def comp_random ( n, k, seed ):
#*****************************************************************************80
#
## COMP_RANDOM selects a random composition of the integer N into K parts.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 22 April 2015
#
# Author:
#
# John Burkardt
#
# Reference:
#
# Albert Nijenhuis Herbert Wilf,
# Combinatorial Algorithms,
# Academic Press, 1978, second edition,
# ISBN 0-12-519260-6.
#
# Parameters:
#
# Input, integer N, the integer to be decomposed.
#
# Input, integer K, the number of parts in the composition.
#
# Input, integer SEED, a seed for the random number generator.
#
# Output, integer A(K), the parts of the composition.
#
# Output, integer SEED, an updated seed for the random number generator.
#
import numpy as np
from ksub_random2 import ksub_random2
b, seed = ksub_random2 ( n + k - 1, k - 1, seed )
a = np.zeros ( k )
for i in range ( 0, k - 1 ):
a[i] = b[i]
a[k-1] = n + k
l = 0
for i in range ( 0, k ):
m = a[i]
a[i] = a[i] - l - 1
l = m
return a, seed
def comp_random(n, k, seed):
#*****************************************************************************80
#
## COMP_RANDOM selects a random composition of the integer N into K parts.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 22 April 2015
#
# Author:
#
# John Burkardt
#
# Reference:
#
# Albert Nijenhuis, Herbert Wilf,
# Combinatorial Algorithms,
# Academic Press, 1978, second edition,
# ISBN 0-12-519260-6.
#
# Parameters:
#
# Input, integer N, the integer to be decomposed.
#
# Input, integer K, the number of parts in the composition.
#
# Input, integer SEED, a seed for the random number generator.
#
# Output, integer A(K), the parts of the composition.
#
# Output, integer SEED, an updated seed for the random number generator.
#
import numpy as np
from ksub_random2 import ksub_random2
b, seed = ksub_random2(n + k - 1, k - 1, seed)
a = np.zeros(k)
for i in range(0, k - 1):
a[i] = b[i]
a[k - 1] = n + k
l = 0
for i in range(0, k):
m = a[i]
a[i] = a[i] - l - 1
l = m
return a, seed
def ksub_to_comp_test():
#*****************************************************************************80
#
## KSUB_TO_COMP_TEST tests KSUB_TO_COMP.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 10 May 2015
#
# Author:
#
# John Burkardt
#
from ksub_random2 import ksub_random2
print ''
print 'KSUB_TO_COMP_TEST'
print ' KSUB_TO_COMP returns the composition corresponding to a K subset.'
ns = 14
ks = 4
seed = 123456789
for i in range(0, 5):
print ''
bs, seed = ksub_random2(ns, ks, seed)
print ' KSUB:',
for j in range(0, ks):
print ' %2d' % (bs[j]),
print ''
nc, kc, ac = ksub_to_comp(ns, ks, bs)
print ' COMP:',
for j in range(0, kc):
print ' %2d' % (ac[j]),
print ''
#
# Terminate.
#
print ''
print 'KSUB_TO_COMP_TEST:'
print ' Normal end of execution.'
return
def ksub_to_compnz_test():
# *****************************************************************************80
#
## KSUB_TO_COMPNZ_TEST tests KSUB_TO_COMPNZ.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 24 May 2015
#
# Author:
#
# John Burkardt
#
from ksub_random2 import ksub_random2
print ""
print "KSUB_TO_COMPNZ_TEST"
print " KSUB_TO_COMPNZ returns the nonzero composition"
print " corresponding to a K subset."
ns = 14
ks = 4
seed = 123456789
for i in range(0, 5):
print ""
bs, seed = ksub_random2(ns, ks, seed)
print " KSUB: ",
for j in range(0, ks):
print " %2d" % (bs[j]),
print ""
nc, kc, ac = ksub_to_compnz(ns, ks, bs)
print " COMPNZ:",
for j in range(0, kc):
print " %2d" % (ac[j]),
print ""
# Terminate.
#
print ""
print "KSUB_TO_COMPNZ_TEST:"
print " Normal end of execution."
return
def ksub_to_comp_test ( ):
#*****************************************************************************80
#
## KSUB_TO_COMP_TEST tests KSUB_TO_COMP.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 10 May 2015
#
# Author:
#
# John Burkardt
#
from ksub_random2 import ksub_random2
print ''
print 'KSUB_TO_COMP_TEST'
print ' KSUB_TO_COMP returns the composition corresponding to a K subset.'
