Program to find size of smallest sublist whose sum at least target in Python

Suppose we have a list of numbers called nums, and an another input called target, we have to find the size of the shortest sublist such that its sum value is same as target or larger. If there is no such sublist then return -1.

So, if the input is like nums = [2, 11, -4, 17, 4] target = 19, then the output will be 2, as we can select [17, 4] to get sum of at least 19.

To solve this, we will follow these steps −

• ps := a list with only one element 0

• for each num in nums, do

  • insert (last element of ps + num) after ps

  • if num >= target, then

    • return 1

• min_size := inf

• q := [0]

• j := 0

• for i in range 1 to size of ps, do

  • j := minimum of j, size of q - 1

    • while j < size of q and ps[i] - ps[q[j]] >= target, do

      • min_size := minimum of min_size and (i - q[j])

      • j := j + 1

    • while q and ps[i] <= ps[last element of q], do

      • delete last element from q

    • insert i at the end of q

• return min_size if min_size < inf otherwise -1

Example 

Let us see the following implementation to get better understanding −

 Live Demo

class Solution:
   def solve(self, nums, target):
      ps = [0]
      for num in nums:
         ps += [ps[-1] + num]
         if num >= target:
            return 1
         min_size = float("inf")
         q = [0]
         j = 0
         for i in range(1, len(ps)):
            j = min(j, len(q) - 1)
            while j < len(q) and ps[i] - ps[q[j]] >= target:
               min_size = min(min_size, i - q[j])
               j += 1
            while q and ps[i] <= ps[q[-1]]:
               q.pop()
            q.append(i)
         return min_size if min_size < float("inf") else -1
ob = Solution()
nums = [2, 11, -4, 17, 4]
target = 19
print(ob.solve(nums, target))

Input

[2, 11, -4, 17, 4], 19

Output

2