How do you solve Minimum Average Difference on LeetCode?

Minimum Average Difference (LeetCode #2256) 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: Using prefix sums allows for efficient average calculations.

What is the time complexity of Minimum Average Difference?

The optimal solution for Minimum Average Difference runs in O(n) time and uses O(1) space. This complexity is O(n) because we traverse the array a constant number of times, and we use a fixed amount of extra space.

What is the brute force solution for Minimum Average Difference?

The brute force approach for Minimum Average Difference is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach calculates the average difference for each index by summing the elements on both sides of the index. It's straightforward but inefficient, as it involves recalculating sums repeatedly. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Average Difference?

Minimum Average Difference uses the following concepts: Array, Prefix Sum. The recommended patterns to study are: Prefix Sum, Array.

What are the interview tips for Minimum Average Difference?

Explain your thought process clearly while coding. Consider edge cases, such as arrays with one element. Discuss the time and space complexity of your solution.

What are common mistakes when solving Minimum Average Difference?

Not handling the case when there are no right elements correctly. Forgetting to round down the averages.

#2256

Minimum Average Difference

Medium

ArrayPrefix SumPrefix SumArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(1)

By using prefix sums, we can calculate the sums of the left and right segments in constant time, significantly reducing the number of operations needed.

⚙️

Algorithm

4 steps

1Step 1: Calculate the total sum of the array.
2Step 2: Initialize a prefix sum variable to keep track of the sum of elements from the start up to the current index.
3Step 3: For each index, calculate the left average using the prefix sum and the total sum for the right average.
4Step 4: Compute the absolute difference and track the minimum difference and its index.

solution.py18 lines

1# Full working Python code
2
3def minimumAverageDifference(nums):
4    n = len(nums)
5    total_sum = sum(nums)
6    prefix_sum = 0
7    min_diff = float('inf')
8    min_index = -1
9    for i in range(n):
10        prefix_sum += nums[i]
11        left_avg = prefix_sum // (i + 1)
12        right_avg = (total_sum - prefix_sum) // (n - i - 1) if n - i - 1 > 0 else 0
13        diff = abs(left_avg - right_avg)
14        if diff < min_diff:
15            min_diff = diff
16            min_index = i
17    return min_index
18

ℹ

Complexity note: This complexity is O(n) because we traverse the array a constant number of times, and we use a fixed amount of extra space.

1Using prefix sums allows for efficient average calculations.
2Rounding down averages is crucial for accurate difference calculations.

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