subset_sum_bottom.py

def count_subsets(num, sum):
  n = len(num)
  dp = [[-1 for x in range(sum+1)] for y in range(n)]

  # populate the sum = 0 columns, as we will always have an empty set for zero sum
  for i in range(0, n):
    dp[i][0] = 1

  # with only one number, we can form a subset only when the required sum is
  # equal to its value
  for s in range(1, sum+1):
    dp[0][s] = 1 if num[0] == s else 0

  # process all subsets for all sums
  for i in range(1, n):
    for s in range(1, sum+1):
      # exclude the number
      dp[i][s] = dp[i - 1][s]
      # include the number, if it does not exceed the sum
      if s >= num[i]:
        dp[i][s] += dp[i - 1][s - num[i]]

  # the bottom-right corner will have our answer.
  return dp[n - 1][sum]