209. Minimum Size Subarray Sum

At a Glance

Topic: sliding-window
Pattern: Sliding Window
Difficulty: Medium
Companies: Google, Amazon, Meta, Goldman Sachs, Microsoft
Frequency: High
LeetCode: 209

Problem (one-liner)

Given an array of positive integers nums and a target target, return the minimal length of a contiguous subarray whose sum is at least target. Return 0 if none exists.

Recognition Cues

Positive integers → window sum monotonic as you extend
"Shortest subarray with sum ≥ target"
Classic variable-size window with shrink-from-left

Diagram

At-a-glance flow (replace with problem-specific Mermaid as you refine this note). camelCase node IDs; no spaces in IDs.

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Approaches

Brute force — all subarrays — O(n³) naïve, O(n²) with prefix sums.
Better — sliding window — O(n) time / O(1) space for positives.
Optimal — same sliding window; not valid if negatives allowed (then prefix sum + deque/monotonic).

Optimal Solution

Go

func minSubArrayLen(target int, nums []int) int {
	left := 0
	sum := 0
	best := len(nums) + 1
	for right := 0; right < len(nums); right++ {
		sum += nums[right]
		for sum >= target {
			width := right - left + 1
			if width < best {
				best = width
			}
			sum -= nums[left]
			left++
		}
	}
	if best == len(nums)+1 {
		return 0
	}
	return best
}

JavaScript

function minSubArrayLen(target, nums) {
	let left = 0;
	let sum = 0;
	let best = nums.length + 1;
	for (let right = 0; right < nums.length; right++) {
		sum += nums[right];
		while (sum >= target) {
			const width = right - left + 1;
			if (width < best) {
				best = width;
			}
			sum -= nums[left];
			left++;
		}
	}
	return best === nums.length + 1 ? 0 : best;
}