Leetcode #643: Maximum Average Subarray I
In this guide, we solve Leetcode #643 Maximum Average Subarray I in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given an integer array nums consisting of n elements, and an integer k. Find a contiguous subarray whose length is equal to k that has the maximum average value and return this value.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Array, Sliding Window
Intuition
We are looking for a contiguous region that satisfies a constraint, which is a classic sliding-window signal.
Expanding and shrinking the window lets us maintain validity without restarting the scan.
Approach
Grow the window with a right pointer, and shrink from the left only when the constraint is violated.
Track the best window as you go to keep the solution linear.
Steps:
- Expand the right end of the window.
- While invalid, move the left end to restore constraints.
- Update the best window found.
Example
Input: nums = [1,12,-5,-6,50,3], k = 4
Output: 12.75000
Explanation: Maximum average is (12 - 5 - 6 + 50) / 4 = 51 / 4 = 12.75
Python Solution
from typing import List
def findMaxAverage(nums: List[int], k: int) -> float:
window = sum(nums[:k])
best = window
for i in range(k, len(nums)):
window += nums[i] - nums[i - k]
if window > best:
best = window
return best / k
Complexity
The time complexity is , where is the length of the array . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.