#643

Easy

auto_awesomeSliding window with running state updates

LeetCode Problem Workspace

Maximum Average Subarray I

Find the maximum average of any contiguous subarray of length k in a given integer array using a sliding window approach.

array sliding window

Problem Statement

You are given an integer array nums of length n and an integer k. Your task is to find the contiguous subarray of length k that has the highest average value, and return this average value. A solution with a precision of at least 10^-5 will be accepted.

For example, given nums = [1,12,-5,-6,50,3] and k = 4, the correct output is 12.75000, as the subarray [12, -5, -6, 50] yields the highest average of 12.75.

Examples

Example 1

Input: nums = [1,12,-5,-6,50,3], k = 4

Output: 12.75000

Maximum average is (12 - 5 - 6 + 50) / 4 = 51 / 4 = 12.75

Example 2

Input: nums = [5], k = 1

Output: 5.00000

Example details omitted.

Constraints

n == nums.length
1 <= k <= n <= 105
-104 <= nums[i] <= 104

Solution Approach

Sliding Window Technique

The sliding window approach allows you to efficiently compute the sum of a contiguous subarray of length k. Initially, compute the sum of the first k elements. Then, slide the window by adding the next element and removing the element that falls out of the window. This ensures that we only need to make constant time updates to the sum, resulting in O(n) time complexity.

Maximizing the Average

While sliding the window, keep track of the maximum sum found and divide it by k to get the maximum average. This approach ensures we only traverse the array once, keeping the space complexity at O(1).

Edge Cases

Ensure to handle edge cases such as when the array contains a single element, or when the window size is equal to the length of the array. These cases are trivial but must be considered for robustness.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity of this solution is O(n) because we only iterate through the array once, and each sliding window update takes constant time. The space complexity is O(1) as we only need a few variables to track the current sum and maximum average.

What Interviewers Usually Probe

Candidates should understand how to implement the sliding window technique and avoid brute force solutions.
Look for an understanding of maintaining a running sum efficiently during window shifts.
Candidates who are familiar with space optimization techniques and avoid unnecessary data structures will perform well.

Common Pitfalls or Variants

Common pitfalls

Candidates may incorrectly compute the sum after sliding the window, resulting in incorrect averages.
Misunderstanding the sliding window approach could lead to a brute-force solution with O(n*k) complexity.
Candidates might forget to handle small edge cases such as when the array has only one element.

Follow-up variants

Consider using a sliding window for other array problems, like finding the maximum sum of subarrays.
What if k was dynamic? How would you adjust the sliding window approach to accommodate varying subarray sizes?
Extend the solution to find the subarray with the maximum product instead of the sum.

FAQ

What is the sliding window approach?

The sliding window approach involves maintaining a fixed-size window over the array, efficiently updating the sum or other calculations as the window slides across the array.

How can I solve the Maximum Average Subarray I problem more efficiently?

Use the sliding window technique to maintain a running sum of the current subarray, updating it as the window slides across the array. This ensures linear time complexity.

Why is the space complexity O(1) in this solution?

The space complexity is O(1) because we only need a few variables to track the current sum and maximum average, and do not require additional data structures.

What happens if k equals the length of the array?

If k equals the length of the array, the only possible subarray is the entire array, and the solution simply computes its average.

Can this approach be extended to other problems?

Yes, the sliding window technique is widely applicable to array problems, including finding maximum sums or products of subarrays, or solving dynamic problems with varying window sizes.

terminal

Solution

Solution 1: Sliding Window

We maintain a sliding window of length $k$, and for each window, we calculate the sum $s$ of the numbers within the window. We take the maximum sum $s$ as the answer.

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class Solution:
    def findMaxAverage(self, nums: List[int], k: int) -> float:
        ans = s = sum(nums[:k])
        for i in range(k, len(nums)):
            s += nums[i] - nums[i - k]
            ans = max(ans, s)
        return ans / k

Continue Practicing

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