rt，无意中发现了这种做法：

//#pragma GCC optimize(3,"Ofast")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native")
#include <bits/stdc++.h>
#define JS ios::sync_with_stdio(false),cin.tie(nullptr),cout.tie(nullptr)
using namespace std;
int n, x, mx, sum[100001], T, t;

int main() {
	JS;
	cin >> T;
	while (T--) {
		mx = -0x3f3f3f, t = 0;
		memset(sum, 0, sizeof(sum));
		cin >> n;
		for (int i = 1; i <= n; i++) {
			cin >> sum[i];
			t += sum[i];
			t = max(0, t);
			mx = max(mx, t);
		}
		cout << mx << '\n';
	}
	return 0;
}

$O(n)$ 本地评测可过，正确性如何证明？