolor='rgba(0,0,0,0)',
        paper_bgcolor='rgba(0,0,0,0)'
    )
    
    # Generate detailed message with HTML formatting
    msg = f"""
    <div style='font-family: Arial, sans-serif; background: linear-gradient(to right, #e0f7fa, #e1bee7); padding: 25px; border-radius: 15px; box-shadow: 0 4px 12px rgba(0,0,0,0.15);'>
        <div style='background: linear-gradient(135deg, #1e3c72 0%, #2a5298 100%); color: white; padding: 20px; border-radius: 10px; margin-bottom: 20px; text-align: center; box-shadow: 0 4px 8px rgba(0,0,0,0.2);'>
            <h1 style='margin: 0; font-size: 28px; text-shadow: 2px 2px 4px rgba(0,0,0,0.3);'>🔍 ANALYSIS OF NUMBER: {n}</h1>
        </div>
        
        <div style='background: {"linear-gradient(135deg, #11998e 0%, #38ef7d 100%)" if is_perfect else "linear-gradient(135deg, #ee0979 0%, #ff6a00 100%)" if classification == "Abundant" else "linear-gradient(135deg, #fc4a1a 0%, #f7b733 100%)"}; padding: 20px; border-radius: 10px; margin-bottom: 20px; box-shadow: 0 4px 8px rgba(0,0,0,0.2);'>
            <h2 style='color: white; margin-top: 0; font-size: 22px; text-shadow: 2px 2px 4px rgba(0,0,0,0.3);'>📌 Classification: {classification} Number {emoji}</h2>
        </div>
        
        <div style='background: white; padding: 20px; border-radius: 10px; margin-bottom: 20px; box-shadow: 0 2px 6px rgba(0,0,0,0.1); border-left: 6px solid #2196F3;'>
            <h3 style='color: #1976D2; margin-top: 0;'>📊 Divisor Information</h3>
            <p style='font-size: 16px; line-height: 1.8; color: #000;'><strong style='color: #000;'>All Divisors:</strong> <span style='color: #0D47A1; font-weight: bold;'>{divs[:20]}{"..." if len(divs) > 20 else ""}</span></p>
            <p style='font-size: 16px; line-height: 1.8; color: #000;'><strong style='color: #000;'>Proper Divisors (excluding {n}):</strong> <span style='color: #0D47A1; font-weight: bold;'>{proper_divs[:20]}{"..." if len(proper_divs) > 20 else ""}</span></p>
        </div>
        
        <div style='background: white; padding: 20px; border-radius: 10px; margin-bottom: 20px; box-shadow: 0 2px 6px rgba(0,0,0,0.1); border-left: 6px solid #FF9800;'>
            <h3 style='color: #F57C00; margin-top: 0;'>🧮 Sum Calculation</h3>
            <p style='font-size: 18px; line-height: 1.8; font-weight: bold;'>
                {' + '.join([f"<span style='background: #FFE0B2; color: #BF360C; padding: 3px 8px; border-radius: 5px; margin: 2px; display: inline-block;'>{d}</span>" for d in proper_divs[:10]])}{" + ..." if len(proper_divs) > 10 else ""} = <span style='background: #FF6F00; color: white; padding: 5px 12px; border-radius: 5px;'>{proper_sum}</span>
            </p>
        </div>
        
        <div style='background: {"linear-gradient(135deg, #00b09b 0%, #96c93d 100%)" if is_perfect else "linear-gradient(135deg, #eb3349 0%, #f45c43 100%)"}; padding: 25px; border-radius: 10px; box-shadow: 0 4px 8px rgba(0,0,0,0.2);'>
            <h3 style='color: white; margin-top: 0; font-size: 20px; text-shadow: 2px 2px 4px rgba(0,0,0,0.3);'>✨ Result</h3>
            <p style='font-size: 24px; line-height: 1.8; color: white; font-weight: bold; text-shadow: 1px 1px 2px rgba(0,0,0,0.5);'>
                {"✅" if is_perfect else "❌"} <span style='background: rgba(0,0,0,0.3); padding: 5px 10px; border-radius: 5px;'>{proper_sum}</span> {"=" if is_perfect else "≠"} <span style='background: rgba(0,0,0,0.3); padding: 5px 10px; border-radius: 5px;'>{n}</span>
            </p>
            <p style='font-size: 18px; color: white; line-height: 1.6; text-shadow: 1px 1px 2px rgba(0,0,0,0.5);'>
                {"🎉 <strong>PERFECT NUMBER!</strong> This is one of the rare perfect numbers!" if is_perfect else f"<strong>NOT PERFECT</strong><br/>{'The sum (<strong>' + str(proper_sum) + '</strong>) is greater than the number (<strong>' + str(n) + '</strong>)<br/>Excess: <strong>' + str(proper_sum - n) + '</strong>' if classification == 'Abundant' else 'The sum (<strong>' + str(proper_sum) + '</strong>) is less than the number (<strong>' + str(n) + '</strong>)<br/>Deficiency: <strong>' + str(n - proper_sum) + '</strong>'}"}
            </p>
        </div>
        
        <div style='margin-top: 30px;'>
            {MATHEMATICIANS}
        </div>
    </div>
    """
    
    return msg, fig

# Create Gradio interface
with gr.Blocks(theme=gr.themes.Soft(), title="Perfect Number Explorer") as demo:
    gr.Markdown("""
    # 🔢 Perfect Number Visualizer & Explorer (Unlimited Range!)
    
    ### What are Perfect Numbers?
    A **perfect number** is a positive integer that equals the sum of its proper divisors (divisors excluding the number itself).
    
    **Example:** 6 is perfect because 1 + 2 + 3 = 6
    
    ### Try these perfect numbers: 6, 28, 496, 8128, 33550336
    ### Or try very large numbers like 2^31-1 (2147483647) or even larger!
    """)
    
    with gr.Row():
        with gr.Column(scale=1):
            number_input = gr.Number(
                label="Enter ANY Positive Integer", 
                value=6,
                precision=0
            )
            analyze_btn = gr.Button("🔍 Analyze Number", variant="primary", size="lg")
            
            gr.Markdown("""
            ### Key Features:
            - **Unlimited Range**: Analyze ANY positive integer (no upper limit!)
            - **Optimized Algorithms**: Efficiently handles very large numbers
            - **Interactive Visualizations**: Zoom, pan, and hover for details
            - **Comprehensive Analysis**: Divisors, factorization, and classification
            """)
    
    with gr.Row():
        result_text = gr.HTML(
            label="📊 Detailed Analysis"
        )
    
    with gr.Row():
        plot_output = gr.Plot(label="📈 Interactive Visual Analysis")
    
    analyze_btn.click(
        fn=create_enhanced_visualization,
        inputs=number_input,
        outputs=[result_text, plot_output]
    )
    
    # Auto-analyze on load
    demo.load(
        fn=create_enhanced_visualization,
        inputs=number_input,
        outputs=[result_text, plot_output]
    )

if __name__ == "__main__":
    demo.launch()