How do you solve Make K-Subarray Sums Equal on LeetCode?

Make K-Subarray Sums Equal (LeetCode #2607) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding the circular nature of the array is crucial for grouping elements.

What is the brute force solution for Make K-Subarray Sums Equal?

The brute force approach for Make K-Subarray Sums Equal is Brute Force, with O(n²) time complexity and O(n) space complexity. The brute force approach involves calculating the sum of every possible subarray of length k and adjusting the elements to make these sums equal. This method is straightforward but inefficient due to its high time complexity. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Make K-Subarray Sums Equal?

Make K-Subarray Sums Equal uses the following concepts: Array, Math, Greedy, Sorting, Number Theory. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Make K-Subarray Sums Equal?

Always start with a brute-force solution to understand the problem better. Look for patterns in the problem, such as grouping elements based on indices. Explain your thought process clearly, especially when transitioning from brute force to optimal solutions.

What are common mistakes when solving Make K-Subarray Sums Equal?

Not considering the circular nature of the array when calculating subarrays. Failing to optimize the solution and resorting to brute force even when a better approach exists.

#2607

Make K-Subarray Sums Equal

Medium

ArrayMathGreedySortingNumber TheoryHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(n)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal approach leverages the properties of the circular array and the greatest common divisor (GCD) to group indices. Each group must have equal elements, and we can minimize operations by adjusting each group to their average.

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Algorithm

4 steps

1Step 1: Calculate the GCD of the length of the array and k to determine the number of groups.
2Step 2: For each group, calculate the total sum and the target value (average) for that group.
3Step 3: Calculate the number of operations needed to make all elements in each group equal to the target value.
4Step 4: Sum the operations across all groups to get the final result.

solution.py16 lines

1from math import gcd
2
3def minOperations(arr, k):
4    n = len(arr)
5    g = gcd(n, k)
6    operations = 0
7    for i in range(g):
8        group_sum = 0
9        group_count = 0
10        for j in range(i, n, g):
11            group_sum += arr[j]
12            group_count += 1
13        target_value = group_sum // group_count
14        for j in range(i, n, g):
15            operations += abs(arr[j] - target_value)
16    return operations

ℹ

Complexity note: This complexity is O(n) because we iterate through the array a constant number of times, specifically g times, where g is the GCD of n and k, which is less than or equal to n.

1Understanding the circular nature of the array is crucial for grouping elements.
2Using GCD helps in identifying how many groups we need to balance.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.