README.md

Maximum Average Subarray I

Description

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.

Example 1:

Input: nums = [1,12,-5,-6,50,3], k = 4
Output: 12.75000
Explanation: Maximum average is (12 - 5 - 6 + 50) / 4 = 51 / 4 = 12.75

Example 2:

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

Solution

function findMaxAverage(nums: number[], k: number): number {
  if (k > nums.length) {
    // Return 0 if k is greater than the length of the array
    return 0;
  }

  let maxSum = 0;
  let currentSum = 0;

  // Calculate the sum of the first k elements
  for (let i = 0; i < k; i++) {
    currentSum += nums[i];
  }

  maxSum = currentSum;

  // Calculate the sum of the remaining subarrays
  for (let i = k; i < nums.length; i++) {
    currentSum += nums[i] - nums[i - k];
    // Add the next element and remove the first element of the previous subarray
    maxSum = Math.max(maxSum, currentSum);
  }

  // Return the maximum average
  return maxSum / k;
}

Complexity Analysis

• Time complexity: O(n)
• Space complexity: O(1)