Is Sum of Variable Length Subarrays easy or hard?

Sum of Variable Length Subarrays is categorized as an Easy problem. The main idea is recognizing that each index defines a range ending at i. Using a prefix sum array turns repeated summations into constant-time queries, making the implementation straightforward.

Sum of Variable Length Subarrays Python/Java solution

Most implementations follow the same structure across languages: build a prefix sum array, iterate through the indices, compute start = max(0, i - nums[i]), and accumulate prefix[i + 1] - prefix[start]. The logic is identical in Python, Java, C++, Go, and TypeScript with only syntax differences.

How to solve Sum of Variable Length Subarrays in O(n)?

Construct a prefix sum array where prefix[i] stores the sum of elements before index i. For each index i, compute start = max(0, i - nums[i]). The subarray sum from start to i equals prefix[i + 1] - prefix[start]. Add this to the total while scanning the array once, achieving O(n) time complexity.

What is the best approach for Sum of Variable Length Subarrays?

The prefix sum approach is the most efficient method. Precompute cumulative sums so any subarray sum can be calculated in O(1) time. Then iterate through the array, determine the start index max(0, i - nums[i]), and compute the range sum using prefix values. This results in O(n) time and O(n) space.

Is Sum of Variable Length Subarrays asked at Google/Amazon/Meta?

Problems based on prefix sums and dynamic range calculations appear frequently in interviews at companies like Amazon, Google, and Meta. While this exact problem may not always appear, the underlying pattern of converting repeated subarray sums into prefix-sum queries is a common interview technique.

What data structure is used in Sum of Variable Length Subarrays?

The main structure used is a prefix sum array. It stores cumulative sums so that any range sum can be retrieved in constant time. This technique is widely used for array range queries and optimization of repeated summation tasks.

What is the time complexity of Sum of Variable Length Subarrays?

The optimal solution runs in O(n) time using a prefix sum array. Building the prefix array takes O(n), and each index performs a constant-time range sum query. A naive brute-force solution that recomputes sums for each subarray takes O(n²) time.

Description Hints 1 Solution Video 10:00

3427. Sum of Variable Length Subarrays

Easy85.6% acceptance2 companies

You are given an integer array nums of size n. For each index i where 0 <= i < n, define a subarray nums[start ... i] where start = max(0, i - nums[i]).

Return the total sum of all elements from the subarray defined for each index in the array.

Example 1:

Input: nums = [2,3,1]

Output: 11

Explanation:

i	Subarray	Sum
0	`nums[0] = [2]`	2
1	`nums[0 ... 1] = [2, 3]`	5
2	`nums[1 ... 2] = [3, 1]`	4
Total Sum		11

The total sum is 11. Hence, 11 is the output.

Example 2:

Input: nums = [3,1,1,2]

Output: 13

Explanation:

i	Subarray	Sum
0	`nums[0] = [3]`	3
1	`nums[0 ... 1] = [3, 1]`	4
2	`nums[1 ... 2] = [1, 1]`	2
3	`nums[1 ... 3] = [1, 1, 2]`	4
Total Sum		13

The total sum is 13. Hence, 13 is the output.

Constraints:

1 <= n == nums.length <= 100
1 <= nums[i] <= 1000

Asked at 2 companies

Google Amazon

Topics

Array Prefix Sum

Hints open one at a time

Hint 1

The constraints are small, so brute force for each index.

10:00

Still stuck?Read the written solution, or watch a walkthrough.

Open solution