Leetcode #209: Minimum Size Subarray Sum
In this guide, we solve Leetcode #209 Minimum Size Subarray Sum in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given an array of positive integers nums and a positive integer target, return the minimal length of a subarray whose sum is greater than or equal to target. If there is no such subarray, return 0 instead.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Binary Search, Prefix Sum, Sliding Window
Intuition
We are looking for a contiguous region that satisfies a constraint, which is a classic sliding-window signal.
Expanding and shrinking the window lets us maintain validity without restarting the scan.
Approach
Grow the window with a right pointer, and shrink from the left only when the constraint is violated.
Track the best window as you go to keep the solution linear.
Steps:
- Expand the right end of the window.
- While invalid, move the left end to restore constraints.
- Update the best window found.
Example
Input: target = 7, nums = [2,3,1,2,4,3]
Output: 2
Explanation: The subarray [4,3] has the minimal length under the problem constraint.
Python Solution
class Solution:
def minSubArrayLen(self, target: int, nums: List[int]) -> int:
n = len(nums)
s = list(accumulate(nums, initial=0))
ans = n + 1
for i, x in enumerate(s):
j = bisect_left(s, x + target)
if j <= n:
ans = min(ans, j - i)
return ans if ans <= n else 0
Complexity
The time complexity is O(n log(n)). The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.