#! /usr/bin/env python

# expNumHairpinsInListOfStr.py
# P.Clote

# Program computes the expected number of hairpins in a list
# of secondary structures, where all structures following FASTA
# comment of form ">n" have length n. Used in conjunction with
# program that (1) outputs ALL secondary structures of lengths
# at most n (homopolymer model, theta=1), and another program
# that (2) filters out all but the saturated structures from
# previous list.

import sys,os

def numHairpins(secStr):
  num = 0; prev = 0
  for i in range(len(secStr)):
    if secStr[i]=='(':
      prev = i+1
    elif secStr[i]==')':
      if prev!=0:
        num += 1
        prev = 0
  return num

   
def main(filename):
  file = open(filename)
  line = file.readline()
  D    = {}; D[0]=0; length = 0
  print ">0"
  while line:
    if line[0]=='>':
      keys = D.keys()
      keys.sort()
      #print avg from previous collection of structures
      avg = 0.0; n = 0.0
      for k in keys:
        avg += D[k]*k
        n   += D[k]
      if n==0:
        avg = 0
      else:
        avg = avg/n
      if length == 0:
        avg = 0
      else:
        avg = avg/length
      print avg
      #initialize for new data
      length = float(line.split()[-1])
      D      = {}; D[0]=0
      print line.strip()
    else:
      secStr = line.strip()
      num    = numHairpins(secStr)
      if num not in D.keys():
        D[num]  = 1
      else:
        D[num] += 1
      #print "%s\t%d" % (secStr,numHairpins(secStr))
    line = file.readline()
  file.close()
  keys = D.keys()
  keys.sort()
  #print avg from previous collection of structures
  avg = 0.0; n = 0.0
  for k in keys:
    avg += D[k]*k
    n   += D[k]
  if n==0:
    avg = 0
  else:
    avg = avg/n
  if length == 0:
    avg = 0
  else:
    avg = avg/length
  print avg
  

if __name__ == '__main__':
  if len(sys.argv) < 2:
    print "Usage: %s filename" % sys.argv[0]
    sys.exit(1)
  filename = sys.argv[1]
  main(filename)