easy

Number of Sub-arrays of Size K and Average ≥ Threshold

Count fixed-size subarrays whose average is at least a given threshold.

1. Define the problem

Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold

Given an array of integers arr and two integers k and threshold, return the number of contiguous subarrays of size k whose average is greater than or equal to threshold. Slide a fixed length window of length k and compare the running sum to k * threshold to avoid division each step.

Constraints

  • 1 ≤ arr.length ≤ 105
  • 1 ≤ arri ≤ 104
  • 1 ≤ k ≤ arr.length

Example

Inputarr = [2, 2, 2, 2, 5, 5, 5, 8], k = 3, threshold = 4
Output3

Explanation The qualifying windows are [2, 5, 5] → 4, [5, 5, 5] → 5, and [5, 5, 8] → 6.

2. Know the words first

In plain terms

Contiguous subarray
A run of elements sitting right next to each other in the array, with nothing skipped — not just any subset you could pick.
Threshold
A minimum cutoff value — the average of a window only counts if it is at or above this number, like a passing grade.
3. Visualize the solution

Count windows whose average meets the threshold

Count windows whose average meets the threshold
Statusmiss

Window [2, 2, 2]: avg = 2.0 — below threshold.

What happens in this step

window = [0, 2]  (size 3)
target = k * threshold = 3 * 4 = 12

sum = 2 + 2 + 2 = 6
avg = 6 / 3 = 2.00

sum (6) is below target (12) — this window does not count.
Step 1 of 6

Steps to visualize

  1. Place a window of length k and compare its sum to k * threshold.
  2. If the sum meets the target, increment the answer count.
  3. Slide one step right: drop the leftmost value, add the new rightmost value.
  4. Check the sum against the target again after each slide.
  5. Continue until the window reaches the end of the array.
4. Walk through the code

Walk through the code

Same walkthrough, now with the code. Press Next to move one step and watch which lines run.

Count windows whose average meets the threshold
Statusmiss

Window [2, 2, 2]: avg = 2.0 — below threshold.

What happens in this step

window = [0, 2]  (size 3)
target = k * threshold = 3 * 4 = 12

sum = 2 + 2 + 2 = 6
avg = 6 / 3 = 2.00

sum (6) is below target (12) — this window does not count.
Step 1 of 6
5. Solution

Solution

solution.tsTypeScript
function numOfSubarrays(arr, k, threshold) {
  if (k <= 0 || k > arr.length) {
    throw new Error("k must be between 1 and arr.length");
  }

  const target = k * threshold;

  let windowSum = 0;
  for (let i = 0; i < k; i++) {
    windowSum += arr[i];
  }

  let count = windowSum >= target ? 1 : 0;

  for (let right = k; right < arr.length; right++) {
    const left = right - k;
    windowSum += arr[right] - arr[left];
    if (windowSum >= target) count++;
  }

  return count;
}
Time
O(n)
Space
O(1)
6. Test cases

Test cases

InputExpectedCovers
arr = [2, 2, 2, 2, 5, 5, 5, 8], k = 3, threshold = 43example from the docstring
arr = [5, 5, 5], k = 3, threshold = 51smallest valid input: k === arr.length
arr = [1, 5, 2, 9, 3], k = 1, threshold = 42k === 1 counts elements that meet the threshold directly
arr = [1, 1, 1, 1, 1, 1, 1], k = 2, threshold = 16window must slide across the whole array to count all matches
arr = [4, 4, 4, 4], k = 2, threshold = 43all identical elements: every window qualifies
arr = [1, 1, 1, 1], k = 2, threshold = 100no valid answer: nothing meets the threshold
arr = [11, 13, 17, 23, 29, 31, 7, 5, 2, 3], k = 3, threshold = 56larger, hand-verified case
arr = [1, 2], k = 5, threshold = 1throwsthrows when k is larger than the array

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