1 介绍

本专题用来记录高斯消元相关题目。

2 训练

题目1：207球形空间产生器

C++代码如下，

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <cmath>using namespace std;const int N = 15;int n;
double a[N][N], b[N][N];void gauss() {for (int r = 1, c = 1; c <= n; ++c, ++r) {int t = r;for (int i = r + 1; i <= n; ++i) {if (fabs(b[i][c]) > fabs(b[t][c])) {t = i;}}for (int i = c; i <= n + 1; ++i) swap(b[t][i], b[r][i]);for (int i = n + 1; i >= c; --i) b[r][i] /= b[r][c];for (int i = r + 1; i <= n; ++i) {for (int j = n + 1; j >= c; --j) {b[i][j] -= b[i][c] * b[r][j];}}}for (int i = n; i > 1; --i) {for (int j = i - 1; j; --j) {b[j][n+1] -= b[i][n+1] * b[j][i];b[j][i] = 0;}}
}int main() {scanf("%d", &n);for (int i = 0; i < n + 1; ++i) {for (int j = 1; j <= n; ++j) {scanf("%lf", &a[i][j]);}}for (int i = 1; i <= n; ++i) {for (int j = 1; j <= n; ++j) {b[i][j] += 2 * (a[i][j] - a[0][j]);b[i][n+1] += a[i][j] * a[i][j] - a[0][j] * a[0][j];}}gauss();for (int i = 1; i <= n; ++i) printf("%.3lf ", b[i][n+1]);return 0;
}

题目2：208开关问题

C++代码如下，

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>using namespace std;const int N = 35;int n;
int a[N][N];int gauss() {int r, c;for (r = 1, c = 1; c <= n; c++) {int t = r;for (int i = r + 1; i <= n; ++i) {if (a[i][c]) t = i;}if (!a[t][c]) continue;for (int i = c; i <= n + 1; ++i) swap(a[t][i], a[r][i]);for (int i = r + 1; i <= n; ++i) {for (int j = n + 1; j >= c; --j) {a[i][j] ^= a[i][c] & a[r][j];}}r++;}int res = 1;if (r < n + 1) {for (int i = r; i <= n; ++i) {if (a[i][n+1]) return -1;res *= 2;}}return res;
}int main() {int T;scanf("%d", &T);while (T--) {memset(a, 0, sizeof a);scanf("%d", &n);for (int i = 1; i <= n; ++i) scanf("%d", &a[i][n+1]);for (int i = 1; i <= n; ++i) {int t;scanf("%d", &t);a[i][n+1] ^= t;a[i][i] = 1;}int x, y;while (scanf("%d%d", &x, &y), x || y) a[y][x] = 1;int t = gauss();if (t == -1) puts("Oh,it's impossible~!!");else printf("%d\n", t);}return 0;
}