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Compute iterative sliding-window sum reduction

VmwareSoftware Engineer · Technical Screen
MediumSoftware EngineerTechnical ScreenCoding & Algorithms

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This question tests the ability to implement a sliding window algorithm to compute dynamic reductions, focusing on efficient array traversal and state maintenance.

Problem Statement

Given an integer array nums, a positive integer k, and a reduction function op that represents an associative mathematical operation (e.g., addition, multiplication, or bitwise AND), return an array where the i-th element is the result of applying op to all elements in the window nums[i : i + k].

Function Signature

from typing import List, Callable

def sliding_window_reduce(nums: List[int], k: int, op: Callable[[int, int], int]) -> List[int]:
    pass

Constraints

  • 1 <= k <= len(nums) <= 10^5
  • Elements in nums are integers within [-10^6, 10^6].
  • The operation op is associative.

Example 1

Input: nums = [1, 2, 3, 4, 5], k = 3, op = lambda a, b: a + b
Output: [6, 9, 12]
Explanation: (1+2+3)=6, (2+3+4)=9, (3+4+5)=12.

Example 2

Input: nums = [2, 4, 8, 16], k = 2, op = lambda a, b: a * b
Output: [8, 32, 128]
Explanation: (2*4)=8, (4*8)=32, (8*16)=128.

Edge Cases

  • k = 1: The output should be identical to the input array.
  • k = len(nums): The output should contain exactly one element (the reduction of the entire array).

Hints

Hint 1

A naive approach would recompute the reduction for every window, leading to O(n * k) time complexity.

Hint 2

Consider if the operation has an inverse (like addition/subtraction or multiplication/division) to allow O(1) updates when the window slides.

Hint 3

If the operation does not have a simple inverse, you can use a deque or two stacks to maintain the reduction in O(n) amortized time.

Follow-up questions

  • How would your approach change if the operation 'op' does not have an inverse (e.g., bitwise AND or maximum)?
  • What is the space complexity of your implementation, and can you optimize it to O(1) extra space excluding the output array?
  • How would you handle the case where 'op' is non-commutative?