#! /usr/bin/env python3
#
def pi_digits_test ( ):

#  Reference:
#
#    John D Cook,
#    The coupon collector problem and pi,
#    Posted 12 March 2023.
#    https://www.johndcook.com/blog/2023/03/12/coupon-collector/
#    
  from mpmath import mp
  from sympy import EulerGamma
  import numpy as np

  print ( '' )
  print ( 'pi_digits_test():' )
  print ( '  How many digits of pi must we scan before seeing all 10 digits?' )
  print ( '  Before seeing all 100 pairs, or 1000 triples of digits?' )
  print ( '' )

  mp.dps = 30_000
  s = str(mp.pi)[2:]

  for k in [ 1, 2, 3 ]:

    n = 10**k

#   tuples = [ s[i:i+k] for i in range(0, len(s), k) ]
    tuples = [ s[i:i+k] for i in range(0, len(s) - k) ]
 
    d = dict()

    i = 0
    while len ( d ) < n:
      d[tuples[i]] = 1
      i = i + 1

    print ( i, n * harmonic ( n ), n * np.log ( n + float ( EulerGamma ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'pi_digits_test():' )
  print ( '  Normal end of execution.' )

  return

def harmonic ( n ):

#*****************************************************************************80
#
## harmonic() evaluates a Harmonic sequence number.
#
#  Discussion:
#
#    H(N) = Sum ( 1 <= I <= N ) 1 / I
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    21 May 2022
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer N: the index of the harmonic number.
#
#  Output:
#
#    real VALUE, the value of the harmonic number.
#
  value = 0.0
  for i in range ( 1, n + 1 ):
    value = value + 1.0 / float ( i )

  return value

if ( __name__ == "__main__" ):
  pi_digits_test ( )