leetcode-study

209. Minimum Size Subarray Sum

class Solution:
    def minSubArrayLen(self, target: int, nums: List[int]) -> int:
        """
        Find the minimal length of a contiguous subarray of which the sum is at least target.
        
        Parameters:
            target (int): The target sum that the subarray needs to meet or exceed.
            nums (List[int]): A list of positive integers.
            
        Returns:
            int: The minimal length of a subarray with sum >= target. Returns 0 if no such subarray exists.
        """
        n = len(nums)
        min_len = float('inf')  # Initialize the minimum subarray length to infinity.
        current_sum = 0         # This variable will store the sum of the current sliding window.
        left = 0                # Left pointer for the sliding window.
        
        # Iterate over nums with the right pointer.
        for right, value in enumerate(nums):
            current_sum += value  # Expand the window by adding the current element.
            # Once the current sum reaches or exceeds the target, try to shrink the window.
            while current_sum >= target:
                # Update the minimal length if the current window is smaller.
                min_len = min(min_len, right - left + 1)
                # Shrink the window from the left side.
                current_sum -= nums[left]
                left += 1
        
        # If min_len was never updated, return 0 (no valid subarray found).
        return 0 if min_len == float('inf') else min_len

Summary of Techniques and Approaches:

• Sliding Window Technique:
  The solution employs the sliding window approach by maintaining two pointers, left and right, which dynamically adjust to form a window over the array. The window expands until the sum reaches the target, then contracts to attempt minimizing the subarray length. This technique is highly effective for problems dealing with contiguous subarrays or sequences where the condition (in this case, reaching a target sum) can be met or exceeded in an incremental, linear fashion.

• Single-Pass Iteration:
  By iterating through the list only once and adjusting the window on the fly, the solution achieves an optimal O(n) time complexity. This approach ensures efficiency, especially for large inputs.

• In-Place Optimization:
  The solution modifies the parameters directly using pointers and in-place sum adjustments rather than requiring additional memory for extra data structures. This is valuable in scenarios with memory constraints.

• General Application Tips:

  • Use the sliding window approach for problems involving contiguous segments (e.g., sum, product, or other cumulative properties).
  • Look for conditions where expanding and contracting a segment can help achieve a desired metric (like minimal length or maximal sum).
  • For problems where the input data possesses a monotonic property (here, positive integers that only increase the running sum), the sliding window technique is especially powerful.

These approaches are broadly applicable across numerous DSA problems, aiding in optimizing both time and space complexities.