#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Statistics on coin flipping series of given number of coins.
Comparison with infinite mean solution : binomial distribution and
Pascal's triangle.
"""

import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import random
import collections
 
def nheads(n):
    """
    return number of heads for n equally likely outcomes coin flipping
    """
    return sum([random.choice(values) for i in range(n)])
 
values = [0,1] # tail or head
nflips = 10
# Pascal's triangle :
pt = [[1],[1,1]]
for i in range(len(pt),nflips+1):
    pt.append([1]+[pt[i-1][j-1] + pt[i-1][j] for j in range(1,i)]+[1])
print(pt[nflips], sum(pt[nflips]))  # theoretical distribution
 
nb = 102400
heads = [nheads(nflips) for j in range(nb)]
#print heads
c = collections.Counter(heads)
for i in range(nflips+1):
    print(i,c[i],pt[nflips][i])