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