from sage.all import *

#This is a helper function for some of our experiments: it calculates the
#empirical expectation value of a given statistic by drawing, for each c in c_range, K graphs of size n
#from G(n,scale(n,c)) and applying the statistic function to them.
def empirical_means(n,c_range,statistic,K,verbose=False,scale= lambda n,c: c/n):
    '''
    Generic function to run some Monte-Carlo experiments:
    - Scale is assumed to be a function f(n,c) between 0 and 1.
    - For each c in c_range, we sample K graphs from G(n,p=f(n,c))
    - For each graph G we sample, we compute statistic(G)
    - We take return a list of relative frequencies: 1/K sum_{i=1}^K statistic(G)
    - Verbose tells us what we're currently sampling from (useful to track progress)
    '''
    data = []
    
    for current_c in c_range:
        if verbose:
            print("Currently sampling with c =",current_c)

        s = 0
    
        for k in range(K):
    
            rand_G = graphs.RandomGNP(n,scale(n,current_c))
            s += statistic(rand_G)

        data.append((current_c, s/K))

    return data

from collections import Counter

#same but for the full distribution: returns a list of lists where
#for each c in c_range we sample from G(n,scale(n,c)) the corresponding list 
#records pairs of values observed and their relative frequency
def empirical_dists(n,c_range,statistic,K,verbose=False,scale= lambda n,c: c/n):
    data = []
    
    for current_c in c_range:

        if verbose:
            print("Currently sampling with c =",current_c)

        histo = [] #full histogram of values

        for k in range(K):
    
            rand_G = graphs.RandomGNP(n,scale(n,current_c))
            histo.append(statistic(rand_G))

        counts = Counter(histo)
        if verbose:
            print("Data points:",counts)
        
        values_freqs = sorted([(value, count / K) for value, count in counts.items()],key=lambda x: x[0])
        
        data.append((current_c, values_freqs))

    return data