UVa12169 不爽的裁判

//先贴上暴力代码，再加上 拓展欧几里得算法
//*********************************************************************************
#include <iostream>


using namespace std;
const int mod = 10001;
int t, x[210];


void solve() {
	for (int a = 0; a <= 10000; a++) {
		for (int b = 0; b <= 10000; b++) {
			bool flag = true;
			for (int i = 2; i <= 2 * t; i += 2) {
				x[i] = (a*x[i - 1] + b) % mod;
				if (i + 1 <= 2 * t&&x[i + 1] != ((a*x[i] + b) % mod)) {
					flag = false;
					break;
				}
			}
			if (flag) return;
		}
	}
}


int main() {
	cin >> t;
	for (int i = 1; i <= 2 * t; i += 2) cin >> x[i];
	solve();
	for (int i = 2; i <= 2 * t; i += 2) cout << x[i] << "\n";
	return 0;
}
//***************************************************************************************
#include <iostream>
using namespace std;
const int mod = 10001;
typedef long long ll;
ll x[210];
int t;


void exgcd(ll a, ll b, ll &d, ll&x, ll &y) {
	if (!b) { d = a; x = 1; y = 0; }
	else { exgcd(b, a%b, d, y, x); y -= x*(a / b); }
}


void solve() {
	for (int a = 0; a<mod; a++) {
		ll n, b, g;
		ll temp = x[3] - a*a*x[1];
		exgcd(mod, a + 1, g, n, b);//得到了g n b
		if (temp%g) continue;//没有解
		b = temp / g * b;
		bool flag = true;
		for (int i = 2; i <= 2 * t; i += 2) {
			x[i] = ((ll)x[i - 1] * a + b) % mod;
			if ((i + 1)<(2 * t) && x[i + 1] != ((x[i] * a + b) % mod)) {
				flag = false;
				break;
			}
		}
		if (flag) return;
	}
}


int main() {
	cin >> t;
	for (int i = 1; i <= 2 * t; i += 2) cin >> x[i];
	solve();
	for (int i = 2; i <= 2 * t; i += 2) cout << x[i] << endl;

	return 0;
}
//调试时，生成的.exe不是重新编译的源代码的，白调试好久

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