Largest palindrome mean length problem

## Mean size of the largest palindrome problem.
## by Nicolau Werneck, 2012-01-15
from pylab import *

def largest_palindrome(x,num):
    ## Initialize  palindrome candidates list with the unit palindromes
    seeds = [(1,k) for k in range(x)]
    ## Initial "even" palindrome middles
    seeds += [(2,k) for k in range(x-1) if num[k]==num[k+1]]

    while seeds != []:
        output = seeds[-1][0]
        newseeds = []
        for l,k in seeds:
            if k>0 and k+l<x-1:
                if num[k-1]==num[k+l]:
                    newseeds.append((l+2,k-1))
        seeds = newseeds

    return output


def iteration(x):
    num = randint(0,10,x)
    return largest_palindrome(x,num)


if __name__ == '__main__':
    ion()

    Nsmp = 10000
    Lx = [3,4,5,6,7,8,9,10,32,100,316,1000]

    suptitle('Cumulative probabilities of largest palindromes', size=16, fontweight='bold')
    axes([.1,.2,.8,.7])
    kk=0
    Lll=[]
    for x in Lx:
        kk+=0.04
        cdf = sort([iteration(x) for k in range(Nsmp)])
        p=mgrid[1:Nsmp+1]/(Nsmp+1.)
        ll=plot(cdf+kk,p,'-')[0]
        Lll.append(ll)

    figlegend(Lll,Lx, 'lower center', ncol=6, title='Values of x (number of digits)')
    grid()
    plot([0,10],[.5,.5],'k--')
    xlim(0,10)