Maximum Average Subarray II

You are given an integer array nums consisting of n elements, and an integer k.

Find a contiguous subarray whose length is greater than or 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.

 

Example 1:

Input: nums = [1,12,-5,-6,50,3], k = 4
Output: 12.75000
Explanation:
- When the length is 4, averages are [0.5, 12.75, 10.5] and the maximum average is 12.75
- When the length is 5, averages are [10.4, 10.8] and the maximum average is 10.8
- When the length is 6, averages are [9.16667] and the maximum average is 9.16667
The maximum average is when we choose a subarray of length 4 (i.e., the sub array [12, -5, -6, 50]) which has the max average 12.75, so we return 12.75
Note that we do not consider the subarrays of length < 4.

Example 2:

Input: nums = [5], k = 1
Output: 5.00000

 

Constraints:


Solution:

class Solution {
    public double findMaxAverage(int[] nums, int k) {
        double left = -10000;
        double right = 10000;
        double prevMid = 10000, error = 10000;
        while (error >= 0.00001) {
            double mid = (left + right) / 2;
            if (canFindSubarray(nums, k, mid)) {
                left = mid;
            } else {
                right = mid;
            }
            error = Math.abs(prevMid - mid);
            prevMid = mid;
        }
        return prevMid;
    }
    
    private boolean canFindSubarray(int[] nums, int k, double avg) {
        double sum = 0, prev = 0;
        for (int i = 0; i < k; i ++) {
            sum += nums[i] - avg;
        }
        if (sum >= 0) return true;
        double minPrev = 0;
        for (int i = k; i < nums.length; i ++) {
            sum += nums[i] - avg;
            prev += nums[i - k] - avg;
            minPrev = Math.min(minPrev, prev);
            if (sum >= minPrev) {
                return true;
            }
        }
        return false;
    }
}