You are given an integer array nums and two integers a and b.
For a , let:
x be the number of even elements.y be the number of odd elements.The ratio of even to odd elements in a subarray is defined as x / y, where ratios are compared by their exact rational values.
A subarray is considered valid if:
y > 0, andx / y <= a / b.Return the number of valid subarrays in nums.
Example 1:
Input: nums = [1,2,1,2], a = 3, b = 2
Output: 7
Explanation:
The following are the valid subarrays:
| Subarray | Values | Even Count | Odd Count | Ratio |
|---|---|---|---|---|
nums[0..0] | [1] | 0 | 1 | 0 / 1 |
nums[0..1] | [1, 2] | 1 | 1 | 1 / 1 |
nums[0..2] | [1, 2, 1] | 1 | 2 | 1 / 2 |
nums[0..3] | [1, 2, 1, 2] | 2 | 2 | 2 / 2 |
nums[1..2] | [2, 1] | 1 | 1 | 1 / 1 |
nums[2..2] | [1] | 0 | 1 | 0 / 1 |
nums[2..3] | [1, 2] | 1 | 1 | 1 / 1 |
Thus, the number of valid subarrays is 7.
Example 2:
Input: nums = [2,2,1], a = 2, b = 1
Output: 3
Explanation:
The following are the valid subarrays:
| Subarray | Values | Even Count | Odd Count | Ratio |
|---|---|---|---|---|
nums[0..2] | [2, 2, 1] | 2 | 1 | 2 / 1 |
nums[1..2] | [2, 1] | 1 | 1 | 1 / 1 |
nums[2..2] | [1] | 0 | 1 | 0 / 1 |
Thus, the number of valid subarrays is 3.
Example 3:
Input: nums = [2,2,2], a = 1, b = 1
Output: 0
Explanation:
Every subarray contains 0 odd numbers, so no subarray is valid.
Constraints:
1 <= nums.length <= 10001 <= nums[i] <= 10001 <= a, b <= 1000