#! /usr/bin/env python

# numBasePairsQuasiRandom.py
# P.Clote

# Program computes expected number of base pairs in
# quasi-random saturated structures.
# For rnaSize = 1000, with 5000 repetitions,
# expected number of base pairs is 377.884 with
# stdev 8.18158879254

import sys,math,random
from stats import getSampleStats

THRESHOLD = 1

def f(i,j):
  if j-i>THRESHOLD:
    k = random.choice(range(i,j+1))
    if k-1-(i+1)>THRESHOLD:
      if j-(k+1)>THRESHOLD:
        return 1+f(i+1,k-1)+f(k+1,j)
      else:
        return 1+f(i+1,k-1)
    elif j-(k+1)>THRESHOLD:
      return 1+f(k+1,j)
    else:
      return 1
  return 0

def main(n,numTimes):
  L = []
  for i in range(numTimes):
    L.append(f(1,n))
  mean,stdev,max,min = getSampleStats(L)
  print mean,stdev

if __name__ == '__main__':
  if len(sys.argv)< 2:
    print "Usage: %s rnaSize [numTimes]" % sys.argv[0]
    sys.exit(1)
  rnaSize = int(sys.argv[1])
  if len(sys.argv)>2:
    numTimes = int(sys.argv[2])
  else:
    numTimes = 10
  main(rnaSize,numTimes)