給定元素長度的Python子集總和問題

Question

對於給定的集合，元素的總和和長度，
我想獲取布爾值是否滿足條件

例如...

Input : set = [18,0,2,20], sum = 20, length = 2 <br>
Output : True (subset [18,2] satisfy the sum=20 for given length 2)

---

Input : set = [18,0,2,20], sum = 22, length = 1 <br>
Output : False

如果存在給定的長度限制，我該如何解決該問題？
（如果沒有長度條件，我可以輕松解決它： subset-sum-problem ）

def isSubsetSum(set, n, sum):
    if sum == 0:
        return True
    if (sum != 0) and (n == 0):
        return False
    if (set[n-1] > sum):
        return isSubsetSum(set,n-1,sum)
    # (a) including the last element
    # (b) excluding the last element
    # Not "AND", But "OR" !!!!!
    return isSubsetSum(set,n-1,sum) or isSubsetSum(set,n-1,sum-set[n-1])

Answer 1

如果允許使用導入的模塊，則itertools具有組合功能，可以使此操作非常容易：

from itertools import combinations
set    = [18,0,2,20]
total  = 20
length = 2
result = [ c for c in combinations(set,length) if sum(c) == total ]
if result: 
  print("True, subset ",result[0],"satisfies the sum", total, "given length",length)
else: 
  print("False")

如果需要將其用作遞歸函數，請考慮對於集合中的每個元素X ，如果可以在總計sum-X的后續元素中找到N-1元素的子集，則有sum/length=N

例如：

def subSum(numbers,total,length):
  if len(numbers) < length or length < 1:
    return []
  for index,number in enumerate(numbers):
    if length == 1 and number == total:
      return [number]
    subset = subSum(numbers[index+1:],total-number,length-1)
    if subset: 
      return [number] + subset
  return []

Answer 2

使用itertools.combinations ：

from itertools import combinations

inp = [18,0,2,20]
length = 2
sum_ = 20

def isSubsetSum(data, length, sum_):
    data = [i[0]+i[1] for i in combinations(data,length)]
    if sum_ in data:
        return True
    return False

print(isSubsetSum(inp,length, sum_))