Count Subarrays With Score Less Than K

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Problem Statement

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.

Examples

Example 1

Input: nums = [2,1,4,3,5], k = 10
Output: 6
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
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 <= 10 ^15

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicBinary Search