# -*- coding: utf-8 -*-
# 
# Script to generate in English and French, graphs for the
# birthday problem.
#
# **************************************************************
# http://en.wikipedia.org/wiki/Polydivisible_number
# From Wikipedia, the free encyclopedia:
# In mathematics a polydivisible number is a number with digits
# abcde... that has the following properties :
# 
# Its first digit a is not 0.
# The number formed by its first two digits ab is a multiple of 2.
# The number formed by its first three digits abc is a multiple of 3.
# The number formed by its first four digits abcd is a multiple of 4.
# etc.
#
# Text under the
# Creative Commons Attribution-ShareAlike License
# **************************************************************
#
# Guillaume Jacquenot
# 2013/05/01

from pylab import *
import numpy as np

def getData():
    r=np.array(
        [[ 1,     9,    9],
         [ 2,    45,   45],
         [ 3,   150,  150],
         [ 4,   375,  375],
         [ 5,   750,  750],
         [ 6,  1200, 1250],
         [ 7,  1713, 1786],
         [ 8,  2227, 2232],
         [ 9,  2492, 2480],
         [10,  2492, 2480],
         [11,  2225, 2255],
         [12,  2041, 1879],
         [13,  1575, 1445],
         [14,  1132, 1032],
         [15,   770,  688],
         [16,   571,  430],
         [17,   335,  253],
         [18,   180,  141],
         [19,    90,   74],
         [20,    44,   37],
         [21,    18,   17],
         [22,    12,    8],
         [23,     6,    3],
         [24,     3,    1],
         [25,     1,    1]])
    return r

def makePlot(\
        generateEnglishPlot = True,\
        outputFilename = 'Graph_of_polydivisible_number.svg'):
    if generateEnglishPlot:
        xlabel_ = 'n Number of digits'
        ylabel_ = 'Number of polydivisible numbers'
        leg1 = 'F(n)'
        leg2 = 'Estimate of F(n)'
    else:
        xlabel_ = 'n Nombre de digits'
        ylabel_ = 'Nombre de nombres polydivisibles'
        leg1 = 'F(n)'
        leg2 = 'Estimée de F(n)'
    r=getData()
    plot(r[:,0], r[:,1], marker = 'o', label = unicode(leg1, 'utf8'))
    plot(r[:,0], r[:,2], marker = '^', label = unicode(leg2, 'utf8'))
    grid(True, ls='-', c='#a0a0a0')
    legend(loc='right')
    xlabel(xlabel_)
    ylabel(ylabel_)
    savefig(outputFilename)
    show()

makePlot(generateEnglishPlot = True, outputFilename = 'Graph_of_polydivisible_number.svg')
makePlot(generateEnglishPlot = False, outputFilename = 'Graphe_des_nombres_polydivisibles.svg')