Katkat
Back

Compute sum over consecutive-step subarrays

GoogleMachine Learning Engineer · Onsite
MediumMachine Learning EngineerOnsiteCoding & Algorithms

Last updated

This problem tests your ability to identify contiguous subarrays that follow an arithmetic progression with a common difference of 1 (consecutive steps) and calculate the sum of elements within these subarrays efficiently.

Problem Statement

You are given an array of integers nums. A 'consecutive-step subarray' is defined as a contiguous subarray of length at least 2 where each element is exactly 1 greater than the previous element (e.g., [3, 4, 5] or [-1, 0]).

Your task is to return the sum of all elements across all possible consecutive-step subarrays found within nums. Since the sum can be very large, use 64-bit integers.

Function Signature

def sum_consecutive_subarrays(nums: List[int]) -> int:

Examples

Example 1: Input: nums = [1, 2, 3] Consecutive-step subarrays: [1, 2], [2, 3], [1, 2, 3] Sums: 3 + 5 + 6 = 14 Output: 14

Example 2: Input: nums = [1, 2, 4, 5] Consecutive-step subarrays: [1, 2], [4, 5] Sums: 3 + 9 = 12 Output: 12

Constraints

  • 1 <= nums.length <= 10^5
  • -10^9 <= nums[i] <= 10^9

Edge Cases

  • Array with length < 2.
  • Arrays with no consecutive-step segments.
  • Arrays with all elements in a single consecutive sequence.

Hints

Hint 1

Identify the longest contiguous segments where `nums[i] == nums[i-1] + 1`.

Hint 2

For a segment of length `L`, you need to calculate the sum of all possible subarrays of length 2 to `L`.

Hint 3

Using the formula for the sum of an arithmetic progression can help calculate the total sum of any subarray in O(1) time once identified.

Follow-up questions

  • How would the solution change if the common difference could be any integer `k`?
  • Can you solve this problem in O(n) time and O(1) space?
  • What changes would you make if you needed to support point updates to the array and query the total sum dynamically?