# include <cstdlib>
# include <iomanip>
# include <iostream>

using namespace std;

# include "change_dynamic.hpp"

//****************************************************************************80

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

//****************************************************************************80
//
//  Purpose:
//
//    change_dynamic() solves the change making problem with dynamic programming.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    30 June 2017
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int COIN_NUM, the number of coin denomiations.
//
//    int COIN_VALUE[COIN_NUM], the value of each coin.
//    These values should be positive integers.
//
//    int TARGET, the desired sum.
//
//  Output:
//
//    int change_dynamic_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 = new int[target+1];
  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] = min ( a[j] - 1, a[j-coin_value[i]] ) + 1;
      }
    }
  }

  return a;
}