114 lines
2.8 KiB
C++
114 lines
2.8 KiB
C++
#include<cstdio>
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#include<cstring>
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#include<algorithm>
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typedef long long LL;
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#define MAXN 60
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#define P 200000000000000003LL
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#define S 100000000000000000LL
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using namespace std;
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LL x[MAXN], g[MAXN][MAXN], a[MAXN][MAXN], b[MAXN][MAXN];
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int n;
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inline LL Mod(LL x) {
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if (x >= P)
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return x - P;
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return x;
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}
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LL MulMod(LL a, LL b) {
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LL res;
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for (res = 0; b; b >>= 1) {
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if (b & 1)
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res = Mod(res + a);
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a = Mod(a + a);
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}
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return res;
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}
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LL ExtGcd(LL a, LL b, LL &x, LL &y) {
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if (b == 0) {
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x = 1;
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y = 0;
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return a;
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}
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LL t, d;
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d = ExtGcd(b, a % b, x, y);
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t = x;
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x = y;
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y = t - a / b * y;
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return d;
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}
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LL InvMod(LL a, LL n) {
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LL x, y;
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ExtGcd(a, n, x, y);
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return (x % n + n) % n;
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}
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void Gauss() {
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int i, j, k;
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LL inv, tmp;
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for (i = 0; i < n; i++) {
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for (j = i; j < n; j++) {
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if (g[j][i])
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break;
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}
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if (i != j) {
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for (k = i; k <= n; k++)
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swap(g[i][k], g[j][k]);
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}
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inv = InvMod(g[i][i], P);
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for (j = i + 1; j < n; j++) {
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if (g[j][i]) {
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tmp = MulMod(g[j][i], inv);
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for (k = i; k <= n; k++) {
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g[j][k] -= MulMod(tmp, g[i][k]);
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g[j][k] = (g[j][k] % P + P) % P;
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}
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}
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}
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}
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for (i = n - 1; i >= 0; i--) {
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tmp = 0;
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for (j = i + 1; j < n; j++) {
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tmp += MulMod(x[j], g[i][j]);
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if (tmp >= P)
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tmp -= P;
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}
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tmp = g[i][n] - tmp;
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tmp = (tmp % P + P) % P;
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x[i] = MulMod(tmp, InvMod(g[i][i], P));
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}
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}
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int main() {
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int c, ca = 1;
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int i, j;
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LL tmp;
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scanf("%d", &c);
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while (c--) {
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scanf("%d", &n);
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memset(g, 0, sizeof(g));
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memset(b, 0, sizeof(b));
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for (i = 0; i <= n; i++) {
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for (j = 0; j < n; j++) {
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scanf("%I64d", &a[i][j]);
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a[i][j] += S;
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b[i][n] += MulMod(a[i][j], a[i][j]);
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if (b[i][n] >= P)
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b[i][n] -= P;
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}
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}
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for (i = 0; i < n; i++) {
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for (j = 0; j < n; j++) {
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tmp = a[i + 1][j] - a[i][j];
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tmp = (tmp % P + P) % P;
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g[i][j] = MulMod(tmp, 2);
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}
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g[i][n] = b[i + 1][n] - b[i][n];
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g[i][n] = (g[i][n] % P + P) % P;
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}
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Gauss();
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printf("Case %d:\n", ca++);
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printf("%I64d", x[0] - S);
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for (i = 1; i < n; i++)
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printf(" %I64d", x[i] - S);
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putchar('\n');
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}
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return 0;
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}
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