高斯消元发

#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>
using namespace std;
typedef long long LL;
const LL MOD = (LL)200000000 * 1000000000 + 3;/* 一个大于2*10^17的质数 */
const LL CORRECT = (LL)100000000 * 1000000000;/* 10^17 */

#define MAXN 50

LL broaden[MAXN][MAXN + 1]; /* 增广矩阵 */
LL ans[MAXN]; /* 用于保存答案 */
LL dataX[MAXN + 1][MAXN]; /* 原数据点 */

/* 计算a的模MOD值 */
LL getMod(LL a)
{
	if (a < 0){
		a += MOD;
	}
	else if (a >= MOD){
		a -= MOD;
	}
	return a;
}

/* 二分方法计算a*b的值 */
LL multiMod(LL a, LL b)
{
	LL ans = 0, base = a%MOD;
	while (b){
		if (b & 1){
			ans = getMod(base+ans);
		}
		base = getMod(base << 1);
		b >>= 1;
	}
	return ans;
}

/* 计算第i行的增广矩阵，即第i个式子 Σ[bn(i+1,j)^2-bn(i,j)^2]=2Σ[bn(i+1,j)-bn(i,j)]x(j) */
void calLineBroaden(int i, int n)
{
	LL nb = 0;
	for (int j = 0; j < n; ++j){
		broaden[i][j] = getMod((dataX[i + 1][j] - dataX[i][j]) << 1);
		nb += multiMod(dataX[i + 1][j], dataX[i + 1][j]) - multiMod(dataX[i][j], dataX[i][j]);
		nb = getMod(nb);
	}
	broaden[i][n] = nb;
}

/* 计算增广矩阵 */
void calBroaden(int n)
{
	for (int i = 0; i < n; ++i){
		calLineBroaden(i, n);
	}
}

/* 扩展欧几里德a*x+b*y=gcd(a,b) */
LL exGCD(LL a, LL b, LL&x, LL&y)
{
	LL tmp, d;
	if (b == 0){
		x = 1, y = 0;
		return a;
	}
	d = exGCD(b, a%b, x, y);
	tmp = x, x = y, y = tmp - a / b*y;
	return d;
}

/* 高斯消元，求解答案 */
void Gauss(int n)
{
	int i, j;
	for (i = 0; i < n; ++i){
		for (j = 0; j < n; ++j){
			if (broaden[i][j])break;
		}
		if (i < j){
			for (int k = 0; k <= n; ++k){
				swap(broaden[i][k], broaden[j][k]);
			}
		}
	}
	for (i = 0; i < n - 1; ++i){
		for (j = i + 1; j < n; ++j){
			for (int k = i + 1; k <= n; ++k){
				broaden[j][k] = getMod(multiMod(broaden[j][k], broaden[i][i]) - multiMod(broaden[i][k], broaden[j][i]));
			}
		}
	}
	LL x, y, g;
	for (i = n - 1; i >= 0; --i){
		g = exGCD(broaden[i][i], MOD, x, y);
		ans[i] = multiMod(x, broaden[i][n]);
		for (j = 0; j < i; ++j){
			broaden[j][n] = getMod(broaden[j][n] - multiMod(broaden[j][i], ans[i]));
		}
	}
}

/* 打印结果 */
void printAns(int n)
{
	for (int i = 0; i < n; ++i){
		printf(i == 0 ? "%lld" : " %lld", (ans[i]-CORRECT)%CORRECT);
	}
	printf("
");
}

void gen()
{
	int n;
	scanf("%d", &n);
	for (int i = 0; i <= n; ++i){
		for (int j = 0; j < n; ++j){
			scanf("%lld", &dataX[i][j]);
			dataX[i][j] += CORRECT;
		}
	}
	calBroaden(n);
	Gauss(n);
	printAns(n);
}

int main()
{
	int t;
	scanf("%d", &t);
	for (int iCase = 1; iCase <= t; ++iCase){
		printf("Case %d:
", iCase);
		gen();
	}
	return 0;
}