# Minimum Size Subarray Sum

Given an array of positive integers `nums` and a positive integer `target`, return the minimal length of a contiguous subarray `[numsl, numsl+1, ..., numsr-1, numsr]` of which the 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: 2Explanation: 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] <= 105`

Implementation:

We could keep 2 pointers ,one for the start and another for the end of the current subarray, and make optimal moves so as to keep the sum greater than s as well as maintain the lowest size possible.

Algorithm

• Initialize left pointer to 0 and sum to 0
• Iterate over the nums:
• While sum is greater than or equal to s:
• Update result=min(result,i+1−left), where i+1−left is the size of current subarray.
• It means that the first index can safely be incremented, since, the minimum subarray starting with this index with sum≥s has been achieved
• Subtract nums[left] from sum and increment left.

Complexity analysis

• Time complexity: O(n). Single iteration .
• Space complexity: O(1) extra space.