209. Minimum Size Subarray Sum

 

Mastering the Minimum Size Subarray Sum Problem with the Sliding Window Technique

In this blog post, we’ll dive into a classic algorithm problem known as the Minimum Size Subarray Sum. This problem challenges us to find the minimal length of a contiguous subarray in a given array, where the sum is at least equal to a specified target. We’ll explore an efficient solution using the sliding window technique, and discuss the intuition, approach, and complexity analysis.

Problem Description

Given an array of positive integers nums and a positive integer target, find the minimal length of a contiguous subarray [nums[l], nums[l+1], ..., nums[r-1], nums[r]] of which the sum is greater than or equal to target. If there is no such subarray, return 0 instead.

Intuition

The challenge is to find a contiguous subarray whose sum is at least target and has the smallest possible length. Using a brute force approach to check all possible subarrays would be inefficient, especially for large arrays. Instead, we can use the sliding window technique to dynamically adjust the size of the subarray and efficiently find the minimum length.

Approach

1. Initialization:

   • Initialize res to a value larger than the length of the array (nums.length + 1), which helps us determine if a valid subarray was found.

   • Set left to 0, representing the start of the sliding window.

   • Initialize sum to 0, which will store the sum of the elements within the current window.

2. Expand the Window:

   • Iterate through the array with a for-loop.

   • For each element at index i, add it to sum.

3. Shrink the Window:

   • While sum is greater than or equal to target, update res to the minimum length found so far (i - left + 1).

   • Subtract the element at the left index from sum and increment left to shrink the window from the left side.

4. Return Result:

   • After the loop, check if res was updated. If it was not, return 0. Otherwise, return the value of res.

Complexity Analysis

• Time Complexity: The time complexity is $O(n)O(n)$, where $nn$ is the length of the array. Each element is processed at most twice, making the algorithm linear.

• Space Complexity: The space complexity is $O(1)O(1)$ as we only use a few extra variables (res, left, sum).

Code

Here’s the JavaScript implementation of the solution:

javascript

var minSubArrayLen = function(target, nums) {
    let res = nums.length + 1;
    let left = 0;
    let sum = 0;
    for(let i = 0; i < nums.length; i++) {
        sum += nums[i];
        while(sum >= target) {
            res = Math.min(res, i - left + 1);
            sum -= nums[left];
            left++;
        }
    }
    return res === nums.length + 1 ? 0 : res;
};

This code effectively finds the minimum length of a subarray whose sum is at least target using the sliding window technique.

Conclusion

The sliding window technique is a powerful tool for solving problems that involve processing a continuous subset of elements in an array or string. It allows us to dynamically adjust the window size, making it an efficient and optimal solution for this type of problem.

By mastering this technique, you’ll be better equipped to tackle a variety of algorithmic challenges. If you found this post helpful, or if you have any questions or additional insights, feel free to share in the comments!

Happy coding! 😊

LeetCode Solution Link : https://leetcode.com/problems/minimum-size-subarray-sum/solutions/6160974/easy-and-simple-to-understand-solution-b-v6he/