HDU 7105 Power Sum

题目链接：HDU 7105 Power Sum

题目大意：

题解：
易知\((x+1)^2-(x+2)^2-(x+3)^2+(x+4)^2=4\)，所以可以令\(n\)对\(4\)取模，根据余数\(0,1,2,3\)取不同的\(01\)序列，后面加上\(\frac{n}{4}\)个“\(1001\)”即可。

#include <iostream>
#include <string>
using namespace std;

int t, n;
const int ki[] = {0, 1, 4, 2};
const string ti[] = {"", "1", "0001", "01"};

int main() {
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    cin >> t;
    while (t--) {
        cin >> n;
        string ans = ti[n % 4];
        int k = ki[n % 4];
        while (n >= 4) {
            ans += "1001";
            k += 4;
            n -= 4;
        }
        cout << k << endl << ans << endl;
    }
    return 0;
}