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import sys

def minSteps(level,startGoods,targetGoods):
  if startGoods >= targetGoods:
      return 0
  if (level,startGoods,targetGoods) in stepsDict:
      return stepsDict[(level,startGoods,targetGoods)]
  steps = 1 + minSteps(level,startGoods+level,targetGoods)
  if startGoods >= level:
      nextLevelSteps = minSteps(level+1,startGoods-level,targetGoods)
      if nextLevelSteps < steps:
          steps = nextLevelSteps
  stepsDict[(level,startGoods,targetGoods)] = steps
  return steps

if __name__ == '__main__':
  stepsDict = dict()
  sys.setrecursionlimit(3000)
  goods = 1200
  steps = minSteps(6,0,goods)
  print(f"Minimale Schrittzahl für {goods} Güter = {steps}")

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import sys

def cache(fc):
    def cache_fc(f):
        def f_cached(a,b,c):
            if not (a,b,c) in fc: fc[(a,b,c)] = f(a,b,c)
            return fc[(a,b,c)]
        return f_cached
    return cache_fc

@cache({})
def minSteps(level,startGoods,targetGoods):
  if startGoods >= targetGoods:
      return 0
  steps = 1 + minSteps(level,startGoods+level,targetGoods)
  if startGoods >= level:
      nextLevelSteps = minSteps(level+1,startGoods-level,targetGoods)
      if nextLevelSteps < steps:
          steps = nextLevelSteps
  return steps

if __name__ == '__main__':
  sys.setrecursionlimit(10000)
  goods = 1200
  steps = minSteps(6,0,goods)
  print(f"Minimale Schrittzahl für {goods} Güter = {steps}")