P3389 【模板】高斯消元法
1 #include <bits/stdc++.h>
2 using namespace std;
3 const int maxn = 105;
4 typedef double Matrix[maxn][maxn];
5 void gauss_elimination(Matrix &A, int n) {
6 // 消元过程
7 int i, j, k, r;
8 for (i = 0; i < n; ++i) {
9 // 选一行r并与第i行交换
10 r = i;
11 for (j = i+1; j < n; ++j)
12 if (fabs(A[j][i]) > fabs(A[r][i])) r = j;
13 if (r != i) for (j = 0; j <= n; ++j) swap(A[r][j], A[i][j]);
14
15 if (!A[i][i]) {
16 puts("No Solution");
17 exit(0);
18 }
19 /*
20 // 与第i+1~n进行消元，低精度
21 for (k = i+1; k < n; ++k) {
22 double f = A[k][i] / A[i][i];
23 for (j = i; j <= n; ++j) A[k][j] -= f * A[i][j];
24 }
25 */
26 for (j = n; j >= i; --j)
27 for (k = i+1; k < n; ++k)
28 A[k][j] -= A[k][i]/A[i][i] * A[i][j];
29 }
30 // 回代过程
31 for (i = n-1; i >= 0; --i) {
32 for (j = i+1; j < n; ++j)
33 A[i][n] -= A[j][n] * A[i][j];
34 A[i][n] /= A[i][i];
35 }
36 }
37 int main() {
38 Matrix mat;
39 int n; scanf("%d",&n);
40 for (int i = 0; i < n; ++i) {
41 for (int j = 0; j < n+1; ++j) {
42 scanf("%lf",&mat[i][j]);
43 }
44 }
45 gauss_elimination(mat,n);
46 for (int i = 0; i < n; ++i) {
47 printf("%.2f\n",mat[i][n]);
48 }
49 return 0;
50 }
