643. 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

Constraints:

• n == nums.length
• 1 <= k <= n <= 10^5
• -10^4 <= nums[i] <= 10^4

My Solution

 
// failed: Time Limit Exceeded
/**
 * @param {number[]} nums
 * @param {number} k
 * @return {number}
 */
var findMaxAverage = function (nums, k) {
  let maxAverage = 0
  if (nums.length === 1) {
    return nums[0];
  }
  for (let i = 0; i <= nums.length - k; i++) {
    let sum = 0
    for (let j = i; j < k + i; j++) {
      sum += nums[j]
    }
    if (i === 0) {
      maxAverage = sum / k
    } else {
      maxAverage = Math.max(maxAverage, sum / k)
    }
  }
  return maxAverage
}
 

Solution from others

 
// using sliding window
/**
 * @param {number[]} nums
 * @param {number} k
 * @return {number}
 */
var findMaxAverage = function(nums, k) {
  let sum = 0;
  for (let i = 0; i < k; i++) {
    sum += nums[i];
  }
  
  let max = sum;
  for (let i = k; i < nums.length; i++) {
    // Subtract the element leaving the window and 
    // add the new element entering the window.
    sum = sum - nums[i - k] + nums[i];
    max = Math.max(max, sum);
  }
  
  return max / k;
};
 

Explanation

1. Start Sum: First, add up the first 'k' numbers to get a starting sum.
2. Initial Max: Keep this sum as the initial highest sum.
3. Sliding Window: Imagine a moving window that covers 'k' numbers in the array.
4. Move Window: Each time, move the window one number to the right.
5. Update Sum: Subtract the number that's left behind and add the new number into the sum.
6. Check Max: Compare the new sum with the highest sum found so far. If it's higher, make this the new highest sum.
7. Repeat: Keep moving the window and updating the sum until you reach the end of the array.
8. Calculate Average: Divide the highest sum by 'k' to find the highest average.
9. Done: Now, you have the highest average of 'k' consecutive numbers.