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The sliding window technique allows us to keep track of the sum of a subarray of fixed length k by adding one new element and removing the first element of the previous window, thus achieving O(n) time complexity.
Time Complexity: O(n)
Space Complexity: O(1)
1function findMaxAverage(nums, k) {
2 let sum = 0;
3 for (let i = 0; i < k; i++) {
4 sum += nums[i];
5 }
6 let maxSum = sum;
7 for (let i = k; i < nums.length; i++) {
8 sum = sum - nums[i - k] + nums[i];
9 maxSum = Math.max(maxSum, sum);
10 }
11 return maxSum / k;
12}
13
14const nums = [1, 12, -5, -6, 50, 3];
15const k = 4;
16console.log(findMaxAverage(nums, k));The JavaScript solution also employs a sliding window technique, where it keeps a sum of the first k elements, and as the loop progresses, it subtracts the element that goes out of the window and adds the new element entering the window. It updates and tracks the maximum sum found so far to determine the result.
The brute force approach involves checking every possible subarray of length k and calculating its average, then keeping track of the maximum average found. However, this approach is not efficient for large inputs.
Time Complexity: O(n*k)
Space Complexity: O(1)
1using System;
public class Solution {
public double FindMaxAverage(int[] nums, int k) {
double maxAvg = -10001.0;
for (int i = 0; i <= nums.Length - k; i++) {
int sum = 0;
for (int j = i; j < i + k; j++) {
sum += nums[j];
}
double avg = (double)sum / k;
if (avg > maxAvg) {
maxAvg = avg;
}
}
return maxAvg;
}
public static void Main(string[] args) {
Solution sol = new Solution();
int[] nums = {1, 12, -5, -6, 50, 3};
int k = 4;
Console.WriteLine(sol.FindMaxAverage(nums, k));
}
}The C# brute force implementation evaluates every possible subarray of k elements to find their sum, computes the average, and checks if it exceeds the maximum average recorded.