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Given an array of positive integers nums and a positive integer target, return the minimal length of a contiguous subarray 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: 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

Clarifying Questions

  1. Can the input array nums be empty?
    • No, as per the problem constraints, nums will always contain at least one positive integer.
  2. Will target always be a positive integer?
    • Yes, target is guaranteed to be positive.
  3. How large can nums be?
    • The problem will likely specify constraints for the length of nums when given in a real setting. Common constraints can be (10^5) or (10^6).

Strategy

We will use the sliding window/two-pointer technique for this problem. This involves maintaining a window defined by two pointers (left and right) that will efficiently find the minimal length subarray with the sum greater than or equal to target.

  1. Initialize:
    • Two pointers: left starting at the beginning of the array, and right iterating through the array.
    • A variable current_sum to store the current subarray sum.
    • A variable min_length to store the minimal length of valid subarrays. Set it initially to infinity (float('inf')).
  2. Expand the Window:
    • Iterate with right over the array and add nums[right] to current_sum.
  3. Shrink the Window:
    • While current_sum is greater than or equal to target, try to shrink the window by moving left to the right and updating current_sum accordingly. Also, update min_length with the smaller length found.
  4. Check Result:
    • After exiting the loop, if min_length is still infinity, no valid subarray was found. Return 0.
    • Otherwise, return min_length.

Time Complexity

Code

Here’s the code implementing the above strategy:

def minSubArrayLen(target, nums):
    left = 0
    current_sum = 0
    min_length = float('inf')
    
    for right in range(len(nums)):
        current_sum += nums[right]
        
        while current_sum >= target:
            min_length = min(min_length, right - left + 1)
            current_sum -= nums[left]
            left += 1
    
    return 0 if min_length == float('inf') else min_length

# Example usage
print(minSubArrayLen(7, [2,3,1,2,4,3]))  # Output: 2
print(minSubArrayLen(4, [1,4,4]))        # Output: 1
print(minSubArrayLen(11, [1,1,1,1,1,1,1,1]))  # Output: 0

This covers the entire solution including the problem statement, clarifying questions, detailed strategy, time complexity analysis, and the final implementation.

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