Small example with negatives
Input
nums = [2, -1, 2], k = 3
Output
3
The whole array sums to 3, length is 3.
Full lesson preview
Find the shortest subarray with sum at least k
Find the minimal-length contiguous subarray whose sum is >= k (supports negative numbers).
Python practice25 minArrays – Fundamentals & PatternsAdvancedLast updated March 25, 2026
Problem statement
Given an integer array nums (may contain negative numbers) and an integer k, return the length of the shortest, non-empty, contiguous subarray of nums with sum at least k. If no such subarray exists, return -1. This problem requires handling negative values and should be solved using prefix sums plus a monotonic queue for optimal performance.
Task
Use prefix sums and a monotonic deque to compute the shortest subarray with sum at least k in O(n) time.
Examples
Input format
Function signature: shortest_subarray_with_sum_at_least_k(nums: list[int], k: int) -> int
Output format
Return an integer: the minimal length of a contiguous subarray with sum >= k, or -1 if none exists.
Constraints
1 <= len(nums) <= 10^5 for typical inputs, -10^9 <= nums[i] <= 10^9, -10^14 <= k <= 10^14. Expected O(n) time and O(n) extra space.
Samples
Sample 1
Input
nums = [1, 2, 3, 4, 5], k = 11
Output
3
Subarray [3,4,5] sums to 12 and is minimal length 3.