# include <stdio.h>
# include <stdlib.h>
# include <time.h>

# include "change_making.h"

/******************************************************************************/

int *change_making_list ( int coin_num, int coin_value[], int target )

/******************************************************************************/
/*
  Purpose:

    CHANGE_MAKING_LIST solves the change making problem.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    30 June 2017

  Author:

    John Burkardt

  Parameters:

    Input, int COIN_NUM, the number of coin denomiations.

    Input, int COIN_VALUE(COIN_NUM), the value of each coin.
    These values should be positive integers.

    Input, int TARGET, the desired sum.

    Output, int CHANGE_MAKING_LIST[TARGET+1], A(T) lists the smallest number 
    of coins needed to form the sum T, or "Inf" if it is not possible to form
    this sum.
*/
{
  int *a;
  int i;
  int i4_huge = 2147483647;
  int j;

  a = ( int * ) malloc ( ( target + 1 ) * sizeof ( int ) );
  a[0] = 0;
  for ( j = 1; j <= target; j++ )
  {
    a[j] = i4_huge;
  }
/*
   If T is the value of a coin, then A(T) is 1.
*/
  for ( i = 0; i < coin_num; i++ )
  {
    if ( coin_value[i] <= target )
    {
      a[coin_value[i]] = 1;
    }
  }
/*
  To compute A(T) in general, consider getting there by adding
  one coin of value V, and looking at A(T-V).
*/
  for ( j = 1; j <= target; j++ )
  {
    for ( i = 0; i < coin_num; i++ )
    {
      if ( 0 <= j - coin_value[i] )
      {
        a[j] = i4_min ( a[j] - 1, a[j-coin_value[i]] ) + 1;
      }
    }
  }

  return a;
}
/******************************************************************************/

int i4_min ( int i1, int i2 )

/******************************************************************************/
/*
  Purpose:

    I4_MIN returns the smaller of two I4's.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    29 August 2006

  Author:

    John Burkardt

  Parameters:

    Input, int I1, I2, two integers to be compared.

    Output, int I4_MIN, the smaller of I1 and I2.
*/
{
  int value;

  if ( i1 < i2 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
/******************************************************************************/

void timestamp ( )

/******************************************************************************/
/*
  Purpose:

    TIMESTAMP prints the current YMDHMS date as a time stamp.

  Example:

    31 May 2001 09:45:54 AM

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    24 September 2003

  Author:

    John Burkardt

  Parameters:

    None
*/
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct tm *tm;
  time_t now;

  now = time ( NULL );
  tm = localtime ( &now );

  strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );

  fprintf ( stdout, "%s\n", time_buffer );

  return;
# undef TIME_SIZE
}