ProblemWhat are we solving?
You are given a list of positive numbers and a target.
Find the length of the shortest contiguous block (a run of side-by-side numbers) whose sum is greater than or equal to the target.
If no block reaches the target, the answer is infinity — there is no valid window.
ExamplesWorked cases
in: nums = [2, 1, 5, 2, 3, 2], target = 7
out: 2
The block [5, 2] adds up to 7 and has length 2. No single number reaches 7, so 2 is the shortest.
in: nums = [3, 4, 1, 1, 6], target = 6
out: 1
The single number 6 already meets the target, so the shortest window has length 1.
in: nums = [1, 1, 1], target = 9
out: infinity
Even the whole list only sums to 3, so no window ever reaches 9.
WalkthroughStep by step
left0
right—
current_sum0
min_len∞
Python
1def smallest_window(nums, target):2 left = 03 current_sum = 04 min_len = infinity5 for right in range(len(nums)):6 current_sum += nums[right]7 while current_sum >= target:8 min_len = min(min_len, right - left + 1)9 current_sum -= nums[left]10 left += 111 return min_lenStep 1 / 38SetupWe start with a window that has no width yet. left marks the start of the window and sits at index 0.
1 / 38
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CostTime & space
timeO(n)spaceO(1)
left and right each only move forward, so every number is added once and removed at most once — one pass, not a nested scan.