1343. Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold
Description
Given an array of integers arr
and two integers k
and threshold
, return the number of sub-arrays of size k
and average greater than or equal to threshold
.
Example 1:
Input: arr = [2,2,2,2,5,5,5,8], k = 3, threshold = 4 Output: 3 Explanation: Sub-arrays [2,5,5],[5,5,5] and [5,5,8] have averages 4, 5 and 6 respectively. All other sub-arrays of size 3 have averages less than 4 (the threshold).
Example 2:
Input: arr = [11,13,17,23,29,31,7,5,2,3], k = 3, threshold = 5 Output: 6 Explanation: The first 6 sub-arrays of size 3 have averages greater than 5. Note that averages are not integers.
Constraints:
1 <= arr.length <= 105
1 <= arr[i] <= 104
1 <= k <= arr.length
0 <= threshold <= 104
Solutions
Solution 1: Sliding Window
We can multiply threshold
by $k$, so that we can directly compare the sum within the window with threshold
.
We maintain a sliding window of length $k$, and for each window, we calculate the sum $s$. If $s$ is greater than or equal to threshold
, we increment the answer.
The time complexity is $O(n)$, where $n$ is the length of the array arr
. The space complexity is $O(1)$.
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