ns = 14
ks = 4
seed = 123456789
for i in range ( 0, 5 ):
print ''
bs, seed = ksub_random2 ( ns, ks, seed )
print ' KSUB:',
for j in range ( 0, ks ):
print ' %2d' % ( bs[j] ),
print ''
nc, kc, ac = ksub_to_comp ( ns, ks, bs )
print ' COMP:',
for j in range ( 0, kc ):
print ' %2d' % ( ac[j] ),
print ''
#
# Terminate.
#
print ''
print 'KSUB_TO_COMP_TEST:'
print ' Normal end of execution.'
return
def compnz_random(n, k, seed):
#*****************************************************************************80
#
## COMPNZ_RANDOM selects a random composition of the integer N into K nonzero parts.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 22 December 2014
#
# Author:
#
# John Burkardt
#
# Reference:
#
# Albert Nijenhuis and Herbert Wilf,
# Combinatorial Algorithms,
# Academic Press, 1978, second edition,
# ISBN 0-12-519260-6.
#
# Parameters:
#
# Input, integer N, the integer to be decomposed.
#
# Input, integer K, the number of parts in the composition.
# K must be no greater than N.
#
# Input, integer SEED, a seed for the random number generator.
#
# Output, integer A(K), the parts of the composition.
#
# Output, integer SEED, an updated seed for the random number generator.
#
import numpy as np
from ksub_random2 import ksub_random2
a = np.zeros(k, dtype=np.int32)
if (1 < n and 1 < k):
[b, seed] = ksub_random2(n - 1, k - 1, seed)
for i in range(0, k - 1):
a[i] = b[i]
a[k - 1] = n
l = 0
for i in range(0, k):
m = a[i]
a[i] = a[i] - l - 1
l = m
for i in range(0, k):
a[i] = a[i] + 1
return a, seed
def compnz_random ( n, k, seed ):
#*****************************************************************************80
#
## COMPNZ_RANDOM selects a random composition of the integer N into K nonzero parts.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 22 December 2014
#
# Author:
#
# John Burkardt
#
# Reference:
#
# Albert Nijenhuis and Herbert Wilf,
# Combinatorial Algorithms,
# Academic Press, 1978, second edition,
# ISBN 0-12-519260-6.
#
# Parameters:
#
# Input, integer N, the integer to be decomposed.
#
# Input, integer K, the number of parts in the composition.
# K must be no greater than N.
#
# Input, integer SEED, a seed for the random number generator.
#
# Output, integer A(K), the parts of the composition.
#
# Output, integer SEED, an updated seed for the random number generator.
#
import numpy as np
from ksub_random2 import ksub_random2
a = np.zeros ( k, dtype = np.int32 )
if ( 1 < n and 1 < k ):
[ b, seed ] = ksub_random2 ( n - 1, k - 1, seed )
for i in range ( 0, k - 1 ):
a[i] = b[i]
a[k-1] = n
l = 0
for i in range ( 0, k ):
m = a[i]
a[i] = a[i] - l - 1
l = m
for i in range ( 0, k ):
a[i] = a[i] + 1
return a, seed
def count_pose_random ( seed ):
#*****************************************************************************80
#
## COUNT_POSE_RANDOM poses a problem for the game "The Count is Good"
#
# Discussion:
#
# The French television show "The Count is Good" has a game that goes
# as follows:
#
# A number is chosen at random between 100 and 999. This is the GOAL.
#
# Six numbers are randomly chosen from the set 1, 2, 3, 4, 5, 6, 7, 8,
# 9, 10, 25, 50, 75, 100. These numbers are the BLOCKS.
#
# The player must construct a formula, using some or all of the blocks,
# (but not more than once), and the operations of addition, subtraction,
# multiplication and division. Parentheses should be used to remove
# all ambiguity. However, it is forbidden to use subtraction in a
# way that produces a negative result, and all division must come out
# exactly, with no remainder.
#
# This routine poses a sample problem from the show. The point is,
# to determine how to write a program that can solve such a problem.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 06 May 2015
#
# Author:
#
# John Burkardt
#
# Reference:
#
# Raymond Seroul,
# Programming for Mathematicians,
# Springer Verlag, 2000, page 355-357.
#
# Parameters:
#
# Input, integer SEED, a seed for the random number generator.
#
# Output, integer BLOCKS(6), the six numbers available for the formula.
#
# Output, integer GOAL, the goal number.
#
# Output, integer SEED, an updated seed for the random number generator.
#
import numpy as np
from i4_uniform_ab import i4_uniform_ab
from ksub_random2 import ksub_random2
stuff = np.array ( [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, 50, 75, 100 ] )
i4_lo = 100
i4_hi = 999
goal, seed = i4_uniform_ab ( i4_lo, i4_hi, seed )
m = 14
n = 6
ind, seed = ksub_random2 ( m, n, seed )
blocks = np.zeros ( 6 )
for i in range ( 0, 6 ):
blocks[i] = stuff[ind[i]-1]
return blocks, goal, seed
