Is Make K-Subarray Sums Equal easy or hard?

The problem is rated Medium on LeetCode. The main difficulty is discovering that equal k-subarray sums force equality along index cycles defined by k. Once that observation is made, the remaining step is a standard median-based minimization.

Make K-Subarray Sums Equal Python/Java solution

Python and Java implementations follow the same steps: compute gcd(n, k), iterate through cycles, collect values, sort them, and compute the cost relative to the median. The logic remains identical across languages with O(n log n) complexity.

How to solve Make K-Subarray Sums Equal in O(n log n)?

First compute g = gcd(n, k). For each of the g cycles formed by repeatedly adding k modulo n, gather the elements. Sort each group, choose the median, and sum absolute differences to that median. Adding costs across all cycles yields the minimal number of operations.

What is the best approach for Make K-Subarray Sums Equal?

The optimal approach groups indices into cycles using gcd(n, k). Elements in the same cycle must become equal because equal k-length subarray sums imply nums[i] = nums[i+k]. For each cycle, convert all values to the median to minimize the sum of absolute differences. This produces an O(n log n) time and O(n) space solution.

Is Make K-Subarray Sums Equal asked at Google/Amazon/Meta?

Problems involving cycle grouping, median minimization, and gcd-based partitioning appear frequently in interviews at companies like Google and Amazon. Variants of this problem test array manipulation, mathematical observations, and optimization using medians.

What data structure is used in Make K-Subarray Sums Equal?

The solution mainly uses arrays or lists to collect elements belonging to the same cycle. Sorting those lists is required to compute the median efficiently. The mathematical component relies on computing gcd(n, k).

What is the time complexity of Make K-Subarray Sums Equal?

The optimal solution runs in O(n log n) time. Each cycle of indices is collected and sorted to compute the median, which dominates the runtime. Space complexity is O(n) for storing cycle elements.

Description Hints 3 Solution Video 29:35

2607. Make K-Subarray Sums Equal

Medium38.9% acceptance2 companies

You are given a 0-indexed integer array arr and an integer k. The array arr is circular. In other words, the first element of the array is the next element of the last element, and the last element of the array is the previous element of the first element.

You can do the following operation any number of times:

Pick any element from arr and increase or decrease it by 1.

Return the minimum number of operations such that the sum of each subarray of length k is equal.

A subarray is a contiguous part of the array.

Example 1:

Input: arr = [1,4,1,3], k = 2
Output: 1
Explanation: we can do one operation on index 1 to make its value equal to 3.
The array after the operation is [1,3,1,3]
- Subarray starts at index 0 is [1, 3], and its sum is 4 
- Subarray starts at index 1 is [3, 1], and its sum is 4 
- Subarray starts at index 2 is [1, 3], and its sum is 4 
- Subarray starts at index 3 is [3, 1], and its sum is 4

Example 2:

Input: arr = [2,5,5,7], k = 3
Output: 5
Explanation: we can do three operations on index 0 to make its value equal to 5 and two operations on index 3 to make its value equal to 5.
The array after the operations is [5,5,5,5]
- Subarray starts at index 0 is [5, 5, 5], and its sum is 15
- Subarray starts at index 1 is [5, 5, 5], and its sum is 15
- Subarray starts at index 2 is [5, 5, 5], and its sum is 15
- Subarray starts at index 3 is [5, 5, 5], and its sum is 15

Constraints:

1 <= k <= arr.length <= 10⁵
1 <= arr[i] <= 10⁹

Asked at 2 companies

Observeai Morgan Stanley

Topics

Hints open one at a time

Hint 1

Think about gcd(n, k). How will it help to calculate the answer?

Hint 2

indices i and j are in the same group if gcd(n, k) mod i = gcd(n, k) mod j. Each group should have equal elements. Think about the minimum number of operations for each group

Hint 3

The minimum number of operations for each group equals the summation of differences between the elements and the median of elements inside the group.

29:35

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