Maximum Average Subarray I

Problem

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.

Examples

The brute-force approach

For every valid starting index, compute the sum of the k elements starting there, compute the average, and track the maximum.

max_avg = -infinity

for i in 0 .. len(nums) - k:
    total = 0
    for j in i .. i + k - 1:     # ← recomputing overlapping sums
        total += nums[j]
    max_avg = max(max_avg, total / k)

return max_avg

O(n × k), you're recomputing k additions for every starting position. Adjacent windows share k−1 elements; the fixed sliding window exploits that to update the sum in O(1) per step.

Spotting the pattern

This is a Sliding Window problem. The key question to ask yourself:

Can I compute the first window sum once, then slide it across by adding one element and removing one?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.