You are given an integer array nums and two integers a and b.
For a subarray, 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 <= 1051 <= nums[i] <= 1091 <= a, b <= 109Problem Overview: You need to count the number of subarrays in which the ratio of even to odd numbers satisfies a given condition.
Approach 1: Brute Force (O(n^2))
Iterate through all possible subarrays and count the even and odd numbers in each. Check if the ratio meets the condition. This approach is straightforward but inefficient for large arrays.
Approach 2: Prefix Sum with Hash Map (O(n))
Use a prefix sum array to store cumulative counts of even and odd numbers. Employ a hash map to store the frequency of specific ratios. This allows you to efficiently count valid subarrays in linear time. This is the optimal approach for large datasets.
Recommended for interviews: Interviewers expect you to discuss the brute force approach to show understanding, but the optimal solution using prefix sum and hash map demonstrates advanced problem-solving skills.
Solutions for this problem are being prepared.
Try solving it yourself| Approach | Time | Space | When to Use |
|---|---|---|---|
| Brute Force | O(n^2) | O(1) | Small arrays |
| Prefix Sum with Hash Map | O(n) | O(n) | Large arrays |
Super Hard💀DSA Question asked by Leetcode in Weekly Contest 513(Q4,4013) • DSA with Kumar K • 492 views views
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