import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

def monte_carlo_project_simulation(tasks, iterations=10000):

    project_durations = []
    for _ in range(iterations):
        total_duration = 0
        for task, (opt, likely, pess) in tasks.items():
        # Използваме PERT разпределение
            mean = (opt + 4 * likely + pess) / 6
            std = (pess - opt) / 6
            duration = np.random.normal(mean, std)
            total_duration += max(duration, 0)

        project_durations.append(total_duration)

    return np.array(project_durations)


tasks = {
'Иницииране': (8, 10, 15),
'Планиране': (12, 15, 20),
'Разработка': (25, 30, 40),
'Тестване': (15, 20, 30),
'Разгръщане': (10, 15, 25)
}

# Изпълнение на симулацията
durations = monte_carlo_project_simulation(tasks)

# Анализ на резултатите
confidence_levels = {
50: np.percentile(durations, 50),
80: np.percentile(durations, 80),
90: np.percentile(durations, 90),
95: np.percentile(durations, 95)
}

# Визуализация
plt.figure(figsize=(10, 6))
plt.hist(durations, bins=50, density=True, alpha=0.7)
plt.axvline(confidence_levels[80], color='r', linestyle='dashed', label='80% confidence')
plt.axvline(confidence_levels[95], color='g', linestyle='dashed', label='95% confidence')
plt.title('Разпределение на продължителността на проекта')
plt.xlabel('Дни')
plt.ylabel('Вероятност')
plt.legend()
plt.grid(True, alpha=0.3)
plt.show()

print("\nРезултати от анализа на риска:")
for conf, duration in confidence_levels.items():
    print(f"{conf}% вероятност проектът да приключи до {duration:.1f} дни")