2302 - Count Subarrays With Score Less Than K.

Hard

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:

• <code>1 <= nums.length <= 10⁵</code>

• <code>1 <= numsi<= 10⁵</code>

• <code>1 <= k <= 10¹⁵</code>