2302. Count Subarrays With Score Less Than K

Problem

The score of an array is defined as the product of its sum and its length.

• For example, the score of [1, 2, 3, 4, 5] is (1 + 2 + 3 + 4 + 5) * 5 = 75.

Given a positive integer array nums and an integer k, return **the *number of non-empty subarrays* of** nums **whose score is *strictly less* than** k.

A subarray is a contiguous sequence of elements within an array.

  Example 1:

Input: nums = [2,1,4,3,5], k = 10
Output: 6
Explanation:
The 6 subarrays having scores less than 10 are:
- [2] with score 2 * 1 = 2.
- [1] with score 1 * 1 = 1.
- [4] with score 4 * 1 = 4.
- [3] with score 3 * 1 = 3. 
- [5] with score 5 * 1 = 5.
- [2,1] with score (2 + 1) * 2 = 6.
Note that subarrays such as [1,4] and [4,3,5] are not considered because their scores are 10 and 36 respectively, while we need scores strictly less than 10.

Example 2:

Input: nums = [1,1,1], k = 5
Output: 5
Explanation:
Every subarray except [1,1,1] has a score less than 5.
[1,1,1] has a score (1 + 1 + 1) * 3 = 9, which is greater than 5.
Thus, there are 5 subarrays having scores less than 5.

  Constraints:

• 1 <= nums.length <= 10^5

• 1 <= nums[i] <= 10^5

• 1 <= k <= 1015

Solution

class Solution {
    public long countSubarrays(int[] nums, long k) {
        long sum = 0;
        long count = 0;
        int i = 0;
        int j = 0;
        while (i < nums.length) {
            sum += nums[i];
            while (sum * (i - j + 1) >= k) {
                sum -= nums[j++];
            }
            count += i++ - j + 1;
        }
        return count;
    }
}

Explain:

nope.

Complexity:

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