Count how many ways to split an array into two parts so that the difference between their sums is even.
Problem
You are given an integer array nums. Count the number of ways to split the array into two groups, usually thought of as a left part and a right part, such that the difference between the sum of the two groups is even.
A split is considered different if the chosen set of elements on one side differs. Elements may be grouped based on the problem's partitioning rule, and you must count all valid partitions that satisfy the parity condition.
Return the total number of valid partitions.
Notes
- The exact partitioning interpretation is based on the standard interview formulation of this problem: count the number of subsets / splits where the two resulting sums have even difference.
- Focus on the parity relationship rather than the exact magnitude of the sums.
- The answer may be large, so count carefully.
Input Format
- An integer array
numsof lengthn.
Input
nums is the only input.
Output Format
- Return an integer: the number of valid partitions whose sum difference is even.
Constraints
1 <= n <= $10^{5}$in typical interview settingsnums[i]may be positive, zero, or negative unless otherwise specified- Use parity reasoning or counting techniques to avoid brute force enumeration
Example 1
Input
nums = [1, 2, 3]
Output
2
Explanation
The total sum is 6. Valid partitions are those where the two parts have sums with an even difference. For this array, two such splits satisfy the condition.
Example 2
Input
nums = [2, 4, 6]
Output
4
Explanation
All elements are even, so every non-empty split into two parts has sums with even difference.
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