题目中的等式等价于：

$$2 \cdot \sum _{i = 1} ^x a_i = \sum _{i = 1} ^n a_i$$

等式右边是定值，左边可以用一次前缀和 $O(n)$ 算出所有 $x$ 值对应的计算结果，逐个判断即可。

#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 12;
long long t[N];
int main()
{
	long long n, x, s = 0, a = 0;
	while (cin >> n)
	{
		s = 0;
		for (int i = 1; i <= n; i++)
		{
			cin >> x;
			s += x;
			t[i] = s;
		}
		a = 0;
		for (int i = 0; i <= n; i++)
			if (2 * t[i] == s) a++;
		cout << a << endl;
	}
	return 0;
}