Maximum Average Subarray I(#643)
Category: Array, Sliding Window
🧩 Problem Statement
You are given an integer array `nums` containing `n` elements, and an integer `k`. Your task is to find a contiguous subarray of length exactly `k` that has the maximum average. Return this average value. Your answer is considered correct if it is within 10^-5 of the actual answer.
📚 Examples
Input: nums = [1, 12, -5, -6, 50, 3], k = 4
Output: 12.75000
Input: nums = [5], k = 1
Output: 5.00000
🧠 Approach
Approach:
Sliding Window Technique
• First, compute the sum of the first `k` elements and store it as `subArray`.
• Calculate the average `subArray / k` and store it as initial `avg`.
• Slide the window by adding the next element and removing the one that just went out of the window.
• At each step, update the maximum average if the new one is higher.
• Finally, return the maximum average rounded to five decimal places using `.toFixed(5)`.
💻 Code
// 🔹 JavaScript Solution using Sliding Window
var findMaxAverage = function(nums, k) {
let subArray = 0;
for (let i = 0; i < k; i++) {
subArray += nums[i];
}
let avg = subArray / k;
for (let i = k; i < nums.length; i++) {
subArray = subArray + nums[i] - nums[i - k];
avg = Math.max(avg, subArray / k);
}
return avg.toFixed(5);
};
console.log(findMaxAverage([1, 12, -5, -6, 50, 3], 4)); // Output: 12.75000
console.log(findMaxAverage([5], 1)); // Output: 5.00000📈 Complexity
Time: O(n) — We traverse the array once after the initial k-element sum.
Space: O(1) — We use constant extra space.