Dynamic programming problem find number of subsets that add up to target

Question

The problem is to find the number of subsets that add up to a target, for example, if the target is 16 and the array is [2, 4, 6, 10], it should return 2, because 2 + 4 + 10 = 16 and 10 + 6 = 16. I tried to make the recursive solution. I need help to figure out where is the mistake in my code. This is my code:

def num_sum(target, arr, ans=0 ):
if target == 0:
    return 1

elif target < 0:
    return 0

for i in arr:
    arr.remove(i)
    num = num_sum(target - i, arr, ans)
    ans += num
return ans

print(num_sum(16, [2, 4, 6, 10]))

Thanks in advance.

Also, something weird happens: When I put a print statement in the first line of the for loop, it only prints it 4 times, because the length of the array is 4, but I think it should print it more times because the for loop should also run in the recursive calls. — ILikePython
– ILikePython, Commented Jan 29, 2021 at 0:45
Maybe this can help you - stackoverflow.com/questions/65915612 — Daniel Hao
– Daniel Hao, Commented Jan 29, 2021 at 1:06

bob tang · Accepted Answer · 2021-01-29 06:16:49Z

You are trying to use backtracking to calculate the subsets that add up to a target. However, in your code, you keep removing the item from the arr, and it was not added back for backtracking. That's why it prints only 4 times, as the arr size is getting smaller during the recursion.

But in this case, your arr should not be changed, as it can be in different subsets to make up to the target, for example the number 10 in your example. So I would use an index to note the current position ,and then exam the remaining to see if it adds up to a target.

Here is my sample code for your reference. I used an int array as a mutable result holder to hold the result for each recursion.

def num_sum(current_index, target, arr, ans):
    if target == 0:
        ans[0]+=1;
        return

    elif target < 0:
        return

    for i in range(current_index, len(arr)):
        num_sum(i+1, target - arr[i], arr, ans)
        

ans = [0]    
num_sum(0, 16, [2, 4, 6, 10, 8], ans)
print(ans[0])

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