Maximum Average Subarray I

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. Any answer with a calculation error less than 10-5 will be accepted.

Sliding Window - Fixed#

Since every subarray has the same length k, maximizing the average is equivalent to maximizing the sum — we only need to track sums, not averages during the scan. Compute the sum of the first window of size k as a starting point, then slide the window one position at a time: add the incoming element on the right and subtract the outgoing element on the left. This keeps the running sum updated in O(1) per step without re-summing the entire window. Track the maximum sum seen across all windows and divide by k at the end to produce the maximum average.

class Solution {
public:
    double findMaxAverage(vector<int>& nums, int k) {
        int n = nums.size();
        int sum = 0;

        for(int i=0;i<k;i++)
            sum += nums[i];

        int maxSum = sum;

        for(int i=k; i<n;i++){
            sum += nums[i];
            sum -= nums[i-k];

            maxSum = max(sum, maxSum);
        }
        return (double)maxSum/k;
    }
};

Time Complexity: O(n)

Space Complexity: O(1)