分析python动态规划的递归、非递归实现

from functools import wraps
def memoDeco(func):
  '''
  memoDeco主要是缓存已遍历的节点，减少递归内存开销
  '''
  cashe={}
  @wraps(func)
  def wrapper(*args):
    if args not in cashe:
      cashe[args]=func(*args)
    return cashe[args]
  
  return wrapper

@memoDeco
def recMaxArray(array,index):
  if index==0:
    return array[0]
  elif index==1:
    return max(array[0],array[1])
  else:
    return max(recMaxArray(array,index-2)+array[index],recMaxArray(array,index-1))
  
if __name__=="__main__":
  array=(1,2,4,1,7,8,3)
  print(recMaxArray(array,len(array)-1))

def dpMaxArray(array):
  '''
  代码讲解详见引用一：正月点灯笼讲解
  '''
  lens=len(array)
  maxArray=[0]*(lens)
  maxArray[0]=array[0]
  maxArray[1]=max(array[0],array[1])
  for i in range(2,lens):
    maxArray[i]=max(maxArray[i-2]+array[i],maxArray[i-1])
  return maxArray[-1]

  
if __name__=="__main__":
  array=(1,2,4,1,7,8,3)
  print(dpMaxArray(array))

from functools import wraps

#和第一题一样，套用装饰器可以做一个缓存节点作用
def memoDeco(func):
  '''
  memoDeco主要是缓存已遍历的节点，减少递归内存开销
  '''
  cashe = {}
  
  @wraps(func)
  def wrapper(*args):
    if args not in cashe:
      cashe[args] = func(*args)
    return cashe[args]
  
  return wrapper


@memoDeco
def recSubSet(arr, index, tar_num):
  if index == 0:
    return arr[0] == tar_num
  elif tar_num == 0:
    return True
  elif arr[index] > tar_num:
    return recSubSet(arr, index - 1, tar_num)
  else:
    return recSubSet(arr, index - 1, tar_num) or recSubSet(arr, index - 1, tar_num - index)


if __name__ == "__main__":
  arr = (3, 34, 4, 12, 5, 3)
  tar_num = 13
  index = len(arr) - 1
  print(recSubSet(arr, index, tar_num))

'''
多维数组构建用python第三方库numpy比较方便
代码讲解详见引用一：正月点灯笼讲解
'''
import numpy as np


def dpSubSet(arr, tar_num):
  subSet = np.zeros((len(arr), tar_num + 1), dtype=bool)
  subSet[:, 0] = True
  subSet[0, :] = False
  subSet[0, arr[0]] = True
  for i in range(1, len(arr)):
    for j in range(1, tar_num + 1):
      if arr[i] > j:
        subSet[i, j] = subSet[i - 1, j]
      else:
        subSet[i, j] = subSet[i - 1, j] or subSet[i - 1, j - arr[i]]
  return subSet[-1, -1]


if __name__ == "__main__":
  arr = (3, 34, 4, 12, 5, 3)
  tar_num = 13
  print(dpSubSet(arr, tar_num))