# 1664. Ways to Make a Fair Array

You are given an integer array nums. You can choose exactly one index (0-indexed) and remove the element. Notice that the index of the elements may change after the removal.

For example, if nums = \[6,1,7,4,1]:

Choosing to remove index 1 results in nums = \[6,7,4,1]. Choosing to remove index 2 results in nums = \[6,1,4,1]. Choosing to remove index 4 results in nums = \[6,1,7,4]. An array is fair if the sum of the odd-indexed values equals the sum of the even-indexed values.

Return the number of indices that you could choose such that after the removal, nums is fair.

Example 1:

Input: nums = \[2,1,6,4] Output: 1 Explanation: Remove index 0: \[1,6,4] -> Even sum: 1 + 4 = 5. Odd sum: 6. Not fair. Remove index 1: \[2,6,4] -> Even sum: 2 + 4 = 6. Odd sum: 6. Fair. Remove index 2: \[2,1,4] -> Even sum: 2 + 4 = 6. Odd sum: 1. Not fair. Remove index 3: \[2,1,6] -> Even sum: 2 + 6 = 8. Odd sum: 1. Not fair. There is 1 index that you can remove to make nums fair. Example 2:

Input: nums = \[1,1,1] Output: 3 Explanation: You can remove any index and the remaining array is fair. Example 3:

Input: nums = \[1,2,3] Output: 0 Explanation: You cannot make a fair array after removing any index.

Constraints:

1 <= nums.length <= 105 1 <= nums\[i] <= 104

## Solutions

1. **prefix sum**
2. For numbers after the deleted position, sum of odd numbers and even numbers are swapped.

```cpp
class Solution {
public:
    int waysToMakeFair(vector<int>& nums) {
        int osum = 0, esum = 0;
        for (int i = 0; i < nums.size(); i++) {
            if (i % 2)
                osum += nums[i];
            else
                esum += nums[i];
        }

        int res = 0, curosum = 0, curesum = 0;
        for (int i = 0; i < nums.size(); i++) {
            int rosum = curosum + esum - curesum;
            int resum = curesum + osum - curosum;
            if (i % 2) {
                resum -= nums[i];
                curosum += nums[i];
            }
            else {
                rosum -= nums[i];
                curesum += nums[i];
            }

            res += resum == rosum;
        }
        return res;
    }
};
```