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

#*****************************************************************************80
#
## knapsack_dynamic_test() tests knapsack_dynamic().
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    02 November 2022
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform

  print ( '' )
  print ( 'knapsack_dynamic_test():' )
  print ( '  python version: ' + platform.python_version ( ) )
  print ( '  numpy version:  ' + np.version.version )
  print ( '  Test knapsack_dynamic().' )

  for test in range ( 0, 6 ):

    if ( test == 0 ):
      k = 26
      n = 5
      v = np.array ( [  24,  13,  23,  15,  16 ] )
      w = np.array ( [  12,   7,  11,   8,   9 ] )
    elif ( test == 1 ):
      k = 190
      n = 6
      v = np.array ( [  50,  50,  64,  46,  50,   5 ] )
      w = np.array ( [  56,  59,  80,  64,  75,  17 ] )
    elif ( test == 2 ):
      k = 50
      n = 7
      v = np.array ( [  70,  20,  39,  37,   7,   5,  10 ] )
      w = np.array ( [  31,  10,  20,  19,   4,   3,   6 ] )
    elif ( test == 3 ):
      k = 104
      n = 8
      v = np.array ( [ 350, 400, 450,  20,  70,   8,   5,   5 ] )
      w = np.array ( [  25,  35,  45,   5,  25,   3,   2,   2 ] )
    elif ( test == 4 ):
      k = 67
      n = 10
      v = np.array ( [ 505, 352, 458, 220, 354, 414, 498, 545, 473, 543 ] )
      w = np.array ( [  23,  26,  20,  18,  32,  27,  29,  26,  30,  27 ] )
    elif ( test == 5 ):
      k = 165
      n = 10
      v = np.array ( [  92,  57,  49,  68,  60,  43,  67,  84,  87,  72 ] )
      w = np.array ( [  23,  31,  29,  44,  53,  38,  63,  85,  89,  82 ] )

    knapsack_dynamic_test01 ( v, w, k )
#
#  Terminate.
#
  print ( '' )
  print ( 'knapsack_dynamic_test():' )
  print ( '  Normal end of execution.' )

  return

def knapsack_dynamic ( v, w, k ):

#*****************************************************************************80
#
## knapsack_dynamic() uses dynamic programming to solve a knapsack problem.
#
#  Discussion:
#
#    All data must be integers.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    21 November 2024
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer v(n): the profit of each item.
#
#    integer w(n): the weight of each item.
#
#    integer k: the knapsack capacity.
#
#  Output:
#
#    integer item(): the list of item to be taken.
#
  import numpy as np

  m = knapsack_dynamic_table ( v, w, k )

  n = len ( v )
  item = np.array ( [], dtype = int )
  k2 = k

  for i in range ( n - 1, -1, -1 ):
    if ( m[i,k2] < m[i+1,k2] ):
      k2 = k2 - w[i]
      item = np.append ( item, i )

  return item

def knapsack_dynamic_table ( v, w, k ):

#*****************************************************************************80
#
## knapsack_dynamic_table() computes a knapsack problem dynamic programming table.
#
#  Discussion:
#
#    All data must be integers.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    02 November 2022
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer v(n): the profit of each item.
#
#    integer w(n): the weight of each item.
#
#    integer k: the knapsack capacity.
#
#  Output:
#
#    m(0:n,0:k): m(i,j) is the maximum value of the items 
#    that can be stored in the knapsack, selecting from the first 
#    i items, with a weight no more than j.
#
  import numpy as np

  n = len ( v )

  m = np.zeros ( [ n + 1, k + 1 ] )
#
#  Consider object i...
#
  for i in range ( 0, n ):
#
#  Consider the weight limit j from 0 through k.
#
    for j in range ( 0, k + 1 ):
#
#  If item i weighs more than j, then it can't be used.
#
      if ( j < w[i] ):
        m[i+1,j] = m[i,j]
#
#  If item i weighs no more than j, 
#  then it could be used along with the best solution for weight j-w[i].
#  If this gives a better result, update.
#
      else:
        m[i+1,j] = max ( m[i,j], m[i,j-w[i]] + v[i] )
#
#  The value in m[n,k] is the highest profit using n items for a total
#  weight no more than k.
#
  return m

def knapsack_dynamic_test01 ( v, w, k ):

#*****************************************************************************80
#
## knapsack_dynamic_test01() tests knapsack_dynamic().
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    02 November 2022
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer v(n): the value of each item.
#
#    integer w(n): the "weight" or cost of each item.
#
#    integer k: the maximum weight capacity for the knapsack.
#
  n = len ( v )

  print ( '' )
  print ( '  Number of items is', n )
  print ( '  Knapsack capacity is', k )
  print ( '  Item values: ' )
  print ( v )
  print ( '  Item weights:' )
  print ( w )

  item = knapsack_dynamic ( v, w, k )
  d = v / w

  print ( '' )
  print ( '   #  Index  Value  Weight  Density' )
  print ( '' )
  v_total = 0
  w_total = 0
  item_num = len ( item )
  for i in range ( 0, item_num ):
    j = item[i]
    print ( '  %2d     %2d   %5d  %5d  %8.2f' % ( i, item[i], v[j], w[j], d[j] ) )
    v_total = v_total + v[j]
    w_total = w_total + w[j]

  d_total = v_total / w_total
  print ( '         --   -----  -----' )
  print ( '  Total: %2d   %5d  %5d  %8.2f' % ( item_num, v_total, w_total, d_total ) )

  return

def timestamp ( ):

#*****************************************************************************80
#
## timestamp() prints the date as a timestamp.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    21 August 2019
#
#  Author:
#
#    John Burkardt
#
  import time

  t = time.time ( )
  print ( time.ctime ( t ) )

  return

if ( __name__ == '__main__' ):
  timestamp ( )
  knapsack_dynamic_test ( )
  timestamp ( )