Leetcode #862: Shortest Subarray with Sum at Least K
In this guide, we solve Leetcode #862 Shortest Subarray with Sum at Least K 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 integer array nums and an integer k, return the length of the shortest non-empty subarray of nums with a sum of at least k. If there is no such subarray, return -1.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Queue, Array, Binary Search, Prefix Sum, Sliding Window, Monotonic Queue, Heap (Priority Queue)
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: nums = [1], k = 1
Output: 1
Python Solution
class Solution:
def shortestSubarray(self, nums: List[int], k: int) -> int:
s = list(accumulate(nums, initial=0))
q = deque()
ans = inf
for i, v in enumerate(s):
while q and v - s[q[0]] >= k:
ans = min(ans, i - q.popleft())
while q and s[q[-1]] >= v:
q.pop()
q.append(i)
return -1 if ans == inf else ans
Complexity
The time complexity is O(n). The space complexity is O(1) to O(n).
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.