old_contents: """
  You have m types of coins available in infinite quantities
  where the value of each coins is given in the array S=[S0,... Sm-1]
  Can you determine number of ways of making change for n units using
  the given types of coins?
  https://www.hackerrank.com/challenges/coin-change/problem
  """
  
  
  def dp_count(S, m, n):
      """
      >>> dp_count([1, 2, 3], 3, 4)
      4
      >>> dp_count([1, 2, 3], 3, 7)
      8
      >>> dp_count([2, 5, 3, 6], 4, 10)
      5
      >>> dp_count([10], 1, 99)
      0
      >>> dp_count([4, 5, 6], 3, 0)
      1
      """
  
      # table[i] represents the number of ways to get to amount i
      table = [0] * (n + 1)
  
      # There is exactly 1 way to get to zero(You pick no coins).
      table[0] = 1
  
      # Pick all coins one by one and update table[] values
      # after the index greater than or equal to the value of the
      # picked coin
      for coin_val in S:
          for j in range(coin_val, n + 1):
              table[j] += table[j - coin_val]
  
      return table[n]
  
  
  if __name__ == "__main__":
      import doctest
  
      doctest.testmod()
  
new_contents: """
  You have m types of coins available in infinite quantities
  where the value of each coins is given in the array S=[S0,... Sm-1]
  Can you determine number of ways of making change for n units using
  the given types of coins?
  https://www.hackerrank.com/challenges/coin-change/problem
  """
  
  
  def dp_count(S, n):
      """
      >>> dp_count([1, 2, 3], 4)
      4
      >>> dp_count([1, 2, 3], 7)
      8
      >>> dp_count([2, 5, 3, 6], 10)
      5
      >>> dp_count([10], 99)
      0
      >>> dp_count([4, 5, 6], 0)
      1
      >>> dp_count([1, 2, 3], -5)
      0
      """
      if n < 0:
          return 0
      # table[i] represents the number of ways to get to amount i
      table = [0] * (n + 1)
  
      # There is exactly 1 way to get to zero(You pick no coins).
      table[0] = 1
  
      # Pick all coins one by one and update table[] values
      # after the index greater than or equal to the value of the
      # picked coin
      for coin_val in S:
          for j in range(coin_val, n + 1):
              table[j] += table[j - coin_val]
  
      return table[n]
  
  
  if __name__ == "__main__":
      import doctest
  
      doctest.testmod()
  
subject: Fix coin change (#2571)