LeetCode 209: Minimum Size Subarray Sum — Python Solution

Solve LeetCode 209: Minimum Size Subarray Sum in Python with a positive sliding window approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Expand until the positive-number sum reaches the target, then shrink as much as possible while recording the shortest valid length.

Algorithm

1. Expand until the positive-number sum reaches the target, then shrink as much as possible while recording the shortest valid length.
2. Maintain this invariant: Before each expansion, the current window is the shortest examined suffix for its right boundary.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def minSubArrayLen(self, target, nums):
        left = total = 0; best = len(nums) + 1
        for right, value in enumerate(nums):
            total += value
            while total >= target:
                best = min(best, right - left + 1)
                total -= nums[left]; left += 1
        return 0 if best > len(nums) else best

Why this is correct

The proof follows the maintained state: Before each expansion, the current window is the shortest examined suffix for its right boundary. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) time and O(1) extra space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

Return zero when no window reaches the target.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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