Peak shift

Given an integer array hours and an integer k, return the largest sum of any contiguous subarray containing exactly k elements. A contiguous subarray consists of adjacent elements in their original order. The input satisfies 1 ≤ k ≤ len(hours). Values may be negative.

Example:

peak_shift([3, 1, 4, 1, 5], 3)  →  10

The three length-3 subarrays have sums 3+1+4=8, 1+4+1=6 and 4+1+5=10. The maximum is 10.

peak_shift([2, 2, 2], 1)  →  2

With k=1, each subarray has one element. Every candidate has sum 2.

Pattern: sliding_window - sum the first window, then add the next hour and drop the oldest

Need a hint?

Reveal one step at a time. Stop when you have enough to keep going.

1 · What to notice

Two neighboring fragments of length k share k − 1 elements. Which two elements change their sum when you move one step?

2 · Walk through an example

For hours = [3, 1, 4, 1, 5], k = 3, the first sum is 8. Slide right: remove 3 and add 1 to get 6. Slide again: remove 1 and add 5 to get 10. The largest sum is 10. Start the best sum with the first window, because all sums may be negative.

3 · Pseudocode and self-check

Language-independent pseudocode. Indices start at 0; ← means assignment. Ranges with an upper bound exclude that bound.

window_sum ← SUM(hours[0:k])
best ← window_sum
FOR i FROM k TO LENGTH(hours) EXCLUSIVE:
    window_sum ← window_sum + hours[i] - hours[i - k]
    best ← MAX(best, window_sum)
RETURN best

Check your reasoning

[-5, -2, -7], k = 2 → -7, not 0. k = 1 selects the largest element; k = n uses the whole array. Time O(n), auxiliary space O(1).

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Peak shift

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