Maximum Average Subarray I

Problem

Given an array consisting of n integers, find the contiguous subarray of given length k that has the maximum average value. And you need to output the maximum average value.

Example 1:
Input: [1,12,-5,-6,50,3], k = 4
Output: 12.75
Explanation: Maximum average is (12-5-6+50)/4 = 51/4 = 12.75

Note:

• 1 <= k <= n <= 30,000.
• Elements of the given array will be in the range [-10,000, 10,000].

Solution

Sliding Window Solution: O(n) time

public class Solution {
    public double findMaxAverage(int[] nums, int k) {
        double sum = 0;
        for (int i = 0; i < k; i++) sum += nums[i];
        double max = sum;
        for (int i = k; i < nums.length; i++) {
            sum += nums[i] - nums[i - k];
            max = Math.max(max, sum); 
        }
        return max / k;
    }
}

Analysis

Typical Sliding Window Solution
We assume the first k element has the max sum
Then we slide the selection on these k elements and update the max
After one pass, we will get the max subarray