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The Sliding Window approach keeps track of a window using two pointers and dynamically adjusts subarray boundaries to maintain valid subarrays with sums greater than or equal to the target.
1. Initialize two pointers, left and right, both set to the start of the array.
2. Use right to expand the window by including elements in the subarray until the sum is equal to or exceeds the target.
3. Once the sum reaches or exceeds the target, attempt to minimize the window from the left by incrementing left while ensuring the sum remains equal to or greater than the target.
Time Complexity: O(n) where n is the length of the array.
Space Complexity: O(1) because we use a constant amount of extra space.
1def minSubArrayLen(target, nums):
2 left = 0
3 sum_ = 0
4 min_length = float('inf')
5 for right in range(len(nums)):
6 sum_ += nums[right]
7 while sum_ >= target:
8 min_length = min(min_length, right - left + 1)
9 sum_ -= nums[left]
10 left += 1
11 return 0 if min_length == float('inf') else min_length
12
13# Example usage:
14nums = [2, 3, 1, 2, 4, 3]
15target = 7
16print(minSubArrayLen(target, nums))The Python solution uses a sliding window and two pointers to efficiently track and minimize subarray sums as needed, updating the sum dynamically while providing conditions to alter the window.
This approach uses prefix sums and binary search to find the minimal length of subarrays summing to the required target. It builds on the idea that the sum of elements from index i to j can be represented using prefix sums, allowing us to search for valid subarray boundaries efficiently.
1. Compute the prefix sums of the array, which helps us quickly calculate the sum of any subarray.
2. For each starting index, use binary search to find the smallest ending index such that the subarray sum equals or exceeds the target.
Time Complexity: O(n log n) due to binary searching for each possible start index.
Space Complexity: O(n) for the prefix sums array.
In this C solution, we utilize prefix sums and binary search to efficiently locate minimum subarray lengths that meet the target. After constructing the prefix sum array, binary search over this array finds boundaries within a subarray sum condition, reducing it to an efficient search problem.