高斯消元法
【模板】高斯消元法
给定一个线性方程组，对其求解。
\[ \begin{cases} a_{1, 1} x_1 + a_{1, 2} x_2 + \cdots + a_{1, n} x_n = b_1 \\ a_{2, 1} x_1 + a_{2, 2} x_2 + \cdots + a_{2, n} x_n = b_2 \\ \cdots \\ a_{n,1} x_1 + a_{n, 2} x_2 + \cdots + a_{n, n} x_n = b_n \end{cases}\]
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50 | // P3389 【模板】高斯消元法
#include <bits/stdc++.h>
using namespace std;
const int MAXn = 100 + 9;
struct matrix {
int m, n;
double d[MAXn][MAXn];
matrix() {
memset(d, 0, sizeof(d));
}
};
bool solve(matrix & a) {
int n = a.n;
for(int line = 1; line <= n; line ++) {
int swp;
for(swp = line; swp <= n; swp ++)
if(a.d[swp][line]) break;
if(swp > n) return false;
swap(a.d[line], a.d[swp]);
double dvd = 1 / a.d[line][line];
for(int j = 1; j <= n + 1; j ++)
a.d[line][j] *= dvd;
for(int i = 1; i <= n; i ++) {
if(i == line) continue;
double tms = a.d[i][line];
for(int j = 1; j <= n + 1; j ++)
a.d[i][j] -= a.d[line][j] * tms;
}
}
return true;
}
int main() {
int n;
scanf("%d", &n);
matrix a;
a.n = n; a.m = n + 1;
for(int i = 1; i <= n; i++)
for(int j = 1; j <= n + 1; j++)
scanf("%lf", &a.d[i][j]);
bool can = solve(a);
if(can) {
for(int i = 1; i <= n; i++)
printf("%.2lf\n", a.d[i][n + 1]);
}
else printf("No Solution");
return 0;
}
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