minimum_size_subarray_sum.py

"""
Given an array of positive integers nums and a positive integer target, return the minimal length of a 
subarray
 whose sum is greater than or equal to target. If there is no such subarray, return 0 instead.

 

Example 1:

Input: target = 7, nums = [2,3,1,2,4,3]
Output: 2
Explanation: The subarray [4,3] has the minimal length under the problem constraint.
Example 2:

Input: target = 4, nums = [1,4,4]
Output: 1
Example 3:

Input: target = 11, nums = [1,1,1,1,1,1,1,1]
Output: 0
 

Constraints:

1 <= target <= 109
1 <= nums.length <= 105
1 <= nums[i] <= 104
 

Follow up: If you have figured out the O(n) solution, try coding another solution of which the time complexity is O(n log(n)).

"""

class Solution:
    def minSubArrayLen(self, target: int, nums: List[int]) -> int:
        if target in nums:
            return 1
        left = 0
        min_size = float("inf")
        prefix_sum = 0

        for right in range(len(nums)):
            prefix_sum = prefix_sum + nums[right]

            while prefix_sum >= target:
                min_size = min(min_size, right - left + 1)
                prefix_sum = prefix_sum - nums[left]
                left = left + 1
        return 0 if min_size == float("inf") else min_size