Start from the invariant.
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Sliding window
Sliding window
Maintain a valid contiguous interval.
Interview essentialsWhen to use it
Find the longest contiguous array segment whose sum is at most a limit. Every value must be nonnegative.
What stays true
After shrinking, sum equals the total in [left, right] and is at most the limit. Removing another left value cannot produce a longer valid segment ending here.
- Time
- O(n)
- Extra space
- O(1)
sliding_window.py
def longest_window(nums: list[int], limit: int) -> int:
"""Longest segment with sum <= limit; nums must be nonnegative."""
if limit < 0:
return 0
left = total = best = 0
for right, value in enumerate(nums):
total += value
while total > limit:
total -= nums[left]
left += 1
best = max(best, right - left + 1)
return best
Functions and classes only. Call them from your judge’s required entry point.
nums = [2, 1, 3, 1], limit = 4 → 2. Both [2, 1] and [3, 1] have length 2.
Keep the sum at most 4
Extend
- 02(active)
- 11(active)
- 23
- 31
[2, 1] sums to 3 and has length 2.
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