Minimum Size Subarray Sum

Given an array of positive integers, nums, and a positive integer, target, find the minimum length of a contiguous subarray whose sum is greater than or equal to the target. If no such subarray is found, return 0.

Constraints

• 1 ≤ target ≤ 10⁹
• 1 ≤ nums.length ≤ 10⁵
• 1 ≤ nums[i] ≤ 10⁴

Examples

Sample Example 1

Input:

• nums = [2, 3, 1, 2, 4, 3]
• target = 7

Output: 2

Explanation: The subarray [4, 3] has a sum of 7, which meets the target, and its length of 2 is the smallest among all valid subarrays.

Sample Example 2

Input:

• nums = [1, 4, 4]
• target = 4

Output: 1

Explanation: The subarray [4] alone already meets the target sum of 4, so the minimum length is 1.

Sample Example 3

Input:

• nums = [1, 1, 1, 1, 1, 1, 1, 1]
• target = 11

Output: 0

Explanation: The sum of the entire array is 8, which is less than the target of 11, so no valid subarray exists.